Beal's Conjecture
bob_p...@my-deja.com
Fermat's Last Theorem called "Beal's Conjecture". This conjecture would
be very difficult to prove if I understand it correctly. Does anyone
have any information as to who has the prize money and exactly what the
rules are to win it?? Any information on searches for counterexamples??
Sent via Deja.com
http://www.deja.com/
Hull Loss Incident
> I recently heard about a substantial prize offered for a form of
> Fermat's Last Theorem called "Beal's Conjecture".
It is true that a Texas banker named Andrew Beal offers $100000
for solution of a certain math problem generalizing FLT.
It is not true that the problem originates with Beal, or that "Beal
conjecture" is either accurate or accepted as a name for the
mathematical problem.
There was a thorough debunking of the term "Beal Conjecture"
here in sci.math, in August 2000. Mr Andy Beal himself
participated in the discussion, and turned out to be dishonest and
cranky. The discussion was pretty amusing, you can find it in
archives under the following subject headings:
Against the term "Beal Conjecture".
A generalization of FLT.
> This conjecture would be very difficult to prove if I understand it
> correctly.
If it is even true! The $100000 conjecture is supported by very little
evidence other than computer searches, and those searches are far
below the range known to contain large solutions of generalized FLT
(found by Beukers and Zagier).
More plausible versions of the problem have been stated by others,
long before Beal, and are corroborated by substantial theoretical
evidence, but do not enjoy the benefit of prize funding or the
associated PR hype.
Some references to relevant papers and books were given in the
discussion last August. Recently I read that Nils Bruin has proved
that x^2 + y^8 = z^3 has no co-prime solutions other
than 33^2 + 1549034^8 = 15613^3.
> Does anyone
> have any information as to who has the prize money and exactly what the
> rules are to win it?? Any information on searches for counterexamples??
www.math.unt.edu/~mauldin/beal.html is the official prize site.
Since sci.math last hashed this out, a new web site has appeared,
www.bealconjecture.com, giving Beal's version of the history.
Most of the statements there related to attribution of
the problem are either false or misleading, IMO and also as
documented at length in the Aug 2000 discussion.
James Wanless
--
http://members.nbci.com/bearnol/
http://www.grok.ltd.uk
bob_p...@my-deja.com wrote in message <91phda$a8q$1...@nnrp1.deja.com>...
Chip Eastham
"Hull Loss Incident" <x...@y.z.com> wrote in message
news:3A4077BD...@y.z.com...
[snip of background info about "Beal" conjecture]
> Some references to relevant papers and books were given in the
> discussion last August. Recently I read that Nils Bruin has proved
> that x^2 + y^8 = z^3 has no co-prime solutions other
> than 33^2 + 1549034^8 = 15613^3.
>
Minor correction/nit picking:
1549034^2 + 33^8 = 15613^3 is certainly a solution.
-- Chip
sel...@my-deja.com
evidence of prior knowledge of the conjecture. hull loss incident has
been repeatedly asked to cite a single confirmable prior reference and
is unable to do so. Contrary to hull loss incident who has some axe to
grind, the conjecture is accepted by the math community as original and
as significant. Hull loss incident declares that the conjecture may not
be true! Of course it may not be true, that's what makes it a conjecture
hull loss incident writes alot (anonymously I might add) but says very
little that's meaningful, and certaintly has posed no evidence of prior
knowledge.
In article <3A4077BD...@y.z.com>,
jim...@my-deja.com
pen name for Andrew Granville from Georgia
n article <91qt3q$d60$1...@nnrp1.deja.com>,
Fred W. Helenius
>For anyone out there who is interested, Hull Loss Incident is really a
>pen name for Andrew Granville from Georgia
Odd, then, that his message header shows that "Hull Loss Incident"
posted from Harvard.
Speaking of message headers, yours shows that you posted from IP
address 24.4.254.206. Curiously, sel...@my-deja.com, to whom you
are replying, posted from the very same IP address. The originator
of this thread, bob_p...@my-deja.com posted from the same subnet,
with IP address 24.4.254.192. Visiting your deja.com member pages, it
appears that none of you had ever posted--in sci.math or elsewhere--
before today.
Another interesting coincidence involves the posts on this subject
by andy...@my-deja.com back in August. He was posting from IP
address 24.14.87.165, which, like the ones listed above, is used by
cable internet provider @Home for its customers in Texas.
--
Fred W. Helenius <fr...@ix.netcom.com>
Hull Loss Incident
> Don't let hull loss incident anonymously mislead you.
hi there Mr Beal! So far in this thread you've posted under
the false names "bob_paulson", "selivan", and "jim_pl". Last
time you posted under the false name "phil_rogowski" in
support of andy...@my-deja.com. What will you do for an
encore?
> There is no evidence of prior knowledge of the conjecture.
Other than the abundant posted evidence, there is no evidence.
> hull loss incident has been repeatedly asked to cite a single
> confirmable prior reference and is unable to do so.
References such as Tijdeman's lectures, published in 1989,
were posted and excerpted last time we discussed this.
They are prior, and confirmable.
Also posted were references to Darmon and Granville's
work, and proof that it was done well before Beal's
armchair speculations; a reference from Prof. Myerson,
to Granville's posing the problem in the early 90's at a
number theory meeting; and recollections from Bob Silverman,
of discussions at the 1985 Arcata meeting about unequal
exponent FLT in light of Frey's breakthrough.
Of course, as Bremner's Mathscinet review (also posted
earlier) indicates, the problem is as ancient as it is obvious.
> Contrary to hull loss incident who has some axe to
> grind, the conjecture is accepted by the math community as
> original and as significant.
Identify a single number theorist who agrees that Beal has
made a significant original (i.e. unknown at the time) contribution
to mathematics, or that "Beal conjecture" is the proper attribution
for the problem.
>Hull loss incident declares that the conjecture may not be true!
> Of course it may not be true, that's what makes it a conjecture
Evidence is what makes a conjecture. Any bozo can propose
armchair mathematical wagers, and any rich bozo can fund the
wagers with prize money. Your "conjecture" (claiming no solutions,
for no apparent reason) is in exactly that category of publicity stunts.
The more intelligent versions of the problem discussed by Granville,
Darmon, Tijdeman et al, *are* backed by evidence coming
from various different directions. Unlike Beal, none of these
experts would be stupid enough to claim credit for a well-known
problem, or insist that just stating it is an original and significant
event for mathematics.
J. Antonio Ramirez R.
> Another interesting coincidence involves the posts on this subject
> by andy...@my-deja.com back in August. He was posting from IP
> address 24.14.87.165, which, like the ones listed above, is used by
> cable internet provider @Home for its customers in Texas.
To the list of coincidences you can add the post by one "Phil
Rogowski", who curiously also posted (in Beal's support-- no surprise
there) from IP address 24.14.87.165 using Deja account
phil_r...@my-deja.com . The message ID was
<8o9ktu$n3d$1...@nnrp1.deja.com>.
Bob Silverman
Hull Loss Incident <x...@y.z.com> wrote:
<snip>
> The more intelligent versions of the problem discussed by Granville,
> Darmon, Tijdeman et al, *are* backed by evidence coming
> from various different directions. Unlike Beal, none of these
> experts would be stupid enough to claim credit for a well-known
> problem, or insist that just stating it is an original and significant
> event for mathematics.
BINGO!!!!!
--
Bob Silverman
"You can lead a horse's ass to knowledge, but you can't make him think"
Bob Silverman
sel...@my-deja.com wrote:
> Don't let hull loss incident anonymously mislead you. There is no
> evidence of prior knowledge of the conjecture. hull loss incident has
> been repeatedly asked to cite a single confirmable prior reference and
> is unable to do so.
On the contrary! I have provided such first person evidence.
In 1985 there was a conference on computational number theory in
Arcata California. I was there.
Tate gave a superb lecture on the (new) discovery by Frey that
Taniyama-Shimura implied FLT. He discussed the gaps in Frey's
argument (the gap was a conjecture by Serre. The conjecture was
proved shortly thereafter by Ken RIbet).
At the end of the talk, someone in the audience asked Tate if the
result could be extended to the case of UNEQUAL EXPONENTS. This is
Beal's so called conjecture.
Granville, as long ago as 1992 had discussed in public work that he
had done on this conjecture. His papers are a matter of record.
Contrary to hull loss incident who has some axe to
> grind, the conjecture is accepted by the math community as original
and
> as significant.
It is accepted as a conjecture. But it did not originate with BEAL.
Its significance remains to be seen. As an isolated diophantine
equation, it has very little significance per se unless it can be
tied into something else (as Frey tied FLT to T-S)
--
Bob Silverman
"You can lead a horse's ass to knowledge, but you can't make him think"
sel...@my-deja.com
One simply can't tell lies enough such that they become true. Your own
collegue Henri Darmon disagrees with you. Everyone disagrees with you.
As Beal said before, talk and bullshit are cheap. No-one was aware of
the conjecture before Beal conjectured it, including Harold Edwards
from NYU, Earl Taft from Rutgers, Henri Darmon, Ron Graham, and
everyone else that I have ever spoken to, etc. etc. You claimed
priority at one point suggesting that you had once asked a classroom of
students a related question. Vanderpoorten claimed in his 1996 book
that he proposed it, years after Beal widely distributed the
conjecture. Now you are angry with Beal. One cannot "debunk the truth"
with any verbiage, much less lies. We all waited in the August
discussion for a single reference besides your assertion that A+B=C
implies the conjecture
article <3A41A699...@y.z.com>,
Hull Loss Incident <x...@y.z.com> wrote:
> sel...@my-deja.com wrote:
>
> > Don't let hull loss incident anonymously mislead you.
>
> hi there Mr Beal! So far in this thread you've posted under
> the false names "bob_paulson", "selivan", and "jim_pl". Last
> time you posted under the false name "phil_rogowski" in
> support of andy...@my-deja.com. What will you do for an
> encore?
>
> > There is no evidence of prior knowledge of the conjecture.
>
> Other than the abundant posted evidence, there is no evidence.
>
AS I SAID -- NONE-- We all waited in the August discussion for a single
reference besides your suggestion that A+B=C implies the conjecture.
> > hull loss incident has been repeatedly asked to cite a single
> > confirmable prior reference and is unable to do so.
>
> References such as Tijdeman's lectures, published in 1989,
> were posted and excerpted last time we discussed this.
> They are prior, and confirmable.
AND UNRELATED
>
> Also posted were references to Darmon and Granville's
> work, and proof that it was done well before Beal's
> armchair speculations; a reference from Prof. Myerson,
> to Granville's posing the problem in the early 90's at a
> number theory meeting; and recollections from Bob Silverman,
> of discussions at the 1985 Arcata meeting about unequal
> exponent FLT in light of Frey's breakthrough.
>
DARMON HIMSELF DISAGREES, interesting that Darmon was unaware of the
concept since he worked so closely with you.
> Of course, as Bremner's Mathscinet review (also posted
> earlier) indicates, the problem is as ancient as it is obvious.
NO ONE AGREES with you Granville, mush less the facts
>
> > Contrary to hull loss incident who has some axe to
> > grind, the conjecture is accepted by the math community as
> > original and as significant.
>
> Identify a single number theorist who agrees that Beal has
> made a significant original (i.e. unknown at the time) contribution
> to mathematics, or that "Beal conjecture" is the proper attribution
> for the problem.
SEE NAMES ABOVE
>
> >Hull loss incident declares that the conjecture may not be true!
>
> > Of course it may not be true, that's what makes it a conjecture
>
> Evidence is what makes a conjecture. Any bozo can propose
> armchair mathematical wagers, and any rich bozo can fund the
> wagers with prize money. Your "conjecture" (claiming no solutions,
> for no apparent reason) is in exactly that category of publicity
stunts.
> The more intelligent versions of the problem discussed by Granville,
> Darmon, Tijdeman et al, *are* backed by evidence coming
> from various different directions. Unlike Beal, none of these
> experts would be stupid enough to claim credit for a well-known
> problem, or insist that just stating it is an original and significant
> event for mathematics.
>
DO YOU MEAN AS STUPID as you and Vanderpoorten when you both attempted
to claim credit? Beal has your actual letters to Mauldin in 1997 and
1998 where you discussed your claims of "priority"
BEAL HAS ORIGINAL letters from mathematicians in 1994 agreeing it was
unknown and calling it a remarkable discovery
WHY DON'T YOU STOP TELLING LIES
denis-feldmann
<sel...@my-deja.com> wrote in message : 91tefu$eoe$1...@nnrp1.deja.com...
> Hello Andrew Granville:
> One simply can't tell lies enough such that they become true. >
[lots of lies cut]
> WHY DON'T YOU STOP TELLING LIES
> >
PLEASE STOP SHOUTING LIES YOURSELF, DEAR MR BEAL
[plonk*]
David Petry
to "The Beal Prize Conjecture" ?
Meanwhile, I'm going to change my name from
David to Solomon!
sel...@my-deja.com
to look for solutions to FLT with independent exponents, or as
Silverman observed, someone in a crowd asking a speaker if certain
results can be extended to unequal exponents, or Brun's work in the
early 1900's, etc, etc, etc. and Beal's reasoned conjecture that co-
prime bases are impossible. No-one before Beal took the time and effort
to investigate the questions asked and conjecture a reasoned outcome.
Or if they did, they never shared their knowledge and hypothesis with
the world. Beal was the first to do so. Either present some evidence to
the contrary or shut up!!
Granville simply declares that anyone that ever considered 8+8=16
inherently hypothesized Beal's conjecture. It's hard to know what
Vanderpoorten thinks since he "proposed" beal's conjecture himself in
1996.
In article <91t7p6$8dn$1...@nnrp1.deja.com>,
Bob Silverman <bo...@my-deja.com> wrote:
> In article <91qt3q$d60$1...@nnrp1.deja.com>,
> sel...@my-deja.com wrote:
> > Don't let hull loss incident anonymously mislead you. There is no
> > evidence of prior knowledge of the conjecture. hull loss incident
has
> > been repeatedly asked to cite a single confirmable prior reference
and
> > is unable to do so.
>
> On the contrary! I have provided such first person evidence.
>
> In 1985 there was a conference on computational number theory in
> Arcata California. I was there.
>
> Tate gave a superb lecture on the (new) discovery by Frey that
> Taniyama-Shimura implied FLT. He discussed the gaps in Frey's
> argument (the gap was a conjecture by Serre. The conjecture was
> proved shortly thereafter by Ken RIbet).
>
> At the end of the talk, someone in the audience asked Tate if the
> result could be extended to the case of UNEQUAL EXPONENTS. This is
> Beal's so called conjecture.
BEAL'S CONJECTURE IS NOT TO ASK TATE IF HIS RESULT COULD BE EXTENDED TO
UNEQUAL EXPONENTS. Does anyone here understand the distiction??
>
> Granville, as long ago as 1992 had discussed in public work that he
> had done on this conjecture. His papers are a matter of record.
>
GRANVILLE NEVER CAME CLOSE TO SUGGESTING BEAL'S CONJECTURE.
> Contrary to hull loss incident who has some axe to
> > grind, the conjecture is accepted by the math community as original
> and
> > as significant.
>
> It is accepted as a conjecture. But it did not originate with BEAL.
ACTUALLY IT DID!! If you disagree, simply cite your reference.
sel...@my-deja.com
Bob Silverman <bo...@my-deja.com> wrote:
> In article <3A41A699...@y.z.com>,
> Hull Loss Incident <x...@y.z.com> wrote:
>
> <snip>
>
> > The more intelligent versions of the problem discussed by Granville,
> > Darmon, Tijdeman et al, *are* backed by evidence coming
> > experts would be stupid enough to claim credit for a well-known
> > problem
Darmon agrees he was unaware of the conjecture prior to Beal.
Vanderpoorten "proposed" it himself years after Beal, and Granville
suggested in letters to Mauldin that his questions to a class of
students gives him priority. Hmmmmmm.
sel...@my-deja.com
you be a little more specific??
In article <91thlo$ahu$1...@wanadoo.fr>,
sel...@my-deja.com
intelligent.
In article <1du24t066a25foobs...@4ax.com>,
Hull Loss Incident
> Hello Andrew Granville:
And now the conspiracy theories. GRANVILLE IS
EVERYWHERE. Apparently his crime was to try
and disabuse Beal of some megalomanic delusions.
> One simply can't tell lies enough such that they become true.
If so, that spells trouble for the funded PR campaign to
associate the name "Beal" with the mathematical problem.
> Your own collegue Henri Darmon disagrees with you.
If you quote him in full, people here can judge for
themselves whether he agrees with Beal or is just
being misrepresented by Beal.
> Everyone disagrees with you.
Bremner's Mathscinet review states that the problem is ancient.
Granville apparently agrees, along with number theorists Myerson
and Silverman during these sci.math discussions, not to mention
various other knowledgeable participants who publically ridiculed
your claims.
> As Beal said before, talk and bullshit are cheap. No-one was aware of
> the conjecture before Beal conjectured it,
People were aware of the equation for centuries, as you can
confirm by looking over the 50 pages of references to FLT
variants in Dickson's History of the Theory of Numbers.
People were aware of the probabilistic density heuristics for
finiteness of solutions, since the beginnings of 20th century
analytic number theory (or maybe since Gauss circa 1800),
as you can confirm by asking around or looking up the
"circle method".
People were also well aware that finite may equal zero
for various Diophantine problems, and that armchair
guesses as to which alternative holds are unpublishable.
> including Harold Edwards
> from NYU, Earl Taft from Rutgers, Henri Darmon, Ron Graham, and
> everyone else that I have ever spoken to, etc. etc.
So you claim. We are still waiting for a full quote from any of the above
endorsing your claims.
Taft never reviewed your work, he acted in an editorial capacity
delegating it to a referee (who oddly enough did not recommend
publication of this monumental original discovery). You misrepresent
him as having any opinion whatsoever about your work.
Edwards is not an expert on modern FLT developments and, like
the referee, was unimpressed with the evidence you claimed for
the conjecture. They both thought there might be counterexamples, and
Edwards recommended hiring somebody to "run a simple computer
search".
The challenge stands to identify and quote (in full) a single expert
who unambiguously endorses your claims to a significant original
discovery.
> You claimed
> priority at one point suggesting that you had once asked a classroom of
> students a related question.
Granville claiming priority is unlikely. Prior art, certainly -- which
is enough to destroy Beal's priority claims. Prof. Myerson posted
Granville's contribution to a 1992 problem list, predating
and subsuming Beal's work.
> Vanderpoorten claimed in his 1996 book
> that he proposed it, years after Beal widely distributed the
> conjecture. Now you are angry with Beal. One cannot "debunk the truth"
> with any verbiage, much less lies. We all waited in the August
> discussion for a single reference besides your assertion that A+B=C
> implies the conjecture.
What we all saw was multiple references being posted and
Beal refusing to discuss them. If you want to change
the situation you can begin by addressing the excerpt I posted from
Tijdeman's lectures, which were published in 1989.
> > > hull loss incident has been repeatedly asked to cite a single
> > > confirmable prior reference and is unable to do so.
> >
> > References such as Tijdeman's lectures, published in 1989,
> > were posted and excerpted last time we discussed this.
> > They are prior, and confirmable.
>
> AND UNRELATED
The excerpt shows that Tijdeman specifically raised the
possibility of "your" equation not having any solutions
except a few with exponent 2. That covers the "Beal"
conjecture, and more.
> > Also posted were references to Darmon and Granville's
> > work, and proof that it was done well before Beal's
> > armchair speculations; a reference from Prof. Myerson,
> > to Granville's posing the problem in the early 90's at a
> > number theory meeting; and recollections from Bob Silverman,
> > of discussions at the 1985 Arcata meeting about unequal
> > exponent FLT in light of Frey's breakthrough.
> >
> DARMON HIMSELF DISAGREES, interesting that Darmon was
> unaware of the concept since he worked so closely with you.
As I posted, it is on record that Darmon spoke (or was slated
to speak) about his joint work with Granville, at a number theory
conference in July 1993. The title of the talk was "A generalized Fermat
equation". Referring to the published version of their work, we
see that the equation in question is the same as Beal's but with
the slightly more general set of exponents 1/a + 1/b + 1/c < 1.
This predates Beal's work on the problem, which Mauldin's
letter to AMS Notices (also referenced earlier) dates as
beginning in "summer of 1993" with the computer calculations
and other work taking place in August 1993 and "the next several
months".
You can tell us all which part of this information on the public
record, you are now claiming is incorrect.
denis-feldmann
<sel...@my-deja.com> a écrit dans le message :
91us6k$jri$1...@nnrp1.deja.com...
> This is an interesting post. I am not aware where Beal has lied. Could
> you be a little more specific??
>
Then, just answer arguments. Last, stop believing you are answering Andrew
Granville. For the rest, you are a liar. I suppose it is compulsive. But, if
you were not Beal, i would say it is also contagious.
Hull Loss Incident
sel...@my-deja.com wrote:
> There is a HUGE difference between Granville asking a class of students
> to look for solutions to FLT with independent exponents, or as
> Silverman observed, someone in a crowd asking a speaker if certain
> results can be extended to unequal exponents, or Brun's work in the
> early 1900's, etc, etc, etc.
They indicate how obvious the problem is to anyone skilled in the
art. I remember high school competition problems asking for
solutions of FLT with unequal exponent -- teenagers could and
did solve them, under time pressure, based on the well-known
tricks for finding solutions when common factors are allowed.
> and Beal's reasoned conjecture that co-
> prime bases are impossible.
We are waiting to hear what Beal contributed beyond the
obvious well-known at the time: that solutions are
plentiful when common factors are allowed, and that they
are rare when common factors are not allowed. Beal
noticed the first item and ran a short-range computer search
to confirm the second. If there is any other contribution
to knowledge on Beal's part that I've left out in this description,
he is invited to correct it.
> No-one before Beal took the time and effort
> to investigate the questions asked and conjecture a reasoned outcome.
> Or if they did, they never shared their knowledge and hypothesis with
> the world. Beal was the first to do so.
Beal never shared his knowledge with the world.
He shared his claims of having arrived at knowledge, without
revealing the actual knowledge (the investigation performed
and the resulting evidence gathered in support of the
"reasoned conclusion"). In particular, nobody
can replicate his work or learn from any insights
he may (or may not) have developed. Even the most
straightforward aspect, the computer search for solutions,
was not disclosed until our discussion in August, when it
turned out that solutions were ruled out only in the ridiculously
short range of perfect powers less than one million!
> Granville simply declares that anyone that ever considered 8+8=16
> inherently hypothesized Beal's conjecture.
I (not Granville) declared that 8+8=16 and similar trivia
invalidate Beal's claim that explicitly stating "co-prime bases"
distinguishes his problem from Granville's earlier proposal.
Unless you believe that an audience of professional number
theorists could not be expected to notice 8+8=16,
2^n + 2^n = 2^(n+1), etc before Beal came along.
> > Granville, as long ago as 1992 had discussed in public work that he
> > had done on this conjecture. His papers are a matter of record.
> >
> GRANVILLE NEVER CAME CLOSE TO SUGGESTING BEAL'S CONJECTURE.
As posted in sci.math, Granville listed a few solutions
to x^a + y^b = z^c with 1/a + 1/b + 1/c < 1, and
asked whether others existed. This does not
differ from asking whether there are NO other solutions,
which covers the "Beal" conjecture and more.
Beal is apparently claiming that noticing that all
of the solutions listed (there were only three or four!) had
an exponent equal to 2, or that 8+8=16, is a major
breakthrough for number theory.
Bob Silverman
sel...@my-deja.com wrote:
> There is a HUGE difference between Granville asking a class of
students
> to look for solutions to FLT with independent exponents, or as
> Silverman observed, someone in a crowd asking a speaker if certain
> results can be extended to unequal exponents, or Brun's work in the
> early 1900's, etc, etc, etc. and Beal's reasoned conjecture that co-
> prime bases are impossible. No-one before Beal took the time and
effort
This is unadulterated horeshit. The fact that the question was
asked so casually during Tate's talk indicates to anyone with 2
brain cells working (which does not include you) that EITHER:
(1) The problems was well known
(2) The question was obvious
> to investigate the questions asked and conjecture a reasoned outcome.
> Or if they did, they never shared their knowledge and hypothesis with
> the world. Beal was the first to do so. Either present some evidence
to
> the contrary or shut up!!
Others have quoted papers which discussed the subject before Beal did.
You choose to ignore them. You choose to ignore the fact that the
question is obvious to anyone working in the area of diophantine
equations. You are a crank. Go Away.
>
> Granville simply declares that anyone that ever considered 8+8=16
> inherently hypothesized Beal's conjecture. It's hard to know what
> Vanderpoorten thinks since he "proposed" beal's conjecture himself in
> 1996.
You have said this several times. Please give the reference to the
paper in which Alf claims this.
> > sel...@my-deja.com wrote:
> > > Don't let hull loss incident anonymously mislead you.
Hypocrite. You fail to post under your own name.
> > Contrary to hull loss incident who has some axe to
> > > grind,
His "axe to grind" is with phonies claiming original ideas
as their own when they are clearly not.
the conjecture is accepted by the math community as original
> > and
> > > as significant.
> >
> > It is accepted as a conjecture. But it did not originate with BEAL.
>
> ACTUALLY IT DID!! If you disagree, simply cite your reference.
I have. The question was asked in Arcata in 1985. I was there.
Others have given references to papers which precede Beal's claim.
You choose to ignore these.
sel...@my-deja.com
are having the problem with
In article <91v59l$h3u$1...@wanadoo.fr>,
sel...@my-deja.com
TRUTH
article <3A43060E...@y.z.com>,
Hull Loss Incident <x...@y.z.com> wrote:
> andybeal, posing as "sel...@my-deja.com", wrote:
>
> > Hello Andrew Granville:
>
> And now the conspiracy theories. GRANVILLE IS
> EVERYWHERE. Apparently his crime was to try
> and disabuse Beal of some megalomanic delusions.
>
> > One simply can't tell lies enough such that they become true.
>
> If so, that spells trouble for the funded PR campaign to
> associate the name "Beal" with the mathematical problem.
ANDREW GRANVILLE: YOU'RE THE ONE TELLING LIES - NOT BEAL - WE HAVE
REPEATEDLY ASKED YOU TO BE A LITTLE MORE SPECIFIC, BUT YOU DON'T SEEM
VERY INTERESTED
> > Your own collegue Henri Darmon disagrees with you.
>
> If you quote him in full, people here can judge for
> themselves whether he agrees with Beal or is just
> being misrepresented by Beal.
OR THEY CAN SIMPLY TALK WITH DARMON OR DAN MAULDIN OR RON GRAHAM OR
EARL TAFT OR HAROLD EDWARDS OR JERROLD TUNNELL OR ANYONE KNOWLEDGABLE
WITH NUMBER THEORY
> > Everyone disagrees with you.
>
> Bremner's Mathscinet review states that the problem is ancient.
> Granville apparently agrees, along with number theorists Myerson
> and Silverman during these sci.math discussions, not to mention
> various other knowlegeable participants who publically ridiculed
> your claims.
THE PROBLEM IS ANCIENT - UNDERSTANDING IT AND REASONING A CONJECTURE
FOR SOLUTIONS IS NOT. ANDREW GRANVILLE, YOU DON'T SEEM TO UNDERSTAND
THE DISTINCTION
>
> > As Beal said before, talk and bullshit are cheap. No-one was aware
of
> > the conjecture before Beal conjectured it,
>
> People were aware of the equation for centuries, as you can
> confirm by looking over the 50 pages of references to FLT
> variants in Dickson's History of the Theory of Numbers.
>
> People were aware of the probabilistic density heuristics for
> finiteness of solutions, since the beginnings of 20th century
> analytic number theory (or maybe since Gauss circa 1800),
> as you can confirm by asking around or looking up the
> "circle method".
>
> People were also well aware that finite may equal zero
> for various Diophantine problems, and that armchair
> guesses as to which alternative holds are unpublishable.
>
ANDREW GRANVILLE: THEY ARE CLEARLY NOT UNPUBLISHABLE- AND PEOPLE WERE
NOT AWARE THAT FINITE APPARENTLY DOES EQUAL ZERO IN SPECIFIC INSTANCES.
OTHERWISE ZERO WOULD HAVE BEEN HYPOTHESIZED RATHER THAN FINITE. BEAL
WAS THE FIRST TO DO SO FOR A MORE RESTRICTIVE FORM. ACCORDING TO YOUR
DISTORTED LOGIC THE ABC CONJECTURE IS MEANINGLESS SINCE THE EQUATION
HAS BEEN AROUND FOR CENTURIES
> > including Harold Edwards
> > from NYU, Earl Taft from Rutgers, Henri Darmon, Ron Graham, and
> > everyone else that I have ever spoken to, etc. etc.
>
> So you claim. We are still waiting for a full quote from any of the
above
> endorsing your claims.
>
SIMPLY TALK WITH THEM. THEY ALL AGREE THAT THEY WERE UNAWARE THAT
FINITE DOES EQUAL ZERO FOR BEAL'S CONJECTURE.
> Taft never reviewed your work, he acted in an editorial capacity
> delegating it to a referee (who oddly enough did not recommend
> publication of this monumental original discovery). You misrepresent
YOU'RE THE FIRST TO CALL IT "MONUMENTAL"!! BEAL THINKS ITS INTERESTING
BUT HARDLY MONUMENTAL
> him as having any opinion whatsoever about your work.
> Edwards is not an expert on modern FLT developments and, like
> the referee, was unimpressed with the evidence you claimed for
> the conjecture. They both thought there might be counterexamples, and
> Edwards recommended hiring somebody to "run a simple computer
> search".
>
THE COMPUTER SEARCH WAS ALREADY DONE, EDWARDS CALLED IT REMARKABLE,
TAFT AND TUNNELL AGREED IT WAS AN UNKNOWN CONJECTURE AS DID DARMON AND
EVERYONE ELSE EXCEPT GRANVILLE AND VANDERPOORTEN (WHO TRIED TO CLAIM
OR "PROPOSE" IT THEMSELVES)
> The challenge stands to identify and quote (in full) a single expert
> who unambiguously endorses your claims to a significant original
> discovery.
>
ANDREW GRANVILLE: AS I'VE SAID REPEATEDLY, EVERYONE INCLUDING ALL THOSE
NAMED ABOVE AGREE THAT IT IS INTERESTING AND PREVIOUSLY UNKNOWN. NO-ONE
INCLUDING BEAL CLAIMS THAT IT IS EARTH SHAKING IN IMPORTANCE; ONLY THAT
IT IS INTERESTING AND PREVIOUSLY UNKNOWN.
> > You claimed
> > priority at one point suggesting that you had once asked a
classroom of
> > students a related question.
>
> Granville claiming priority is unlikely. Prior art, certainly --
which
> is enough to destroy Beal's priority claims. Prof. Myerson posted
> Granville's contribution to a 1992 problem list, predating
> and subsuming Beal's work.
YES WE ALL KNOW THAT GRANVILLE CLAIMS PRIORITY, BUT OTHER THAN ASKING A
CLASS OF HIS THIS OR THAT, OR LOOKING AT A BROADER FORM OF THE EQUATION
AND SPECULATING INCORRECTLY ABOUT LIMITED SETS OF 2ND POWER SOLUTIONS,
GRANVILLE HAS YET TO DEMONSTRATE ANY PRIOR ART (OR EVEN RANK
SPECULATION) PRIOR TO BEAL'S COMPUTER RUNS AND REASONED CONJECTURE
>
> > Vanderpoorten claimed in his 1996 book
> > that he proposed it, years after Beal widely distributed the
> > conjecture. Now you are angry with Beal. One cannot "debunk the
truth"
> > with any verbiage, much less lies. We all waited in the August
> > discussion for a single reference besides your assertion that A+B=C
> > implies the conjecture.
>
> What we all saw was multiple references being posted and
> Beal refusing to discuss them. If you want to change
> the situation you can begin by addressing the excerpt I posted from
> Tijdeman's lectures, which were published in 1989.
YES, I SUPPOSE BEAL IS TIRED OF ANDREW GRANVILLE'S CONSTANT REFERENCES
TO UNRELATED MATERIAL (INCLUDING TIJDMAN'S LECTURES) AND EXPECTS THAT
ANYONE KNOWLEDGABLE WILL SEE THROUGH THEM TO THE FACTS: NO-ONE HAS EVER
SUGGESTED BEAL'S CONJECTURE AND BEAL HIMSELF HAS ASKED REPEATEDLY FOR
ANY EVIDENCE TO THE CONTRARY. NOTWITHSTANDING GRANVILLE'S CONSTANT
REFERENCES TO UNRELATED WORK WHERE SOMEONE SAID SOMETHING TO THE EFFECT
OF "I WONDER ABOUT INDEPENDENT EXPONENTS???", BEAL'S CONJECTURE IS
ACCEPTED AS PREVIOUSLY UNKNOWN BY EVERYONE THAT I KNOW EXCEPT GRANVILLE
WHO CLAIMS DUBIOUS PRIOR ART AND VANDERPOORTEN WHO ATTEMPTS TO PROPOSE
THE CONJECTURE HIMSELF YEARS AFTER BEAL.
>
> > > > hull loss incident has been repeatedly asked to cite a single
> > > > confirmable prior reference and is unable to do so.
> > >
> > > References such as Tijdeman's lectures, published in 1989,
> > > were posted and excerpted last time we discussed this.
> > > They are prior, and confirmable.
> >
> > AND UNRELATED
>
> The excerpt shows that Tijdeman specifically raised the
> possibility of "your" equation not having any solutions
> except a few with exponent 2. That covers the "Beal"
> conjecture, and more.
WRONG AGAIN!! GRANVILLE AND TIJDEMAN INCORRECTLY AND VERY
DISINGENIOUSLY SPECULATED THAT A SET OF SEVEN SOLUTIONS WITH SECOND
POWERS WERE THE ONLY SOLUTIONS TO A BROADER FORM OF THE EQUATION IN
BEAL'S CONJECTURE. SOMEONE SUBSEQUENTLY DID AN EXTREMELY LIMITED
SEARCH ON A COMPUTER AND DISPROVED THEIR SPECULATION.
>
> > > Also posted were references to Darmon and Granville's
> > > work, and proof that it was done well before Beal's
> > > armchair speculations; a reference from Prof. Myerson,
> > > to Granville's posing the problem in the early 90's at a
> > > number theory meeting; and recollections from Bob Silverman,
> > > of discussions at the 1985 Arcata meeting about unequal
> > > exponent FLT in light of Frey's breakthrough.
> > >
ALL DISCUSSED ABOVE AND IRRELEVANT - DARMON HIMSELF AGREES THAT HE WAS
UNAWARE OF ZERO SOLUTIONS FOR THE FORM OF BEAL'S CONJECTURE.
> > DARMON HIMSELF DISAGREES, interesting that Darmon was
> > unaware of the concept since he worked so closely with you.
>
> As I posted, it is on record that Darmon spoke (or was slated
> to speak) about his joint work with Granville, at a number theory
> conference in July 1993. The title of the talk was "A generalized
Fermat
> equation". Referring to the published version of their work, we
> see that the equation in question is the same as Beal's but with
> the slightly more general set of exponents 1/a + 1/b + 1/c < 1.
>
> This predates Beal's work on the problem, which Mauldin's
> letter to AMS Notices (also referenced earlier) dates as
> beginning in "summer of 1993" with the computer calculations
> and other work taking place in August 1993 and "the next several
> months".
ANDREW GRANVILLE: HERE YOU GO AGAIN PERSONALLY CLAIMING PRIORITY FOR
SOME WORK THAT FELL FAR SHORT OF BEAL'S CONJECTURE. WE ALL KNOW THAT
THE ABC CONJECTURE HYPOTHESIZES A FINITE SET OF SOLUTIONS FOR A
DIFFERENT FORM. IT DOES NOT CONSTITUTE A PRIOR "BEAL CONJECTURE". BEAL
HYPOTHESIZES NO SOLUTIONS FOR A MORE RESTRICTIVE FORM.
>
> You can tell us all which part of this information on the public
> record, you are now claiming is incorrect.
>
I JUST DID THAT FOR YOU. IT'S NOT THAT IT'S INCORRECT, IT'S SIMPLY
IRRELEVANT
sel...@my-deja.com
>
> > There is a HUGE difference between Granville asking a class of
students
> > to look for solutions to FLT with independent exponents, or as
> > Silverman observed, someone in a crowd asking a speaker if certain
> > results can be extended to unequal exponents, or Brun's work in the
> > early 1900's, etc, etc, etc.
>
> They indicate how obvious the problem is to anyone skilled in the
> art. I remember high school competition problems asking for
> solutions of FLT with unequal exponent -- teenagers could and
> did solve them, under time pressure, based on the well-known
> tricks for finding solutions when common factors are allowed.
PERHAPS SO OBVIOUS TO THE GIFTED ANDREW GRANVILLE, BUT NOT TO THE REST
OF US INCLUDING HENRI DARMON, RON GRAHAM, DAN MAULDIN, EARL TAFT,
HAROLD EDWARDS, JERROLD TUNNELL, ANDREW BEAL, AND EVERYONE ELSE THAT I
KNOW EXCEPT (of course) ANDREW GRANVILLE AND VANDERPOORTEN. ALSO SEE
BELOW WHERE GRANVILLE HIMSELF WAS WORKING ON SOLUTION SETS FOR THIS
INCREDIBLY OBVIOUS AND ELEMENTARY PROBLEM.
>
> > and Beal's reasoned conjecture that co-
> > prime bases are impossible.
>
> We are waiting to hear what Beal contributed beyond the
> obvious well-known at the time: that solutions are
> plentiful when common factors are allowed, and that they
> are rare when common factors are not allowed. Beal
> noticed the first item and ran a short-range computer search
> to confirm the second. If there is any other contribution
> to knowledge on Beal's part that I've left out in this description,
> he is invited to correct it.
BEAL CONTRIBUTED A REASONED CONJECTURE THAT SOLUTIONS ARE NOT RARE BUT
IMPOSSIBLE FOR CERTAIN FORMS. HE CONDUCTED THE FIRST LARGE SCALE
COMPUTER RUN INVOLVING 15 COMPUTERS FOR THOUSANDS OF HOURS AND
DISCOVERED HUNDREDS OF NON-COPRIME SOLUTIONS AND MADE THE DATA PUBLIC
THROUGH DAN MAULDIN AT UNT. ANY COMPUTER ANALYSIS WILL NECESSARILY
EXCLUDE BASES AND EXPONENTS SLIGHTLY LARGER THAN THE SCOPE OF THE
ANALYSIS.
ANDREW GRANVILLE LOVES TO CRITISIZE EVERYONE AND EVERYTHING AND
CONSEQUENTLY CRITISIZES BEAL'S CHOICE OF THE RANGE TO EXAMINE.
NONETHELESS, BEAL CONDUCTED THE FIRST LARGE COMPUTER ANALYSIS (WHICH
GRANVILLE DID NOT) AND SUGGESTED THE POSSIBILITY OF NO SOLUTIONS FOR A
MORE RESTRICTED FORM THAN HAD BEEN PREVIOUSLY EXAMINED.
>
> > No-one before Beal took the time and effort
> > to investigate the questions asked and conjecture a reasoned
outcome.
> > Or if they did, they never shared their knowledge and hypothesis
with
> > the world. Beal was the first to do so.
>
> Beal never shared his knowledge with the world.
> He shared his claims of having arrived at knowledge, without
> revealing the actual knowledge (the investigation performed
> and the resulting evidence gathered in support of the
> "reasoned conclusion"). In particular, nobody
> can replicate his work or learn from any insights
> he may (or may not) have developed. Even the most
> straightforward aspect, the computer search for solutions,
> was not disclosed until our discussion in August, when it
> turned out that solutions were ruled out only in the ridiculously
> short range of perfect powers less than one million!
AS DESRIBED ABOVE, YOU ARE WRONG AGAIN ANDREW GRANVILLE: BEAL MADE ALL
HIS COMPUTER RESULTS AVAILABLE THROUGH DAN MAULDIN AT UNT. IF BEAL HAD
MADE ADDITIONAL EFFORTS TO "PUBLISH" THE RESULTS, I'M SURE THAT ANDREW
GRANVILLE WOULD TODAY BE CRITICIZING THE EFFORT AS GRANDSTANDING. THE
ANALYSIS WAS HARDLY RIDICULOUSLY SHORT, PARTICULARLY GIVEN BEAL'S
LIMITED COMPUTER RESOURCES AND PROGRAMING SKILLS IN 1993. IF GRANVILLE
DOESN'T LIKE THE RANGE SELECTED, HE IS CERTAINTLY FREE TO DO HIS OWN
WORK AS HE DEEMS APPROPRIATE. BUT THAT WOULD NOT BE LIKE GRANVILLE AT
ALL: MUCH EASIER FOR HIM TO SIMPLY CRITICIZE OTHERS.
>
> > Granville simply declares that anyone that ever considered 8+8=16
> > inherently hypothesized Beal's conjecture.
>
> I (not Granville) declared that 8+8=16 and similar trivia
> invalidate Beal's claim that explicitly stating "co-prime bases"
> distinguishes his problem from Granville's earlier proposal.
> Unless you believe that an audience of professional number
> theorists could not be expected to notice 8+8=16,
> 2^n + 2^n = 2^(n+1), etc before Beal came along.
>
I WON'T EVEN BOTHER RESPONDING TO THAT
> > > Granville, as long ago as 1992 had discussed in public work that
he
> > > had done on this conjecture. His papers are a matter of record.
> > >
> > GRANVILLE NEVER CAME CLOSE TO SUGGESTING BEAL'S CONJECTURE.
>
> As posted in sci.math, Granville listed a few solutions
> to x^a + y^b = z^c with 1/a + 1/b + 1/c < 1, and
> asked whether others existed. This does not
> differ from asking whether there are NO other solutions,
> which covers the "Beal" conjecture and more.
> Beal is apparently claiming that noticing that all
> of the solutions listed (there were only three or four!) had
> an exponent equal to 2, or that 8+8=16, is a major
> breakthrough for number theory.
>
WRONG AGAIN!! GRANVILLE RANKLY SPECULATED THAT THE FEW SOLUTIONS HE
FOUND WERE THE ONLY SOLUTIONS AND WAS SUBSEQUENTLY PROVEN WRONG BY AN
INCREDIBLY LIMITED OVERNIGHT COMPUTER SEARCH. IN SHARP CONTRAST TO
GRANVILLES AMATEURISH EFFORT, BEAL REASONED NO SOLUTIONS FOR A MORE
RESTRICTED FORM AND HAS YET TO BE PROVEN WRONG.
PERHAPS THIS REALITY HELPS EXPLAIN ANDREW GRANVILLE'S CONSTANT ATTACKS
ON BEAL. ADDITIONALLY, WHY WOULD GRANVILLE EVEN LOOK AT THE EQUATION OR
IT'S SOLUTIONS SINCE HE NOW CLAIMS IT'S SO ELEMENTARY AND EVERYTHING
ABOUT IT AND IT'S SOLUTION SETS IS SUCH COMMON KNOWLEDGE.
sel...@my-deja.com
Bob Silverman <bo...@my-deja.com> wrote:
> In article <91urvf$jot$1...@nnrp1.deja.com>,
> sel...@my-deja.com wrote:
> > There is a HUGE difference between Granville asking a class of
> students
> > to look for solutions to FLT with independent exponents, or as
> > Silverman observed, someone in a crowd asking a speaker if certain
> > results can be extended to unequal exponents, or Brun's work in the
> > early 1900's, etc, etc, etc. and Beal's reasoned conjecture that co-
> > prime bases are impossible. No-one before Beal took the time and
> effort
>
> This is unadulterated horeshit. The fact that the question was
> asked so casually during Tate's talk indicates to anyone with 2
> brain cells working (which does not include you) that EITHER:
>
> (1) The problems was well known
> (2) The question was obvious
>
SEEM TO HAVE THE BRAIN CELLS TO UNDERSTAND THE DIFFERENCE.
> to investigate the questions asked and conjecture a reasoned outcome.
> > Or if they did, they never shared their knowledge and hypothesis
with
> > the world. Beal was the first to do so. Either present some evidence
> to
> > the contrary or shut up!!
>
> Others have quoted papers which discussed the subject before Beal did.
> You choose to ignore them. You choose to ignore the fact that the
> question is obvious to anyone working in the area of diophantine
> equations. You are a crank. Go Away.
YOUR QUESTIONS ARE INDEED OBVIOUS - THE ANSWERS ARE NOT. YOU ARE THE
CRANK - YOU STOP TELLING LIES AND GO AWAY. THERE ARE NO PAPERS THAT
PROPOSE BEAL'S CONJECTURE BEFORE HE DID. YOU THINK THAT ANYONE THAT
EVER LOOKED AT A DIOPHANTINE EQUATION PRESUPPOSED BEAL'S CONJECTURE. SO
WHY ARE YOU, ANDREW GRANVILLE, WORKING ON DIOPHANTINE EQUATIONS.
ACCORDING TO YOUR LOGIC, WHATEVER YOU DISCOVER WILL ALREADY BE COMMON
KNOWLEDGE TO EVERYONE ELSE AND OBVIOUS TO ANYONE THAT EVER ASKED A
RELATED QUESTION.
> >
> > Granville simply declares that anyone that ever considered 8+8=16
> > inherently hypothesized Beal's conjecture. It's hard to know what
> > Vanderpoorten thinks since he "proposed" beal's conjecture himself
in
> > 1996.
>
> You have said this several times. Please give the reference to the
> paper in which Alf claims this.
>
ANDREW GRANVILLE, YOU KNOW WELL WHERE IT IS, BUT FOR OTHER READERS I
WILL REPEAT THAT IT IS ON PAGE 194 OF VANDERPOORTENS 1996 BOOK.
> > > sel...@my-deja.com wrote:
> > > > Don't let hull loss incident anonymously mislead you.
>
> > > Contrary to hull loss incident who has some axe to
> > > > grind,
>
> His "axe to grind" is with phonies claiming original ideas
> as their own when they are clearly not.
THEN HE SHOULD BE CRITICIZING ALF VANDERPOORTEN NOT BEAL. BEAL'S WORK
AND CONJECTURE ARE CLEARLY ORIGINAL AND PROBABLY CORRECT, UNLIKE
GRANVILLES AMATUERISH WORK WITH SECOND POWERS. GRANVILLE APPEARS TO BE
A FRUSTRATED CRANK WITH LITTLE ABILITY WHO LOVES TO CRITICIZE OTHERS.
>
> the conjecture is accepted by the math community as original
> > > and
> > > > as significant.
> > >
> > > It is accepted as a conjecture. But it did not originate with
BEAL.
> >
> > ACTUALLY IT DID!! If you disagree, simply cite your reference.
>
> I have. The question was asked in Arcata in 1985. I was there.
> Others have given references to papers which precede Beal's claim.
> You choose to ignore these.
>
THERE YOU GO AGAIN - BEAL DIDN'T ASK A QUESTION, HE CONJECTURED A
REASONED ANSWER. RELATED QUESTIONS HAVE BEEN ASKED FOR CENTURIES. BEAL
SUGGESTED A REASONED ANSWER TO ONE SUCH QUESTION. BUT YOU SEEM TO LACK
THE ABILITY TO UNDERSTAND THE DIFFERENCE. FORTUNATELY, THE REST OF THE
MATH WORLD DOES. AND FORTUNATELY THE FACTS AND THE TRUTH ARE UNAFFECTED
BY YOUR STUPIDITY.
WHY DON'T YOU GIVE US ALL A BREAK AND HIKE UP TO THE NORTH POLE. WE'RE
ALL TIRED OF READING YOUR STUPID TRASH.
Hull Loss Incident
sel...@my-deja.com wrote:
> In article <91t7um$8g1$1...@nnrp1.deja.com>,
> Bob Silverman <bo...@my-deja.com> wrote:
> > In article <3A41A699...@y.z.com>,
> > Hull Loss Incident <x...@y.z.com> wrote:
> >
> > <snip>
> >
> > > The more intelligent versions of the problem discussed by Granville,
> > > Darmon, Tijdeman et al, *are* backed by evidence coming
> > > from various different directions. None of these
> > > experts would be stupid enough to claim credit for a well-known
> > > problem
>
> Darmon agrees he was unaware of the conjecture prior to Beal.
Darmon can speak for himself. On his web page he writes
that he had results on generalized FLT before Beal even got
started with the problem. I quote from
http://www.math.mcgill.ca/darmon/ :
"In June 1993, Andrew Wiles announced his proof of the
Shimura Taniyama conjecture, conquering Fermat's Last Theorem
in the same stroke. A few months before I had been thinking about
Frey's ideas and applying them to study the generalized Fermat equation
x^p+y^q=z^r. One is interested in integer solutions which are primitive
in the sense that they satisfy gcd(x,y,z)=1, and the generalized
Fermat conjecture states that there are no such solutions when
the exponents p,q,r are greater than 3. At the time I could prove
some partial results [Da2] about x^p+y^p =z^r with r=2 or 3,
assuming the Shimura Taniyama conjecture. Thanks to [TW] and
[W] these results became unconditional.
[Da2] Darmon, Henri. The equations x^n+y^n=z 2 and x^n+y^n=z^3.
Internat. Math. Res. Notices 1993, no. 10, 263--274. "
Confirming the above, we have the reference discussed earlier,
to Darmon's July 1993 lecture on his work with Granville on
generalized FLT.
This nicely contradicts all of Beal's assertions. Darmon's
work was unambiguously prior to Beal, the equation was
well known, and number theorists were indeed aware of
the obvious point that primitive (co-prime) solutions are
the ones of interest, even before Beal showed up to proclaim
that 8+8=16.
> Vanderpoorten "proposed" it himself years after Beal,
Van der Poorten did not propose it "years after Beal".
He published on the subject in 1994 in an expository
article for the Australian math society (written Christmas
1993) and the material later made its way into his 1996
book. Unlike Beal, Van der Poorten has never claimed
ownership of the problem or campaigned to have it named
after himself.
> and Granville
> suggested in letters to Mauldin that his questions to a class of
> students gives him priority. Hmmmmmm.
You are batting .000. It is unlikely that Granville or any other
competent number theorist has ever claimed ownership of the
problem. It would be hilarious to see you quote Granville's
allegedly abusive correspondence here in the newsgroup, so
we can see what he really did say. Until that happens, your
claims about his assertions carry absolute zero credibility.
Hull Loss Incident
> > They indicate how obvious the problem is to anyone skilled in the
> > art. I remember high school competition problems asking for
> > solutions of FLT with unequal exponent -- teenagers could and
> > did solve them, under time pressure, based on the well-known
> > tricks for finding solutions when common factors are allowed.
>
> PERHAPS SO OBVIOUS TO THE GIFTED ANDREW GRANVILLE, BUT NOT TO THE REST OF
> US
As stated above, the obvious point is constructing families
of solutions which are NOT coprime. You choose to equivocate
between this homework exercise and the unsolved research problem
(generalized FLT) that is the coprime case.
> HENRI DARMON, RON GRAHAM, DAN MAULDIN, EARL TAFT,
> HAROLD EDWARDS, JERROLD TUNNELL,
It is on record by now that you misrepresent Darmon, Taft
and Edwards. Mauldin publically disavows any expertise in number
theory, so his opinions are irrelevant here. (Though he does thank Andrew
Granville for help with the AMS Notices article. GRANVILLE IS
EVERYWHERE.) You are welcome to quote, in full, the alleged
endorsements from Graham and Tunnell so that we can see whether
there is anybody on your list who is *not* being misrepresented by
Beal.
> ALSO SEE
> BELOW WHERE GRANVILLE HIMSELF WAS WORKING ON SOLUTION SETS FOR THIS
> INCREDIBLY OBVIOUS AND ELEMENTARY PROBLEM.
Granville made inroads into the hard research problem (coprime solutions),
whereas Beal doesn't grasp the trivial homework exercise (solutions with
common factor allowed). Your equivocation is inane.
Hull Loss Incident
> > We are waiting to hear what Beal contributed beyond the
> > obvious well-known at the time: that solutions are
> > plentiful when common factors are allowed, and that they
> > are rare when common factors are not allowed.
>
> BEAL CONTRIBUTED A REASONED CONJECTURE THAT SOLUTIONS ARE NOT RARE BUT
> IMPOSSIBLE FOR CERTAIN FORMS.
Saying the words "solutions are impossible" is a
declaration of opinion, not a contribution. Asserting
that the statement is "reasoned" is also just a comment
about your own private thought processes.
An actual contribution to knowledge would involve
information that other people can evaluate to see
whether it does or doesn't make the conclusion of
"no solutions" more plausible. Beal has identified
no such contribution other than a badly designed
and mis-targeted computer search.
> HE CONDUCTED THE FIRST LARGE SCALE
> COMPUTER RUN INVOLVING 15 COMPUTERS FOR THOUSANDS OF HOURS
The search was a joke. A home computer over
a weekend could have done better, had Beal
understood the difference between bases and
exponents in this problem. (He searched
for x^a + y^b = z^c with a,b,c *and* x,y,z < 100.)
Of course Mauldin's publicity pieces avoided
discussion of this little detail. It would have
discredited Beal's priority claims, by making
any correct result or conjecture appear to be
a lucky accident rather than a "reasoned conclusion".
> AND
> DISCOVERED HUNDREDS OF NON-COPRIME SOLUTIONS AND MADE THE DATA PUBLIC
> THROUGH DAN MAULDIN AT UNT.
That's hilarious. It is known for centuries how to generate
the non-coprime solutions. Publicizing this "discovery" would
discredit your priority claims almost as much as the computer
search design. Really, you should go ask Prof Mauldin to "make this
data public" on his web page about the problem, and see
how he squirms --- strangely enough he forgot to mention in his
articles that this valuable solution data was available for the asking.
> NONETHELESS, BEAL CONDUCTED THE FIRST LARGE COMPUTER ANALYSIS
It is likely that Beukers and Zagier searches were done earlier.
They found large solutions of generalized FLT, 9 orders of
magnitude beyond Beal's search range. I hope somebody
reading this can tell us when and how they conducted their
searches.
> AS DESRIBED ABOVE, YOU ARE WRONG AGAIN ANDREW GRANVILLE: BEAL MADE ALL
> HIS COMPUTER RESULTS AVAILABLE THROUGH DAN MAULDIN AT UNT.
Funny that Mauldin never publicized this valuable computer data.
> IF BEAL HAD
> MADE ADDITIONAL EFFORTS TO "PUBLISH" THE RESULTS,
Beal contacted 15-20 mathematicians and journals. Which ones
recommended publication?
> IF GRANVILLE
> DOESN'T LIKE THE RANGE SELECTED, HE IS CERTAINTLY FREE TO DO HIS OWN
> WORK AS HE DEEMS APPROPRIATE.
Right. He made major theoretical contributions to the problem
and appears to be one of the leading contenders to win the
Beal Prize of 100000. That would be amusing!
Steve Lord
> SORRY ANDREW GRANVILLE: YOUR PROBLEM REMAINS SIMPLY MISREPRESENTING THE
> TRUTH
*snip*
Whoever you are, _please_ press your Caps Lock key once. Posting in all
caps is considered shouting, and posting entire messages in all caps is
considered _extremely_ rude. Also, please take this argument to email --
sci.math isn't really the place for "I'm right!" "No, I'm right!"-style
arguments.
Steve L
Chip Eastham
"Bob Silverman" <bo...@my-deja.com> wrote in message
news:91vq30$9n8$1...@nnrp1.deja.com...
> In article <91urvf$jot$1...@nnrp1.deja.com>,
> sel...@my-deja.com wrote:
> > There is a HUGE difference between Granville asking a class of
> students
> > to look for solutions to FLT with independent exponents, or as
> > Silverman observed, someone in a crowd asking a speaker if certain
> > results can be extended to unequal exponents, or Brun's work in the
> > early 1900's, etc, etc, etc. and Beal's reasoned conjecture that co-
> > prime bases are impossible.
> >
> > Granville simply declares that anyone that ever considered 8+8=16
> > inherently hypothesized Beal's conjecture. It's hard to know what
> > Vanderpoorten thinks since he "proposed" beal's conjecture himself in
> > 1996.
>
> You have said this several times. Please give the reference to the
> paper in which Alf claims this.
>
selivan's original statement was "Vanderpoorten claimed in his 1996 book
that he proposed it, years after Beal widely distributed the conjecture."
For those who find selivan's all caps reply difficult to parse, I believe
this must be none other than Alf's "Notes on Fermat's Last Theorem".
Indeed we do find on page 194 the sentence "Led by this, I propose that
if a,b,c are relatively prime, then a^t + b^u = c^v has no solution in
integers if all of t,u,v are at least 3. If one exponent is allowed to be
2,
things are different. [etc.]" This selection is from Appendix A, which
Alf says appeared in Aus. Math. Soc. Gaz. 21, [Dec. 1994], p 150-159,
and from the context and narrowed margination of this passage, it may
be a redaction from something he says he began writing Christmas, 1993.
In any case, one notes his phrase "[led] by this" follows the statements:
"Fermat's claim says that if n > 2 ... According to Darmon and Granville
(1993), Fermat might have chosen a different generalization."
Elsewhere in the book, in the chapter titled Lecture XIV, one finds more
about what Alf terms the Generalized Fermat Conjecture. He connects
it as of March 1994 with a preprint by Darmon and Granville, with a
lecture in June 1994 by Frits Beukers describing a characterization of
all the solutions with 1/t + 1/u + 1/v >= 1 in terms of finitely many
parametric families, and with comments by Rob Tijdeman about a simple
way of constructing solutions when common factors are allowed. The
first two of these three connections are revisited in a parenthetical note
added to Appendix A, strengthening the impression that it was originally
written not long after Wiles "premature" announcement of a proof of
FLT in late 1993 and prior to the preprint release of the two papers
(one jointly with Taylor) in October 1994.
Regards,
Chip
sel...@my-deja.com
>
> > > We are waiting to hear what Beal contributed beyond the
> > > obvious well-known at the time: that solutions are
> > > plentiful when common factors are allowed, and that they
> > > are rare when common factors are not allowed.
> >
> > BEAL CONTRIBUTED A REASONED CONJECTURE THAT SOLUTIONS ARE NOT RARE
BUT
> > IMPOSSIBLE FOR CERTAIN FORMS.
>
> Saying the words "solutions are impossible" is a
> declaration of opinion, not a contribution.
DECLARATION OF OPINION LACKING PROOF
Asserting
> that the statement is "reasoned" is also just a comment
> about your own private thought processes.
THAT IS TRUE, IT IS ALSO TRUE OF ANY SIMILIAR STATEMENT THAT ANYONE
MAKES. WHETHER THE REASONING IS ADEQUETE OR NOT IS GENERALLY REVEALED
BY THE LIFESPAN OF THE CONJECTURE. THIS IS WHY GRANVILLE HAS SUCH A
PROBLEM WITH BEAL. BEAL'S REASONING HAS CREATED AN INTERESTING
CONJECTURE WITH A LONG LIFESPAN WHILE GRANVILLES RARELY SURVIVE THE
LIGHT OF DAY
>
> An actual contribution to knowledge would involve
> information that other people can evaluate to see
> whether it does or doesn't make the conclusion of
> "no solutions" more plausible. Beal has identified
> no such contribution other than a badly designed
> and mis-targeted computer search.
>
THE ORIGINAL CONJECTURE ITSELF IS THE CONTRIBUTION TO STIMULATE
THOUGHT, IT DOENS'T REQUIRE A PROOF OR IT WOULD BE A THEOREM. GRANVILLE
ALSO HAS A HARD TIME WITH THIS CONCEPT, AND SIMPLY ENJOYS CRITICIZING
CONTRIBUTIONS BY OTHERS. BEAL'S SEARCH WAS ADEQUETE FOR HIS PURPOSES.
IT FOUND HUNDREDS OF SOLUTIONS THAT ALLOWED BEAL TO LOOK AT THEIR
CHARACTERISTICS. SUBSEQUENT MORE EXPANSIVE COMPUTER SEARCHES BY OTHERS
HAVE FOUND NO COUNTEREXAMPLES. ANY COMPUTER SEARCH IS INADEQUETE AND
SUBJECT TO CRITICISM. BEAL ALSO OBVIOUSLY DID LIMITED SEARCHES WITH
LARGER BASES LIMITED TO A SMALL RANGE OF EXPONENTS. THESE ARE EASILY
DONE BY ANYONE AND BEAL DIDN'T CONSIDER ANY OF HIS COMPUTER SEARCHES
PARTICULARLY SIGNIFICANT AND HAS NEVER CLAIMED THAT THEY WERE EARTH
SHAKING. THEY WERE HOWEVER, THE MOST EXHAUSTIVE DONE AT THAT TIME AND
SUFFICIENT TO ALLOW BEAL TO REASON AN UNKNOWN AND INTERESTING
CONJECTURE.
> > HE CONDUCTED THE FIRST LARGE SCALE
> > COMPUTER RUN INVOLVING 15 COMPUTERS FOR THOUSANDS OF HOURS
>
> The search was a joke. A home computer over
> a weekend could have done better, had Beal
> understood the difference between bases and
> exponents in this problem. (He searched
> for x^a + y^b = z^c with a,b,c *and* x,y,z < 100.)
>
BEAL OBVIOUSLY UNDERSTOOD THE DIFFERENCE. HE WAS SIMPLY INTERESTED IN
FINDING SOLUTIONS NOT PREDICTED BY HIS LOGIC ALGORITHMS (THAT DO EASILY
FIND COMMON FACTOR SOLUTIONS). THE GOAL WAS NOT TO FIND COMMON FACTOR
SOLUTIONS, RATHER TO FIND FACTORS THAT WERE NOT PREDICTABLE BY HIS
LOGIC ALGORITHMS. GRANVILLE DOESN'T SEEM TO UNDERSTAND THESE CONCEPTS
EITHER.
> Of course Mauldin's publicity pieces avoided
> discussion of this little detail. It would have
> discredited Beal's priority claims, by making
> any correct result or conjecture appear to be
> a lucky accident rather than a "reasoned conclusion".
>
WHETHER IT WAS A LUCKY ACCIDENT OR A REASONED (TO WHATEVER STANDARD
GRANVILLE BELIEVES THE TERM REQUIRES) CONCLUSION ISN'T EVEN RELEVANT.
GRANVILLE ALSO HAS A HARD TIME WITH THAT CONCEPT.
> > AND
> > DISCOVERED HUNDREDS OF NON-COPRIME SOLUTIONS AND MADE THE DATA
PUBLIC
> > THROUGH DAN MAULDIN AT UNT.
>
> That's hilarious. It is known for centuries how to generate
> the non-coprime solutions. Publicizing this "discovery" would
> discredit your priority claims almost as much as the computer
> search design. Really, you should go ask Prof Mauldin to "make this
> data public" on his web page about the problem, and see
> how he squirms --- strangely enough he forgot to mention in his
> articles that this valuable solution data was available for the
asking.
>
ANDREW GRANVILLE, IF YOU WERE NOT SUCH AN ASSHOLE YOU WOULD UNDERSTAND
THAT BEAL MADE THE RESULTS AVAILABLE BECAUSE PEOPLE BEGAN REQUESTING
THEM AND BEAL AND MAULDIN WANTED TO ACCOMODATE THEIR REQUESTS. NIETHER
BEAL NOR MAULDIN THOUGHT THE COMPUTER RESULTS PARTICULARLY "NESSESARY".
YOU ARE SUCH AN ARROGANT ASSHOLE. OF COURSE IT'S EASY TO GENERATE
COMMON FACTOR SOLUTIONS, THAT WAS NOT THE GOAL OF THE SEARCH.
> > NONETHELESS, BEAL CONDUCTED THE FIRST LARGE COMPUTER ANALYSIS
>
> It is likely that Beukers and Zagier searches were done earlier.
> They found large solutions of generalized FLT, 9 orders of
> magnitude beyond Beal's search range. I hope somebody
> reading this can tell us when and how they conducted their
> searches.
>
BEUKERS AND ZAGIERS SEARCHES WERE INCREDIBLY SMALLER THAN BEAL'S. YES
THEY DID LIMITED SEARCHES WITH LARGE BASES BUT THE TERM QUANTITIES THAT
THEY WERE WORKING WITH WERE MILLIONS OF ORDERS OF MAGNITUDE SMALLER
THAN BEAL'S SEARCHES (100^100 IS FAR BEYOND THE QUANTIES THAT BEUKERS
AND ZAGIERS DEALT WITH). BEUKERS AND ZAGIERS SEARCHES DID OFFER SOME
ADDITIONAL INSIGHT AT THE TIME THEY WERE DONE, BUT THEY WERE VERY
DIFFERENT AND HAD VERY DIFFERENT GOALS FROM BEAL'S. THIS IS ANOTHER
CONCEPT THAT GRANVILLE DOESN'T SEEM TO GRASP.
> > AS DESRIBED ABOVE, YOU ARE WRONG AGAIN ANDREW GRANVILLE: BEAL MADE
ALL
> > HIS COMPUTER RESULTS AVAILABLE THROUGH DAN MAULDIN AT UNT.
>
> Funny that Mauldin never publicized this valuable computer data.
>
> > IF BEAL HAD
> > MADE ADDITIONAL EFFORTS TO "PUBLISH" THE RESULTS,
>
> Beal contacted 15-20 mathematicians and journals. Which ones
> recommended publication?
REALLY GRANVILLE - YOU'RE GETTING TO THE BOTTOM OF THE BARREL: BEAL
NEVER ATTEMPTED TO PUBLISH THE RESULTS AND NEVER EVEN SUGGESTED THEY BE
PUBLISHED. I SIMPLY SAID EARLIER THAT IF BEAL HAD DONE SO YOU WOULD BE
CRITICIZING HIM FOR GRANDSTANDING. SO HERE YOU ARE, CRITICIZING BOTH
MAKING THEM AVAILABLE AND THE FACT THAT BEAL DIDN'T MAKE THEM AVAILABLE
UNTIL ASKED TO DO SO.
>
> > IF GRANVILLE
> > DOESN'T LIKE THE RANGE SELECTED, HE IS CERTAINTLY FREE TO DO HIS OWN
> > WORK AS HE DEEMS APPROPRIATE.
>
> Right. He made major theoretical contributions to the problem
> and appears to be one of the leading contenders to win the
> Beal Prize of 100000. That would be amusing!
>
I WOULD LOVE TO SEE ANY "MAJOR CONTRIBUTION" THAT ANDREW GRANVILLE MADE
TO ANYTHING THAT DIDN'T INVOLVE CRITICIZING OTHERS. THE ODDS THAT
GRANVILLE WILL PROVE OR DISPROVE BEAL'S CONJECTURE ARE EXACTLY ZERO.
NOW THERE IS A CONJECTURE THAT DEFY'S REASONING CRITICISM.
sel...@my-deja.com
particularly in messages with a number of responses. I agree with
your "i'm right - No- I'm right" comments. Unfortunately, Andrew
Granvilles lies and misreresentaions must be responded to for what they
are.
In article <Pine.OSF.4.30.00122...@kingfisher.WPI.EDU>,
sel...@my-deja.com
>
> > > They indicate how obvious the problem is to anyone skilled in the
> > > art. I remember high school competition problems asking for
> > > solutions of FLT with unequal exponent -- teenagers could and
> > > did solve them, under time pressure, based on the well-known
> > > tricks for finding solutions when common factors are allowed.
> >
> > PERHAPS SO OBVIOUS TO THE GIFTED ANDREW GRANVILLE, BUT NOT TO THE
REST OF
> > US
>
> As stated above, the obvious point is constructing families
> of solutions which are NOT coprime. You choose to equivocate
> between this homework exercise and the unsolved research problem
> (generalized FLT) that is the coprime case.
>
You don't seem to understand that the two are closely related. By
looking at the properties of common factors and looking for common
factor solutions not generated by elementary algorithms, one gains
insight into the problem. That process is all the more interesting
since we do not have co-prime solutions to examine.
> > HENRI DARMON, RON GRAHAM, DAN MAULDIN, EARL TAFT,
> > HAROLD EDWARDS, JERROLD TUNNELL,
>
> It is on record by now that you misrepresent Darmon, Taft
> and Edwards.
How and where is it on the record?? Henri Darmon personally told Beal
that he was unaware of the Beal conjecture prior to Beal's work. Ron
Graham personally told Beal the Same. Dan Mauldin personally told Beal
the same. Earl Taft wrote the same to Beal. Harold Edwards wrote and
said the same to Beal. Jerrold Tunnell wrote the same to Taft who
forwarded it to Beal. Where have I or Andrew Beal misrepresented
anyone????
Mauldin publically disavows any expertise in number
> theory, so his opinions are irrelevant here. (Though he does thank
Andrew
> Granville for help with the AMS Notices article. GRANVILLE IS
> EVERYWHERE.)
Why is an expertise in number theory a prerequisite?? The fact is that
mathematicians in general were unfamiliar with the concepts of the Beal
conjecture. I have demonstrated this by repeating statements from both
number theorists and non-number theorists. (in case number theorists
were unaware but non-number theorists knew it all along. -- this is a
joke for purposes of humor)
You are welcome to quote, in full, the alleged
> endorsements from Graham and Tunnell so that we can see whether
> there is anybody on your list who is *not* being misrepresented by
> Beal.
>
They are paraphrased above - All personally told Beal and others that
his conjecture was original and that they were previously unaware of
any assertion that no solutions were possible to the form Beal
proposed. In fact some were so surprised by the assertion that they
suggested solutions would be found by a simple computer search (so much
for common knowledge that there were none). Why don't you name any
expert that claims such prior knowledge?? I will personally contact
them so that you don't again simply make up some names or make false
attributions. No, I'm not remotely interested in Andrew Granvilles
undocumented verbal assertions. You are welcome to contact those people
named above.
Additionally, since talk is so cheap: why don't you cite a single
written reference prior to Vanderpoortens "I propose" of Beal's
conjecture on page 194 of his 1996 book.
Please spare us all your famous written references to anyone that wrote
any form of A^X + B^Y = C^Z (yes including different variable symbols)
without suggesting anything related to the beal conjecture.
> > ALSO SEE
> > BELOW WHERE GRANVILLE HIMSELF WAS WORKING ON SOLUTION SETS FOR THIS
> > INCREDIBLY OBVIOUS AND ELEMENTARY PROBLEM.
>
> Granville made inroads into the hard research problem (coprime
solutions),
> whereas Beal doesn't grasp the trivial homework exercise (solutions
with
> common factor allowed). Your equivocation is inane.
The problem that Granville has is that he thinks solution sets with
common factors are totally independent of, and unrelated to, solution
sets without common factors. I'd love to see any inroads that Granville
has made beyong his incorrect speculation with second powers. In
contrast, intelligent people recognize that any solutions or results
for a given function provide insight into the properties of results or
solution sets for that function
Steve Lord
> Responses in all caps helps to differentiate them from previous text,
> particularly in messages with a number of responses.
However, they are quite annoying. Please stop posting in all caps. Thank
you.
> I agree with your "i'm right - No- I'm right" comments. Unfortunately,
> Andrew Granvilles lies and misreresentaions must be responded to for
> what they are.
Actually, from what Bob Silverman has stated, you are incorrect. He has
been posting for quite a while longer than you have, and I have not seen
him post deliberately misleading or mistaken statements. I also don't see
why you think he (and the other posters in this thread) are this Andrew
Granvilles.
Steve L
sel...@my-deja.com
Hull Loss Incident <x...@y.z.com> wrote:
>
>
> sel...@my-deja.com wrote:
>
> > In article <91t7um$8g1$1...@nnrp1.deja.com>,
> > Bob Silverman <bo...@my-deja.com> wrote:
> > > In article <3A41A699...@y.z.com>,
> > > Hull Loss Incident <x...@y.z.com> wrote:
> > >
> > > <snip>
> > >
> > > > The more intelligent versions of the problem discussed by
Granville,
> > > > Darmon, Tijdeman et al, *are* backed by evidence coming
> > > > from various different directions. None of these
> > > > experts would be stupid enough to claim credit for a well-known
> > > > problem
> >
conjecture in 1996 on page 194 in his book. As well as Darmon's person
to person discussion with Beal where Darmon said he was unaware of any
version of Beal's conjecture or its implications prior to Beal's
distribution of it.
> Darmon agrees he was unaware of the conjecture prior to Beal.
>
> Darmon can speak for himself.
Actually he did speak for himself: he declared that he was unaware of
no solutions for beal's conjecture prior to beal distributing it.
On his web page he writes
> that he had results on generalized FLT before Beal even got
> started with the problem. I quote from
> http://www.math.mcgill.ca/darmon/ :
>
> "In June 1993, Andrew Wiles announced his proof of the
> Shimura Taniyama conjecture, conquering Fermat's Last Theorem
> in the same stroke. A few months before I had been thinking about
> Frey's ideas and applying them to study the generalized Fermat
equation
> x^p+y^q=z^r. One is interested in integer solutions which are
primitive
> in the sense that they satisfy gcd(x,y,z)=1, and the generalized
> Fermat conjecture states that there are no such solutions when
> the exponents p,q,r are greater than 3. At the time I could prove
> some partial results [Da2] about x^p+y^p =z^r with r=2 or 3,
> assuming the Shimura Taniyama conjecture. Thanks to [TW] and
> [W] these results became unconditional.
>
> [Da2] Darmon, Henri. The equations x^n+y^n=z 2 and x^n+y^n=z^3.
> Internat. Math. Res. Notices 1993, no. 10, 263--274. "
>
> Confirming the above, we have the reference discussed earlier,
> to Darmon's July 1993 lecture on his work with Granville on
> generalized FLT.
>
> This nicely contradicts all of Beal's assertions.
Actually, it contradicts nothing. Would you be so kind as to be
specific about exactly what was contradicted??? Beal never asserted
that Darmon had never considered any of several generalized forms of
FLT. Nonetheless, Darmon himself says that he was unaware that Beal's
form has no solutions. Many people were considering many things about
many variations of FLT. No-one disputes this. No-one other than
Granville disputes that Beal was the first to reason and propose that a
specific generalization has no solutions. Darmon even discusses beal's
conjecture in the above as "the generalized Fermat conjecture".
Darmon's
> work was unambiguously prior to Beal, the equation was
> well known, and number theorists were indeed aware of
> the obvious point that primitive (co-prime) solutions are
> the ones of interest, even before Beal showed up to proclaim
> that 8+8=16.
We all agree on this except that Granville was the first to bring
8+8=16 and A+B=C into the discusions as evidence of prior art of Beal's
conjecture.
>
> > Vanderpoorten "proposed" it himself years after Beal,
>
> Van der Poorten did not propose it "years after Beal".
There you go lying again: anyone can look on page 194 of his book and
judge for themselves. You cannot tell lies enough such that they become
true.
> He published on the subject in 1994 in an expository
> article for the Australian math society (written Christmas
> 1993) and the material later made its way into his 1996
> book. Unlike Beal, Van der Poorten has never claimed
> ownership of the problem or campaigned to have it named
> after himself.
>
Another lie: Vanderpooretn writes for all the world to see: "I propose
[beal's conjecture]" it's on page 194 of his 1996 book published years
after beal's widespread distribution of his conjecture.
Beal has never claimed ownership of the problem or campaigned to have
it named after himself. He simply was the first to propose no solutions
to a specific form and many people have subsequently shown an interest
in it. He agreed to offer a prize when Dan Mauldin wanted to write an
article about it in 1997
> > and Granville
> > suggested in letters to Mauldin that his questions to a class of
> > students gives him priority. Hmmmmmm.
>
> You are batting .000. It is unlikely that Granville or any other
> competent number theorist has ever claimed ownership of the
> problem. It would be hilarious to see you quote Granville's
> allegedly abusive correspondence here in the newsgroup, so
> we can see what he really did say. Until that happens, your
> claims about his assertions carry absolute zero credibility.
>
Wrong again; Vanderpoorten claims he "proposed" it (as detailed
repeatedly previously) and Granville claims his elementary questions
to a class of students somehow pre-empts beal's conjecture. He has said
as much in these discussion groups - go read for youself under any one
of several of Granville's pen names.
I have never received or claimed to have received "abusive
correspondence" from Granville. However, I do find Granville to be an
arrogant and uninformed individual who apparently loves to criticize
others through whatever means he can devise, including
misrepresentation and outright lies. He has crucified Beal who did no
more than propose a conjecture and offer a prize for its solution. Many
mathematicians think this is wonderful. Granville is disturbed by it.
ma...@mimosa.csv.warwick.ac.uk
Yes, Bob Silverman's assertions carry conviction, and I believe them.
Unfortunately, I find the postings of both of the other two principal
protagonists in this debate, "Hull loss incident" and "selivan" equally
unconvincing and lacking in content. This is mainly because both are
posting anonymously. I don't remember anyone posting anonymously to
this Newsgroup until a year or two ago. Why do people do it or find it
necessary?
In practice a large part of a person's credibility is derived from their
identity and proven track record. If Bloggs on a Newsgroup claims to
have read something somewhere or to have heard somebody say something,
and others dispute it, then there are three possibilities:
a) Bloggs assertion is correct
b) Bloggs is honest but mistaken
c) Bloggs is being deliberately misleading.
I can only make an sensible guess at which of these is correct if I know
something about Bloggs.
Derek Holt.
sel...@my-deja.com
definition of truth.
You can believe Henri Darmon and Jarrold Tunnell and Earl Taft and Dan
Mauldin and Harold Edwards and Ron Graham or you can not believe them.
They all stated that they were unaware of Beal's conjecture before he
made it. Some said they suspected counterexamples would be easily found
(so much for previous common knowledge that there are none as Silverman
asserts). Silverman says that is "horeshit". Beal himself has
repeatedly asked for any written confirmable prior reference. There
apparently are none. Silverman and Granville answer by demonstrating
that someone once asked "what about independent exponents", as though
that is the extent of Beal's conjecture.
Silverman may well be another pen name for Granville. Silverman and
Granville both refuse to cite any confirmable prior reference other
than "many are posted before" which is simply untrue (posted where??).
Both Silverman and Granville seem to think that if they say something
long enough it will become true. Both deny that page 194 of
Vanderpooten's 1996 book "proposes" Beal's conjecture as though
Vanderpoorten originated it (so much for Vanderpooretn believing it was
common prior knowledge). Anyone can look at Vanderpoortens book and
judge for themselves who is telling the truth or anyone can simply call
other people liars and believe whatever they please.
Some of us post anonymously because we simply don't want to be
personally involved in the politics of things. Judge the message, not
the messenger. Truth is truth; whoever carries the message.
In article <924mb8$n4v$1...@wisteria.csv.warwick.ac.uk>,
ma...@mimosa.csv.warwick.ac.uk () wrote:
> In article <Pine.OSF.4.30.0012232313350.17179-
100...@kingfisher.WPI.EDU>,
Chip Eastham
sel...@my-deja.com wrote:
> You may believe whoever or whatever you desire. That isn't the
> definition of truth.
[editorializing and speculation about possible
identity of Bob Silverman and Andrew Granville
deleted]
> Both Silverman and Granville seem to think that if they say
> something long enough it will become true. Both deny that
> page 194 of Vanderpooten's 1996 book "proposes" Beal's conjecture
> as though Vanderpoorten originated it (so much for Vanderpooretn
> believing it was common prior knowledge). Anyone can look at
> Vanderpoortens book and judge for themselves who is telling the
> truth or anyone can simply call other people liars and believe
> whatever they please.
>
Elsewhere in this thread I have given the relevant quote
from Alf van der Poorten's excellent expository book,
Notes on Fermat's Last Theorem. Both there and in a msg
on this thread by Bob Silverman, dating of Alf's writing
in Appendix A of his 1996 copyrighted book is traced to
late 1993 (Christmas!) or at worst early 1994.
I believe that anyone who reads the passage will likely
agree that van der Poorten is saying that he was led to
conjecture by (reports of) work by Darmon and Granville
in 1993 that:
"if a,b,c are relatively prime, then a^t + b^u = c^v has
no solution in integers if all of t,u,v are at least 3"
Elsewhere in the book, including a parenthetical note
appended to the end of Appendix A (clearly designed
to update the reader to the status following the Oct. 94
submissions by Wiles and Taylor of the two final papers
that finished FLT), one finds van der Poorten referring
to this as the Generalized Fermat Conjecture.
One searches in vain in this thread for a statement of
Beal's Conjecture, except by selivan's equation of it
with the above. One similarly finds no such explicit
statement at www.bealconjecture.com, but at the other
Web page giving the conditions for Beal's award:
http://www.math.unt.edu/~mauldin/beal.html
one finds the following statement:
BEAL'S CONJECTURE: If A^x + B^y = C^z , where A, B, C,
x, y and z are positive integers and x, y and z are all
greater than 2, then A, B and C must have a common factor.
I agree with selivan's assessment that these two are
mathematically equivalent, differing only in inessential
ways such as the consideration of negative bases and the
emphasis on co-primality making solutions impossible vs.
the presence of a common factor to all three bases when
a solution exists.
What I don't fully buy is selivan's idea that van der
Poorten, by stating his conjecture, is also "claiming
priority" for it. Perhaps selivan, with apparent inside
knowledge of Beal's development of the conjecture, may
feel by analogy with the importance to Beal of such a
claim of priority, that it would be of equal importance
to any "rival discoverer". It is rare for academics to
squabble over priority in connection with conjectures,
notwithstanding the well-publicized controversy about
the Tanayama-Shimura-Weil conjecture that turned out to
be critical to the Wiles/Taylor FLT proof (building on
work by Serre, Frey, and Ribet among others).
Bearing in mind the expository nature of the book Notes
on Fermat's Last Theorem, and particularly the credit
given to Darmon and Granville, it seems to me what Alf
intended was to inform nonspecialists like myself of the
state of the art with respect to the unequal exponents
variation of FLT. To do this he used the Generalized
Fermat Conjecture as a pedagogical device, through which
the work of Darmon and Granville on coprime cases with
reciprocal exponents summing less than 1, the work of
Zaiger and Beukers on coprime cases with reciprocal
exponents summing to 1 or greater, and constructions he
credits to Tidjeman for non-coprime solutions. In the
course of this he is able to drag in with some details
the bearing of the ABC-conjecture and Mordell's [Thm.]
on the sum less than 1 issues.
I think a reasonable person can be of two minds about
this "priority," granted that for sake of argument it
would be worth squabbling over. The charitable view is
that in 1993 both Beal and van der Poorten independently
made the Generalized Fermat Conjecture.
The less charitable view would be to recognize for the
purpose of priority only publication, as if this were an
proof-like priority! This, at least as regards Alf's
side of things, would seem to be selivan's approach, but
in ascribing to Alf the 1996 date for the book copyright,
selivan overlooks the Dec. 1994 date of the precedent
paper in Aus. Math. Soc. Gaz. 21. Against this I would
only have the Dec. 1997 publication in Notices of the AMS
an article by Dan Mauldin describing Beal's conjecture
and prize money. [Ironically that article acknowledges
the assistance of Granville in its preparation.]
I prefer the charitable interpretation. I'm more of a
teacher than a researcher, so perhaps this is in the way
of "suffering fools gladly," no doubt in part because I'm
closer to their level than to the other extreme.
Regards,
Chip
Richard Tobin
>Responses in all caps helps to differentiate them from previous text,
Responses in all caps help to differentiate complete-and-utter-loonies
from the rest of us, and are thus extremely helpful to the casual
reader. Please keep it up.
-- Richard
--
Spam filter: to mail me from a .com/.net site, put my surname in the headers.
printf("%.*s\n", len, str);
Hull Loss Incident
> This is totally contradicted by Vanderpoorten's "proposal" of the
> conjecture in 1996 on page 194 in his book.
Your ravings about Van der Poorten are crackpot. He is not
trying to steal credit for your (non) discovery, or otherwise acting
as the Dutch-Australian wing of a worldwide Granville conspiracy
against you.
If you bother to actually read the book, Van der Poorten makes it
clear that all his information about recent FLT-related developments
is at second hand, that he hasn't worked in that area for many years,
that he is reporting on work of others, etc. He goes into some detail
about which lectures and articles he is extracting the information from,
and scrupulously credits pretty much everything in the book to others.
The "proposal" you are trying to make capital of, is clearly presented as
based on ideas from a 1993 preprint of Darmon and Granville which,
as he states, he hadn't yet seen at the time of writing and was merely
quoting the results. There is no pretense of originality whatsoever,
let alone Beal-like grandiose claims of a "significant discovery" for
mathematics.
> > > Vanderpoorten "proposed" it himself years after Beal,
> >
> > Van der Poorten did not propose it "years after Beal".
>
> There you go lying again: anyone can look on page 194 of his book and
> judge for themselves.
They can also look a few pages earlier, where the appendix begins,
and read Van der Poorten's statement that it was written Christmas 1993,
not "years after Beal" as you continue to claim after being repeatedly
corrected on this point. The work of Darmon and Granville he refers
to, was in circulation in 1993 before you got started on the problem.
Darmon is also listed as speaking about it at a conference
in July 1993, as you can confirm at the web site I referenced earlier;
that certainly predates Beal's work.
> > He published on the subject in 1994 in an expository
> > article for the Australian math society (written Christmas
> > 1993) and the material later made its way into his 1996
> > book. Unlike Beal, Van der Poorten has never claimed
> > ownership of the problem or campaigned to have it named
> > after himself.
> >
> Another lie: Vanderpooretn writes for all the world to see: "I propose
> [beal's conjecture]" it's on page 194 of his 1996 book published years
> after beal's widespread distribution of his conjecture.
Read the book, retard. Other people have already done the homework
for you and posted the details in this thread. You have been informed
repeatedly in the August thread as well as now, that Van der Poorten's
remarks were written1993 and published 1994. That is, the "Beal"
conjecture was made public by Van der Poorten before Beal --- and
Van der Poorten doesn't even consider it worthy of claiming credit.
> Beal has never claimed ownership of the problem
These sci.math threads prove otherwise.
> or campaigned to have it named after himself.
Beal has paid to advertise his claims to the conjecture.
The www.bealconjecture.com web site is bought and
paid for propaganda as was the highly irregular article
by Mauldin in AMS Notices.
> He simply was the first to propose no solutions
> to a specific form and many people have subsequently shown an interest
> in it. He agreed to offer a prize when Dan Mauldin wanted to write an
> article about it in 1997
Mauldin's article in AMS Notices (Dec 1997) was highly irregular.
Could it have something to do with Beal being the largest single
individual donor to AMS that year (see "Acknowledgement
of Contributions" in the1998 Notices), and a major benefactor
of Mauldin's math department and university? Mauldin also heads
the prize committee for the Beal award, which is curious considering
his lack of qualification in number theory.
It appears that Mauldin needed to placate a determined
donor -- to bring his work to a mathematical audience -- while
somehow shielding Beal from the indifference and outright ridicule
his slim contribution and grandiose claims would have elicited.
Solution: place a puff piece in a trade journal, thus publishing the
unpublishable while granting Beal the credibility he craved.
Mauldin was evidently at pains to "explain" this shameless PR piece,
as witness his sheepish followup letter a few months later.
Strangely, although ostensibly written about some interesting mathematics
done by an amateur, Mauldin's articles carefully avoid explaining to
an audience of mathematicians what Beal actually *did*. A disclosure
that the computer search was of "all terms up to 99^99", would
have nullified Beal's claims to a discovery based on reasoned evidence
rather than lucky accident, and Mauldin chose not to share that tidbit.
Also undisclosed was that Beal's results were available by request
from Mauldin; Beal's "remarkable" contributions were too remarkable
to see the light of day.
> > You are batting .000. It is unlikely that Granville or any other
> > competent number theorist has ever claimed ownership of the
> > problem. It would be hilarious to see you quote Granville's
> > allegedly abusive correspondence here in the newsgroup, so
> > we can see what he really did say. Until that happens, your
> > claims about his assertions carry absolute zero credibility.
> >
> Wrong again; Vanderpoorten claims he "proposed" it (as detailed
> repeatedly previously) and Granville claims his elementary questions
> to a class of students somehow pre-empts beal's conjecture. He has said
> as much in these discussion groups - go read for youself under any one
> of several of Granville's pen names.
Granville and Van der Poorten are not participating in these discussions
so far. Your conspiracy theories are crackpot.
> I have never received or claimed to have received "abusive
> correspondence" from Granville.
In August 2000 you stated that Granville had been "abusive and
ill-informed" to you. It would be fun to see his comments posted
here.
Chip Eastham
"Hull Loss Incident" <x...@y.z.com> wrote in message
news:3A49D931...@y.z.com...
> sel...@my-deja.com wrote:
>
> > I have never received or claimed to have received "abusive
> > correspondence" from Granville.
>
> In August 2000 you stated that Granville had been "abusive and
> ill-informed" to you. It would be fun to see his comments posted
> here.
>
Perhaps selivan's point is a non-denial denial that he or she is Beal.
All that we can know so far is that, unlike yourself, Bob Silverman,
denis-feldmann and perhaps others who stand accused by selivan of secretly
being Andrew Granville, the postings under selivan, jim_pl, and bob_paulson
(thread originator) are restricted to this one forum, one thread, and hence
this one topic, all since Dec. 20, 2000.
Regards,
Chip
Antonio Ramirez
We know more than that... they also originated from very similar IP
addresses hosted by the same ISP, and in several cases the _same_ IP
address. Look at the NNTP-Posting-Host header for this piece of
information. These not only seem to be sock puppets for Beal, but very
badly executed ones.
>
> Regards,
> Chip
simp...@my-deja.com
> collegue Henri Darmon disagrees with you. Everyone disagrees with you.
> As Beal said before, talk and bullshit are cheap. No-one was aware of
> from NYU, Earl Taft from Rutgers, Henri Darmon, Ron Graham, and
> priority at one point suggesting that you had once asked a classroom
of
> students a related question. Vanderpoorten claimed in his 1996 book
> that he proposed it, years after Beal widely distributed the
> with any verbiage, much less lies. We all waited in the August
> discussion for a single reference besides your assertion that A+B=C
> implies the conjecture
>
> Hull Loss Incident <x...@y.z.com> wrote:
> > sel...@my-deja.com wrote:
> >
> > > Don't let hull loss incident anonymously mislead you.
> >
> > the false names "bob_paulson", "selivan", and "jim_pl". Last
> > time you posted under the false name "phil_rogowski" in
> > support of andy...@my-deja.com. What will you do for an
> > encore?
> >
> > > There is no evidence of prior knowledge of the conjecture.
> >
> > Other than the abundant posted evidence, there is no evidence.
> >
> AS I SAID -- NONE-- We all waited in the August discussion for a
single
> reference besides your suggestion that A+B=C implies the conjecture.
>
> > > hull loss incident has been repeatedly asked to cite a single
> > > confirmable prior reference and is unable to do so.
> >
> > References such as Tijdeman's lectures, published in 1989,
> > were posted and excerpted last time we discussed this.
> > They are prior, and confirmable.
>
> AND UNRELATED
> >
> > work, and proof that it was done well before Beal's
> > armchair speculations; a reference from Prof. Myerson,
> > to Granville's posing the problem in the early 90's at a
> > number theory meeting; and recollections from Bob Silverman,
> > of discussions at the 1985 Arcata meeting about unequal
> > exponent FLT in light of Frey's breakthrough.
> >
> concept since he worked so closely with you.
>
> > earlier) indicates, the problem is as ancient as it is obvious.
>
> NO ONE AGREES with you Granville, mush less the facts
> >
> > > Contrary to hull loss incident who has some axe to
> > > original and as significant.
> >
> > Identify a single number theorist who agrees that Beal has
> > made a significant original (i.e. unknown at the time) contribution
> > to mathematics, or that "Beal conjecture" is the proper attribution
> > for the problem.
>
> SEE NAMES ABOVE
> >
> > >Hull loss incident declares that the conjecture may not be true!
> >
> > > Of course it may not be true, that's what makes it a conjecture
> >
> > Evidence is what makes a conjecture. Any bozo can propose
> > armchair mathematical wagers, and any rich bozo can fund the
> > wagers with prize money. Your "conjecture" (claiming no solutions,
> > for no apparent reason) is in exactly that category of publicity
> stunts.
> > The more intelligent versions of the problem discussed by Granville,
> > Darmon, Tijdeman et al, *are* backed by evidence coming
> > experts would be stupid enough to claim credit for a well-known
significant
> > event for mathematics.
> >
> DO YOU MEAN AS STUPID as you and Vanderpoorten when you both attempted
> to claim credit? Beal has your actual letters to Mauldin in 1997 and
> 1998 where you discussed your claims of "priority"
>
> BEAL HAS ORIGINAL letters from mathematicians in 1994 agreeing it was
> unknown and calling it a remarkable discovery
>
> WHY DON'T YOU STOP TELLING LIES
> >
>
Hull Loss Incident
> "Chip Eastham" <eas...@bellsouth.net> writes:
> > "Hull Loss Incident" <x...@y.z.com> wrote in message
> >
> > Perhaps selivan's point is a non-denial denial that he or she is Beal.
> >
> > All that we can know so far is that, unlike yourself, Bob Silverman,
> > denis-feldmann and perhaps others who stand accused by selivan of secretly
> > being Andrew Granville,
The evil genius Dr Granville must have truly superhuman capabilities.
Messages in this thread indicate that he crossed the Atlantic twice
in one day, in under 80 minutes the first trip and just 20 minutes for
the return.
02:43 AM 12/22/00 Hull Loss Incident (posting from Boston)
04:01 AM 12/22/00 denis-feldmann (posting from France)
04:20 AM 12/22/00 Hull Loss Incident (Boston)
09:56 AM 12/22/00 Bob Silverman (New England)
Of course, with Prof Granville's stealth control of the international
computer networks, this could all be just a clever ruse to dupe us
into believing that "Hull Loss" and "Feldmann" and "Silverman" are
not his puppets.
> > the postings under selivan, jim_pl, and bob_paulson
> > (thread originator) are restricted to this one forum, one thread, and hence
> > this one topic, all since Dec. 20, 2000.
>
> We know more than that... they also originated from very similar IP
> addresses hosted by the same ISP, and in several cases the _same_ IP
> address. Look at the NNTP-Posting-Host header for this piece of
> information. These not only seem to be sock puppets for Beal, but very
> badly executed ones.
Don't forget the similarity of writing styles, spelling errors, repetition of
words and phrases from andy...@my-deja.com, combined with a
detailed knowledge of Beal's private correspondence and conversations.
It is certainly Possible that 5 separate people, using the same software,
posting through the same USENET service, via the same ISP in Texas,
are all simultaneously obsessed with the priority and attribution of
Beal's math problem -- as possible as a Georgia math professor
crossing the Atlantic in 20 minutes.
Hull Loss Incident
for resolving it, prior to Beal! See quotation below...
sel...@my-deja.com wrote:
> As well as Darmon's person to person discussion
> with Beal where Darmon said he was unaware of any
> version of Beal's conjecture or its implications prior to Beal's
> distribution of it.
It is on record that Darmon gave conference lectures about
his work (with Granville) on a "version of Beal's conjecture"
in July 1993, which is prior to Beal stating or distributing
anything about the problem. You have been told this repeatedly
and can check it at the conference web address posted earlier.
> >> Darmon agrees he was unaware of the conjecture prior to Beal.
> >
> > Darmon can speak for himself.
>
> Actually he did speak for himself: he declared that he was unaware of
> no solutions for beal's conjecture prior to beal distributing it.
Again, the public record indicates that you misrepresent or
misunderstand Darmon's statements. Beal distributing his
conjecture happened in "summer and fall of 1994" according
to Mauldin's (pro-Beal) letter to the AMS Notices.
Meanwhile, quoting from the transcript of Darmon's
Aisenstadt prize lecture (C.R. Math Rep Acad Sci
Canada vol 19 (1) 1997 pp. 3-14):
" In [DG], Andrew Granville and I made the following
conjecture:
GENERALIZED FERMAT CONJECTURE: If
1/p + 1/q + 1/r < 1 then [x^p + y^q = z^r] has no
non-trivial primitive solutions except the following:
[gives list of 10 known solutions including the 5 large
solutions of Beukers and Zagier].
This conjecture is really more of a "provocation" to
borrow a term from Barry Mazur. (The five larger
solutions were found by a computer search by Beukers
and Zagier, after I had conjectured that they did not
exist!) But as a measure of the stock I now place in the
conjecture, I will offer a reward of
300 ( 1/(1/p + 1/q + 1/r -1) - 1)
(Canadian) dollars for a non-trivial primitive solution
to x^p + y^q = z^r which does not appear in the
above list."
Van der Poorten's book dates Beukers' computer
searches as happening not later than November 1993,
and Darmon's stating the conjecture happened before
that (probably it was at the July 1993 conference, where
both Beukers and Zagier are also listed as speakers).
This all precedes Beal, but the most amusing part is
that Darmon in his prize lecture of March 1997 offered
prize money for the problem before Beal's Dec 1 1997
prize!
Here are some more relevant quotes, from another
authority....
"talk and bullshit are cheap. CITE A SINGLE WRITTEN
REFERENCE!!!!! -- not your memory of some old
conversation" -- andy...@my-deja.com 8/28/2000
"SO CITE A SINGLE WRITTEN REFERENCE!!!!!
No-one is interested in your memory of this or that."
--- andy...@my-deja.com, 8/28/2000
He states that he was working on generalized FLT using Frey's
method, before Beal. Frey's method is a way of proving
that no solutions exist for various equations of this type, so
it's obvious what the goal was.
> Beal never asserted that Darmon had never considered any of several
> generalized forms of FLT.
Beal is, however, equivocating with this comment on "several forms".
Darmon's work (and later on, which is to say earlier than Beal, his
joint work with Granville) was considering the exact same
equation, not "any of several generalized forms". He says so clearly
in the quote above, and in the prize lecture also quoted, and in his
1993 paper ([Da2] above) where he writes:
"this work grew out of a joint project with Andrew Granville
on the generalized Fermat equation x^p + y^q = z^r."
> Nonetheless, Darmon himself says that he was unaware that Beal's form
> has no solutions.
He proposed the problem himself in 1993, so he was
not "unaware". You either misunderstand or misrepresent
his statements, if you in fact ever talked to him.
Hull Loss Incident
> [discussing the Diophantine equation x^a + y^b = z^c]
> > As stated above, the obvious point is constructing families
> > of solutions which are NOT coprime. You choose to equivocate
> > between this homework exercise and the unsolved research problem
> > (generalized FLT) that is the coprime case.
>
> You don't seem to understand that the two are closely related.
You're mistaken.
The structure of the solutions is well understood,
and fits a common mathematical pattern. Namely,
solutions come in families generated by certain "minimal"
solutions. Writing down all the solutions in all the families
is very easy (simple formulas exist) but questions about
the minimal solutions run up against completely different
and much harder problems.
This is similar to trivial algebraic questions about ALL
numbers becoming very hard when asked about PRIME
numbers, and information about the first situation is
useless in dealing with the second.
> By looking at the properties of common factors and looking for common
> factor solutions not generated by elementary algorithms, one gains
> insight into the problem. That process is all the more interesting
> since we do not have co-prime solutions to examine.
We already have ALL of the solutions at our disposal, generated
by simple formulas. Finding solutions not covered by your private
algorithms may reveal something about those algorithms, but it
is useless for the actual problem of interest.
>The problem that Granville has is that he thinks solution sets with
> common factors are totally independent of, and unrelated to, solution
> sets without common factors.
If that is what he thinks, he is right.
> I'd love to see any inroads that Granville
> has made beyong his incorrect speculation with second powers.
His joint work with Darmon proved finiteness of primitive
solutions for x^a + y^b = z^c with a,b,c fixed. That is
major progress and it uses major tools (Faltings' theorem
formerly known as the Mordell conjecture).
> In contrast, intelligent people recognize that any solutions or results
> for a given function provide insight into the properties of results or
> solution sets for that function
So just publish your solution tables and all your other results on
the web site, so that Intelligent People can evaluate your (Beal's)
contributions. The results may be amusing.
Hull Loss Incident
sel...@my-deja.com wrote:
> > The search was a joke. A home computer over
> > a weekend could have done better, had Beal
> > understood the difference between bases and
> > exponents in this problem. (He searched
> > for x^a + y^b = z^c with a,b,c *and* x,y,z < 100.)
> >
> BEAL OBVIOUSLY UNDERSTOOD THE DIFFERENCE. HE WAS SIMPLY INTERESTED IN
> FINDING SOLUTIONS NOT PREDICTED BY HIS LOGIC ALGORITHMS (THAT DO EASILY
> FIND COMMON FACTOR SOLUTIONS).
Beal clearly does not understand the difference, because while
the search may have achieved the goal described above, he continues
to advertise it as also giving a serious test of the conjecture in the
astronomically large range "up to 99^99". In reality it went up to
10^6 plus an irrelevant tiny sample of potential large solutions.
> WHETHER IT WAS A LUCKY ACCIDENT OR A REASONED (TO WHATEVER STANDARD
> GRANVILLE BELIEVES THE TERM REQUIRES) CONCLUSION ISN'T EVEN RELEVANT.
The relevance is to whether Beal, even if he were first to state
the problem, deserves to have the problem named after himself.
In the event of a lucky guess the answer is an obvious NO.
> > > NONETHELESS, BEAL CONDUCTED THE FIRST LARGE > > COMPUTER ANALYSIS
> >
> > It is likely that Beukers and Zagier searches were done earlier.
> > They found large solutions of generalized FLT, 9 orders of
> > magnitude beyond Beal's search range. I hope somebody
> > reading this can tell us when and how they conducted their
> > searches.
> >
> BEUKERS AND ZAGIERS SEARCHES WERE INCREDIBLY SMALLER THAN BEAL'S.
Bullshit. They found solutions with numbers of about 15 digits. In
that range, Beal's search touched about one millionth (0.0001 per cent)
of the potential solutions, which is as good as not searching at all.
As covered in August, Beal's search was exhaustive up to one million
(x^a + y^b = z^c < 10^6) and basically worthless for larger numbers.
It does not even rule out 101^3 being a sum of two fourth powers.
> YES
> THEY DID LIMITED SEARCHES WITH LARGE BASES BUT THE TERM QUANTITIES THAT
> THEY WERE WORKING WITH WERE MILLIONS OF ORDERS OF MAGNITUDE SMALLER
> THAN BEAL'S SEARCHES
Do you (= Beal) understand what "orders of magnitude" even means?
Statements like the above suggest that you have no grasp on
the very basics of the problem.
> (100^100 IS FAR BEYOND THE QUANTIES THAT BEUKERS
> AND ZAGIERS DEALT WITH). BEUKERS AND ZAGIERS SEARCHES DID OFFER SOME
> ADDITIONAL INSIGHT AT THE TIME THEY WERE DONE,
They found large solutions in the 15-digit range. That gives the insight
that a computer search should go much higher than Beal's 10^6 to
give any indication about the conjecture.
sel...@my-deja.com
>
> > This is totally contradicted by Vanderpoorten's "proposal" of the
> > conjecture in 1996 on page 194 in his book.
>
> Your ravings about Van der Poorten are crackpot. He is not
> trying to steal credit for your (non) discovery, or otherwise acting
> as the Dutch-Australian wing of a worldwide Granville conspiracy
> against you.
>
> If you bother to actually read the book, Van der Poorten makes it
> clear that all his information about recent FLT-related developments
> is at second hand, that he hasn't worked in that area for many years,
> that he is reporting on work of others, etc. He goes into some detail
> about which lectures and articles he is extracting the information
from,
> and scrupulously credits pretty much everything in the book to others.
> The "proposal" you are trying to make capital of, is clearly
presented as
> based on ideas from a 1993 preprint of Darmon and Granville which,
> as he states, he hadn't yet seen at the time of writing and was merely
> quoting the results. There is no pretense of originality whatsoever,
> let alone Beal-like grandiose claims of a "significant discovery" for
> mathematics.
Typical crackpot Andrew Granville Lies and Bullshit. Vanderpoorten's
word's couldn't be clearer (notwithstanding Granvilles bullshit lies).
Better yet, no-one needs to take my word for it, anyone can look it up
themselves, it's there in black and white for the world to see on page
194 of Vanderpporten's 1996 book: "Led by this , I propose [Beal's
conjecture]"
> > > > Vanderpoorten "proposed" it himself years after Beal,
> > >
> > > Van der Poorten did not propose it "years after Beal".
> >
> > There you go lying again: anyone can look on page 194 of his book
and
> > judge for themselves.
>
> They can also look a few pages earlier, where the appendix begins,
> and read Van der Poorten's statement that it was written Christmas
1993,
> not "years after Beal" as you continue to claim after being repeatedly
> corrected on this point. The work of Darmon and Granville he refers
> to, was in circulation in 1993 before you got started on the problem.
> Darmon is also listed as speaking about it at a conference
> in July 1993, as you can confirm at the web site I referenced earlier;
> that certainly predates Beal's work.
Vanderpooretn can say he wrote it in 1942 for all anyone cares, until
he diseminated or published it, it was no more than his personal notes.
>
> > > He published on the subject in 1994 in an expository
> > > article for the Australian math society (written Christmas
> > > 1993) and the material later made its way into his 1996
> > > book. Unlike Beal, Van der Poorten has never claimed
> > > ownership of the problem or campaigned to have it named
> > > after himself.
Except that he claim's to have "proposed" it year's after Beal (see
above). The first written verifiable correspondance to anyone in the
world predates Vanderpoorten and is Beal's mid 1994 correspondence to
Edward's, Tunnell, Taft, Etc. Unlike Granville's meager words asking
someone to look for solutions, Beal clearly assert's there are no
solutions and is the first to do so in verifiable correspondence to
others.
> > >
> > Another lie: Vanderpooretn writes for all the world to see: "I
propose
> > [beal's conjecture]" it's on page 194 of his 1996 book published
years
> > after beal's widespread distribution of his conjecture.
>
> Read the book, retard. Other people have already done the homework
> for you and posted the details in this thread. You have been informed
> repeatedly in the August thread as well as now, that Van der Poorten's
> remarks were written1993 and published 1994. That is, the "Beal"
> conjecture was made public by Van der Poorten before Beal --- and
> Van der Poorten doesn't even consider it worthy of claiming credit.
>
YOU READ THE BOOK, RETARDED ANDREW GRANVILLE: Vanderpoorten's book was
first published in 1997, years after beal. Even Vanderpoorten's
first "published remarks" that he claims in late 1994 were many month's
after beal. Vanderpoorten claims to be "proposing" it in his 1997 book,
who knows what he claimed in his purported 1994 papers. These facts are
indisputable: unless your name is Andrew Granville and you care nothing
about the truth. You're the one talking about conspiracies, I'm simply
demonstrating what a lier Granville is.
> > Beal has never claimed ownership of the problem
>
> These sci.math threads prove otherwise.
>
I repeat, Beal has never claimed ownership of the problem and still
does not. The facts do seem to make him the first one to have asserted
no solutions, to have diseminated the results, and to have received
confirminmg responses from knowledgeable number theorists. Beal is
simply incensed over Granville's repeated lies and misrepresentations
suggesting beal did no more than post a prize.
> > or campaigned to have it named after himself.
>
> Beal has paid to advertise his claims to the conjecture.
> The www.bealconjecture.com web site is bought and
> paid for propaganda as was the highly irregular article
> by Mauldin in AMS Notices.
There was nothing irregular about the AMS article. The
bealconjecture.com site was only opened to defend beal against the lies
that andrew granville was spreading and to present the truth. If
anything on the site is not true, please simply write or e-mail beal or
Mauldin and it will be corrected.
>
> > He simply was the first to propose no solutions
> > to a specific form and many people have subsequently shown an
interest
> > in it. He agreed to offer a prize when Dan Mauldin wanted to write
an
> > article about it in 1997
>
> Mauldin's article in AMS Notices (Dec 1997) was highly irregular.
> Could it have something to do with Beal being the largest single
> individual donor to AMS that year (see "Acknowledgement
> of Contributions" in the1998 Notices), and a major benefactor
> of Mauldin's math department and university? Mauldin also heads
> the prize committee for the Beal award, which is curious considering
> his lack of qualification in number theory.
No, it could not, you jerk. Beal's article was published in 1997, not
1998. Beal has been an ardent supporter of math and science for years.
Now here you are, criticizing Mauldin too. Mauldin was simply kind
enough to volunteer when the AMS didn't want to administer the prize.
Mauldin is the first to concede he is not a number theorist: that
hardly makes him innapropriate to oversee and monitor the prize.
>
> It appears that Mauldin needed to placate a determined
> donor -- to bring his work to a mathematical audience -- while
> somehow shielding Beal from the indifference and outright ridicule
> his slim contribution and grandiose claims would have elicited.
> Solution: place a puff piece in a trade journal, thus publishing the
> unpublishable while granting Beal the credibility he craved.
> Mauldin was evidently at pains to "explain" this shameless PR piece,
> as witness his sheepish followup letter a few months later.
Those very words (lies) from Andrew Granville are what made the
bealconjecture.com website necessary. The beal conjecture or the
generalized fermat conjecture, whichever you prefer, is hardly
unpublishable. Beal appears to have been the first person to reason and
propose it. Henri Darmon, Ron Graham, Jarell Tunnell, Earl Taft, Harold
Edward's etc. etc. all agree that they are unaware of anyone earlier
than Beal. On the other hand you have Granville alone (with many pen
names posting many messages) stating that Beal is an egomaniac who
simply posted a prize. Granville can't even accept the printed reality
that Vanderpoorten "proposed" it himself years after beal. Granville
appears to be a misguided lunatic who motives are hard to understand.
>
> Strangely, although ostensibly written about some interesting
mathematics
> done by an amateur, Mauldin's articles carefully avoid explaining to
> an audience of mathematicians what Beal actually *did*. A
disclosure
> that the computer search was of "all terms up to 99^99", would
> have nullified Beal's claims to a discovery based on reasoned evidence
> rather than lucky accident, and Mauldin chose not to share that
tidbit.
> Also undisclosed was that Beal's results were available by request
> from Mauldin; Beal's "remarkable" contributions were too remarkable
> to see the light of day.
Beal was simply the first to propose the generalized fermat conjecture.
That is all. That is what the article is about. Beal's computer search
was the most extensive done at that time but was hardly touted as
remarkable, it wasn't even referenced. It doesn't claim "remarkable"
contributions beyond reasoning the conjecture.
>
> > > You are batting .000. It is unlikely that Granville or any other
> > > competent number theorist has ever claimed ownership of the
> > > problem. It would be hilarious to see you quote Granville's
> > > allegedly abusive correspondence here in the newsgroup, so
> > > we can see what he really did say. Until that happens, your
> > > claims about his assertions carry absolute zero credibility.
> > >
> > Wrong again; Vanderpoorten claims he "proposed" it (as detailed
> > repeatedly previously) and Granville claims his elementary
questions
> > to a class of students somehow pre-empts beal's conjecture. He has
said
> > as much in these discussion groups - go read for youself under any
one
> > of several of Granville's pen names.
>
> Granville and Van der Poorten are not participating in these
discussions
> so far. Your conspiracy theories are crackpot.
Hull Loss Incident (among others) is beleived to be Andrew Granvilles
pen name. Granville does not constitute a conspiracy, just a crackpot.
>
> > I have never received or claimed to have received "abusive
> > correspondence" from Granville.
>
> In August 2000 you stated that Granville had been "abusive and
> ill-informed" to you. It would be fun to see his comments posted
> here.
You are also unable to differentiate between "abusive correspondence"
and an abusive and ill-informed person.
Antonio Ramirez
> [...]
> Hull Loss Incident (among others) is beleived to be Andrew Granvilles
> pen name.
By no one but you. How do you explain that Hull Loss Incident's posts
come, verifiably, from a Netscape newsreader running on a Macintosh
computer at the Harvard Science Center? All of this information can be
derived from the headers. If Hull Loss Incident were posting from a
Unix machine, your claim wouuld at least pass the laugh test-- it
would be possible for him to dial in to a Harvard account. Not so
using a Mac.
On the other hand, the headers in _your_ posts are suspiciously like
those in Beal's posts of the past, as well as those from other
supporting personae. Care to address this directly?
> [...]
jim...@my-deja.com
Andrew Beal are consequently identified as beal puppets while Andrew
Granville, who posts under many pen names, can simply call ISP's in
other cities (like Boston) and cover his tracks to fool you.
In article <r4isnn9...@szego6.Stanford.EDU>,
jim...@my-deja.com
long distance to other cities and overseas to other service providers.
Computer cookies can demonstrate this most clearly. Sorry, there is no
superman required.
In article <3A4B4E5F...@y.z.com>,
Antonio Ramirez
> It is ironic that several of us who live in the same Dallas area as
> Andrew Beal are consequently identified as beal puppets while Andrew
> Granville, who posts under many pen names, can simply call ISP's in
> other cities (like Boston) and cover his tracks to fool you.
As it happens, I spent the last five years in Boston. I *know* exactly
where Hull Loss Incident is posting from, because I have *been* to the
very same building. Any dolt with a modicum of Internet knowledge can
tell that it is *not* possible for his posts to have been sent using a
remote connection to Boston: they originate from Harvard University
computer cluster machines that support no dial-up.
As to your innocence from puppetting: Even this post I'm replying to
was sent from IP address 24.4.254.206, the EXACT same IP address that
originated selivan's post from 40 minutes ago. Do you know what this
means? It means they were sent from the VERY SAME physical
computer. It is simply not credible that they were sent by different
people.
sel...@my-deja.com
of elementary ways for Granville to appear to post from other isp's and
from university LAN's. Additionally they both parrot the same
repetitious bullshit that anyone can see through. They have been
thoroughly debunked and proven unable to cite a single prior reference
that is more specific than A+B=C. Additionally, many number theory
experts agree with beal including Darmon who Granville cites as a
source. Granville can cite no-one supporting his baloney. As if that's
not enough, Vanderpoortens written words are clear and unambigous,
again totally discrediting hull loss incident (read Andrew Granville).
In article <r4ik88j...@szego6.Stanford.EDU>,
sel...@my-deja.com
post from other isp's and university LAN's. Additionally, Granville and
his alias's all parrot the same bullshit, and cannot reference a single
real prior reference beyond A+B=C.
n article <r4iofxv...@szego6.Stanford.EDU>,
sel...@my-deja.com
> for resolving it, prior to Beal! See quotation below...
>
> sel...@my-deja.com wrote:
>
> > As well as Darmon's person to person discussion
> > with Beal where Darmon said he was unaware of any
> > version of Beal's conjecture or its implications prior to Beal's
> > distribution of it.
>
> It is on record that Darmon gave conference lectures about
> his work (with Granville) on a "version of Beal's conjecture"
> in July 1993, which is prior to Beal stating or distributing
> anything about the problem. You have been told this repeatedly
> and can check it at the conference web address posted earlier.
He did not know or state beal's conjecture in the talks. Darmon himself
agrees that he was unaware of no solutions to beal's conjecture
> > >> Darmon agrees he was unaware of the conjecture prior to Beal.
> > >
> > > Darmon can speak for himself.
> >
> > Actually he did speak for himself: he declared that he was unaware
of
> > no solutions for beal's conjecture prior to beal distributing it.
>
> Again, the public record indicates that you misrepresent or
> misunderstand Darmon's statements. Beal distributing his
> conjecture happened in "summer and fall of 1994" according
> to Mauldin's (pro-Beal) letter to the AMS Notices.
> Meanwhile, quoting from the transcript of Darmon's
> Aisenstadt prize lecture (C.R. Math Rep Acad Sci
> Canada vol 19 (1) 1997 pp. 3-14):
>
> " In [DG], Andrew Granville and I made the following
> conjecture:
> GENERALIZED FERMAT CONJECTURE: If
> 1/p + 1/q + 1/r < 1 then [x^p + y^q = z^r] has no
> non-trivial primitive solutions except the following:
> [gives list of 10 known solutions including the 5 large
> solutions of Beukers and Zagier].
This is not beal's conjecture and Darmon himself agrees he was unaware
of no solutions for beal's form. Darmon say's he was simply trying to
find additional solutions, not asserting that none existed.
>
> This conjecture is really more of a "provocation" to
> borrow a term from Barry Mazur. (The five larger
> solutions were found by a computer search by Beukers
> and Zagier, after I had conjectured that they did not
> exist!) But as a measure of the stock I now place in the
> conjecture, I will offer a reward of
> 300 ( 1/(1/p + 1/q + 1/r -1) - 1)
> (Canadian) dollars for a non-trivial primitive solution
> to x^p + y^q = z^r which does not appear in the
> above list."
>
There probably exist larger 2nd power solutions which will prove the
assertion wrong. In any event this expanded 1997 assertion by Darmon is
well after beal's 1994 correct assertion. Darmon and Granville's 1994
speculation that only 5 solutions existed to their conjecture was
subsequently proven incorrect.
> Van der Poorten's book dates Beukers' computer
> searches as happening not later than November 1993,
> and Darmon's stating the conjecture happened before
> that (probably it was at the July 1993 conference, where
> both Beukers and Zagier are also listed as speakers).
> This all precedes Beal, but the most amusing part is
> that Darmon in his prize lecture of March 1997 offered
> prize money for the problem before Beal's Dec 1 1997
> prize!
Darmon and Granville's 1993 conjecture of five 2nd power solutions was
subsequently proven incorrect. Beal and Darmon and Granville were not
even aware of each others work during 93. Darmon and Granville
speculated and derived an incorrect conjecture. Beal, independently,
and unaware of Darmon's and Granville's work, derived a conjecture that
has withstood the test of time (so far). After Beal's widespread
disemination of his conjecture in 1994, Darmon and Grandville
subsequently ammended their conjecture to include 10 known solutions.
Beal already knew of some of the larger 2nd power solutions that
disproved Darmon and Granville's conjecture in 1993 at the time he was
formulating his own correct (so far) conjecture.
>
> Here are some more relevant quotes, from another
> authority....
>
> "talk and bullshit are cheap. CITE A SINGLE WRITTEN
> REFERENCE!!!!! -- not your memory of some old
> conversation" -- andy...@my-deja.com 8/28/2000
>
> "SO CITE A SINGLE WRITTEN REFERENCE!!!!!
> No-one is interested in your memory of this or that."
> --- andy...@my-deja.com, 8/28/2000
>
YES-- WE"RE STILL WAITING
----WE'RE STILL WAITING
-- WE'RE STILL WAITING
HELLO???? There is no disagreement here - Many people were working on
various version's of FLT. Beal simply made the correct conjecture
first. Darmon and Granville were certaintly looking at variations of
FLT in 1993 (and previuosly and subsequently). Their work led them to
an erronious conjecture that was subsequently proven incorrect.
>
> > Beal never asserted that Darmon had never considered any of several
> > generalized forms of FLT.
>
> Beal is, however, equivocating with this comment on "several forms".
>
> Darmon's work (and later on, which is to say earlier than Beal, his
> joint work with Granville) was considering the exact same
> equation, not "any of several generalized forms". He says so clearly
> in the quote above, and in the prize lecture also quoted, and in his
> 1993 paper ([Da2] above) where he writes:
>
> "this work grew out of a joint project with Andrew Granville
> on the generalized Fermat equation x^p + y^q = z^r."
WRONG AGAIN. Darmon and Granvilles limited work on this form led them
to the wrong assertion, that only five solutions existed, which was
subsequently proven incorrect by extremely limited efforts.
>
> > Nonetheless, Darmon himself says that he was unaware that Beal's
form
> > has no solutions.
>
> He proposed the problem himself in 1993, so he was
> not "unaware". You either misunderstand or misrepresent
> his statements, if you in fact ever talked to him.
WRONG AGAIN - see above. Darmon himself does not disagree with this -
How can you???
sel...@my-deja.com
By claiming to "propose" it, rather than refering to another source, it
is reasonable to conclude that Vanderpoorten thought the conjecture new
and interesting and original. My primary reason for citing
Vanderpoorten was to demonstrate that it was unknown and not "common
knowledge, contrary to Andrew Granville's dramatic assertions.
Additionally, when beal or Vanderpooretn derived the conjecture is not
as important as when they diseminated it. Beal wrote widely in 1994 and
received written confirmations from well regarded number theorists that
it was regarded as unknown, unique, and "remarkable". Vanderpoorten's
first confirmable date is the books publication in 1997. Incidentally,
Beal was first even without regard to disemination. Beal's computer
work was done in August and September of 1993 as was his reasoning of
the conjecture.
EXACTELY!!! and from all this work he thought he was "proposing" a new
conjecture, ie: not previously proposed.
> I think a reasonable person can be of two minds about
> this "priority," granted that for sake of argument it
> would be worth squabbling over. The charitable view is
> that in 1993 both Beal and van der Poorten independently
> made the Generalized Fermat Conjecture.
>
> The less charitable view would be to recognize for the
> purpose of priority only publication, as if this were an
> proof-like priority! This, at least as regards Alf's
> side of things, would seem to be selivan's approach, but
> in ascribing to Alf the 1996 date for the book copyright,
> selivan overlooks the Dec. 1994 date of the precedent
> paper in Aus. Math. Soc. Gaz. 21. Against this I would
> only have the Dec. 1997 publication in Notices of the AMS
> an article by Dan Mauldin describing Beal's conjecture
> and prize money. [Ironically that article acknowledges
> the assistance of Granville in its preparation.]
>
This process totally disregards beal's written correspondence to 30 or
40 experts and periodicals in june of 1994 with written responses from
Harold Edward's, Jarell Tunnell, Earl Taft, and others. Beal and
Mauldin have originals or copies of all these responses which are
verifieable and unanimously agree that the conjecture is unknown. Short
of Beal publishing his own book, what else was he supposed to do?
Nonetheless, I don't think Beal particulary cares about priority as
much as simply discrediting Andrew Granvilles slanderous remarks that
all Beal did was offer a prize for a well known conjecture. Beal did a
lot of work on this problem and discovered other interesting things
about it. He can hardly believe Andrew Granville's malicious and
unfounded attacks. No-one has yet cited a single prior reference to the
conjecture.
Hull Loss Incident
> > What I don't fully buy is selivan's idea that van der
> > Poorten, by stating his conjecture, is also "claiming
> > priority" for it.
>
> By claiming to "propose" it, rather than refering to another source, it
> is reasonable to conclude that Vanderpoorten thought the conjecture new
> and interesting and original.
Ridiculous. First, as he states, Van der Poorten's article was written
for publication in a newspaper(!), so there is no pretense of making
any contribution to mathematical research. If he were stating a new
conjecture he could have publicized it immediately on a number
theory e-mail list read by professionals, rather than waiting a year for
publication.
Second, if you read the passage, you will see that Van der Poorten
is not saying anything other than that:
(a) Darmon and Granville's work suggests the 1/a + 1/b + 1/c < 1
generalization of FLT;
(b) but some solutions of this are known when exponent 2 is allowed
(he lists one);
(c) all exponents > 2 still covers FLT but has no known solutions,
so this gives a nice, simply stated generalization of FLT.
These observations are so trivial that no competent number theorist
would claim them as a new conjecture. At best they would be treated
as a minor repackaging of ideas already developed by Darmon and
Granville. Likewise, no professional would treat 1/a + 1/b + 1/c < 1
as being essentially different from the (less natural, ad hoc) Beal version
with a,b,c > 2, to the point that it should be considered a separate
problem.
> My primary reason for citing
> Vanderpoorten was to demonstrate that it was unknown and not "common
> knowledge, contrary to Andrew Granville's dramatic assertions.
You have been equivocating between what I (and others) have
and have not described as common knowledge.
The equation X^a + Y^b = Z^c was common knowledge,
and people published on it well before the 1990's.
It was also common knowledge how to find solutions
in the non-coprime case, and this was material for high school
math competitions, math journal problem sections, recreational
mathematics journals, and the like. Within the number theory
community, it was common knowledge that the ABC conjecture
is highly relevant, and that probabilistic "density" arguments
indicate primitive solutions are rare.
Meanwhile, the generalized Fermat equation was not
a major research topic until Wiles made it seem more approachable,
and until Darmon, Granville et al linked it to interesting mathematics.
Nobody would have bothered to publish grandiose conjectures
for their own sake when FLT and the Catalan conjecture remained
open as very special cases. So there is no surprise that people
Beal wrote to, hadn't heard of the problem, or his specific version.
This doesn't contradict the fact that the problem has been around
for a LONG time, it was just dormant until the mid-90's.
> Additionally, when beal or Vanderpooretn derived the conjecture is not
> as important as when they diseminated it.
If dissemination is the standard, Beal unambiguously loses.
Beukers' computer searches were triggered by Darmon
stating a conjecture on generalized FLT (including Beal's problem),
and Van der Poorten's book dates the searches as
happening no later than November 1993. Beal's
correspondence with mathematicians started later, in 1994.
This is all in addition to Tijdeman publishing essentially
the same problem in1989; Granville posing it at
a 1992 number theory conference (problem list circulated 1993);
Darmon speaking in July1993 on generalized FLT (this may
have been where the conjecture was stated triggering Beukers
and Zagier searches); and Darmon and Granville's work, which
explicitly states the "Beal" conjecture, circulating in 1993 (as
recorded in Van der Poorten's book), available as as a UGA
preprint in 1994, and submitted to a journal in 1994.
> Beal wrote widely in 1994 and received written confirmations from well
> regarded number theorists that
> it was regarded as unknown, unique, and "remarkable".
Beal thoroughly misrepresents his correspondence, which does
not support such priority claims.
People writing to Beal saying they hadn't personally seen that
exact conjecture, is not too surprising. It does not, however, rise
to the level of a confirmation that the work is "unknown" or
"unique". For that one would need to search the literature, and it is
*extremely* unlikely that any of those well regarded number
theorists would characterize Beal's work as "unknown" or
"unique" if also shown the prior work and publications
of Tijdeman, Granville etc discussed in these threads.
> Vanderpoorten's first confirmable date is the books publication in 1997.
1994 is on the record, verifiable, and at this point, you are well
past the crackpot stage in trying to gainsay it.
Van der Poorten's article that you have been blithering about, is
REPRINTED as Appendix A of his 1997 book. It was ORIGINALLY
published in 1994, in the Australian Mathematical Society Gazette,
21, no. 5, pp. 150-159. The reprint is a DUPLICATE of the original,
including the margination and including the explicit statement of
the "Beal" conjecture. This is all stated in the footnote to Appendix A
in the book, and Chip Eastham has done the homework for you by
posting it in this thread, and I have also brought these facts to your
attention in both this discussion and its August 2000 predecessor.
sel...@my-deja.com
>
> > > What I don't fully buy is selivan's idea that van der
> > > Poorten, by stating his conjecture, is also "claiming
> > > priority" for it.
> >
> > By claiming to "propose" it, rather than refering to another
source, it
> > is reasonable to conclude that Vanderpoorten thought the conjecture
new
> > and interesting and original.
>
> Ridiculous. First, as he states, Van der Poorten's article was
written
> for publication in a newspaper(!), so there is no pretense of making
> any contribution to mathematical research.
ABSURD - Vanderpoorten clearly says he is "proposing" the conjecture,
and even discusses what "led" him to propose it. You deny that and say
he is "proposing" nothing. Perhaps Vanderpoorten doesn't understand the
english language. Everyone should read page 194 for themselves. This is
typical Andrew Granville. Deny the truth and obvious long enough and
maybe people will begin to believe you.
What can anyone possibly say: You are so ignorant that a clear and
unambigous sentence supporting Beal's assertions is simply
reconstructed by you to fit your lies. What's the point of even
corresponding with you.
If he were stating a new
> conjecture he could have publicized it immediately on a number
> theory e-mail list read by professionals, rather than waiting a year
for
> publication.
>
> Second, if you read the passage, you will see that Van der Poorten
> is not saying anything other than that:
> (a) Darmon and Granville's work suggests the 1/a + 1/b + 1/c < 1
> generalization of FLT;
> (b) but some solutions of this are known when exponent 2 is allowed
> (he lists one);
> (c) all exponents > 2 still covers FLT but has no known solutions,
> so this gives a nice, simply stated generalization of FLT.
>
You cannot tell a lie long enough that it becomes true. Vanderpoorten
is clearly proposing beal's conjecture years after beal's widespread
disemination of it.
> These observations are so trivial that no competent number theorist
> would claim them as a new conjecture. At best they would be treated
> as a minor repackaging of ideas already developed by Darmon and
> Granville. Likewise, no professional would treat 1/a + 1/b + 1/c
< 1
> as being essentially different from the (less natural, ad hoc) Beal
version
>
> with a,b,c > 2, to the point that it should be considered a separate
> problem.
Granville is the only one that thinks so. Darmon himself disagrees and
concedes he never reasoned no solutions for beal's conjecture. You are
again confusing the asking of a high school question (granville's work)
with the first apparently correct (so far) reasoned answer to the
question (beal's work). Many people asked the question, beal was simply
the first to correctly reason an answer: you confuse these two
processes. Granville's rank speculation of an answer (being five second
power solutions) was subsequently proven incorrect.
>
> > My primary reason for citing
> > Vanderpoorten was to demonstrate that it was unknown and not "common
> > knowledge, contrary to Andrew Granville's dramatic assertions.
>
> You have been equivocating between what I (and others) have
> and have not described as common knowledge.
WRONG AGAIN - YOU have been equivocating throughout YOUR posts. YOU
ignorantly suppose that anyone asking a high school question
(Granvilles question) inherently presupposed the correct answer (beal's
conjecture). This is the crux of the problem here. You continously cite
references to people asking about a generalized FLT and confuse the
asking of the question (ala Granville, Tidjeman, Brun, etc.) with a
reasoned correct response (beal's work). You cannot cite a single prior
reference to beal's conjecture that is confirmable, YOU HAVE BEEN
REPEATEDLY ASKED TO DO SO - AND YOU ALWAYS RESPOND WITH LIES ABOUT WHAT
VANDERPOORTEN WROTE OR evidence that Granville once asked his class of
students to look for solutions or Tidjeman asked a group to look for
solutions,etc. etc. etc.
WHY DON"T YOU PUT UP OR SHUT UP - As Beal likes to say "talk and
bullshit are cheap"
> The equation X^a + Y^b = Z^c was common knowledge,
> and people published on it well before the 1990's.
> It was also common knowledge how to find solutions
> in the non-coprime case, and this was material for high school
> math competitions, math journal problem sections, recreational
> mathematics journals, and the like.
NO DOUBT ABOUT IT - NO DISAGREEMENT HERE - YOU SIMPLY CONFUSE THIS HIGH
SCHOOL QUESTION WITH THE ANSWER TO IT.
Within the number theory
> community, it was common knowledge that the ABC conjecture
> is highly relevant, and that probabilistic "density" arguments
> indicate primitive solutions are rare.
>
> Meanwhile, the generalized Fermat equation was not
> a major research topic until Wiles made it seem more approachable,
> and until Darmon, Granville et al linked it to interesting
mathematics.
> Nobody would have bothered to publish grandiose conjectures
> for their own sake when FLT and the Catalan conjecture remained
> open as very special cases. So there is no surprise that people
> Beal wrote to, hadn't heard of the problem, or his specific version.
> This doesn't contradict the fact that the problem has been around
> for a LONG time, it was just dormant until the mid-90's.
NO DOUBT ABOUT IT - NO DISAGREEMENT HERE - YOU SIMPLY AGAIN EQUIVOCATE
AND CONFUSE THE QUESTION AND THE EQUATION (GRANVILLES WORK) WITH A
REASONED ANSWER TO IT (BEAL'S WORK)
>
> > Additionally, when beal or Vanderpooretn derived the conjecture is
not
> > as important as when they diseminated it.
>
> If dissemination is the standard, Beal unambiguously loses.
> Beukers' computer searches were triggered by Darmon
> stating a conjecture on generalized FLT (including Beal's problem),
> and Van der Poorten's book dates the searches as
> happening no later than November 1993. Beal's
> correspondence with mathematicians started later, in 1994.
>
WRONG AGAIN - YOU AGAIN CONFUSE ASKING THE QUESTION (ALA GRANVILLE,
BEUKER, ETC) WITH AN ANSWER TO THE QUESTION (BEAL IN 1993 AND 1994 AND
SUBSEQUENTLY VANDERPOORTEN IN 1996 AND 1997)
> This is all in addition to Tijdeman publishing essentially
> the same problem in1989; Granville posing it at
> a 1992 number theory conference (problem list circulated 1993);
> Darmon speaking in July1993 on generalized FLT (this may
> have been where the conjecture was stated triggering Beukers
> and Zagier searches); and Darmon and Granville's work, which
> explicitly states the "Beal" conjecture, circulating in 1993 (as
> recorded in Van der Poorten's book), available as as a UGA
> preprint in 1994, and submitted to a journal in 1994.
WRONG AGAIN - YOU AGAIN CONFUSE ASKING THE QUESTION (GRANVILLE,
TIDJEMAN, DARMON, BEUKER, ZAGIER, ETC. ETC.) WITH THE CORRECT ANSWER(
BEAL'S CONJECTURE). In this particular paragraph you additionally
confuse the correct answer(Beal's work) with an incorrect answer
(Darmon and Granville's incorrect assertion that five second powers
were the only solutions)
> > Beal wrote widely in 1994 and received written confirmations from
well
> > regarded number theorists that
> > it was regarded as unknown, unique, and "remarkable".
>
> Beal thoroughly misrepresents his correspondence, which does
> not support such priority claims.
>
HERE YOU GO AGAIN : HOPEING THAT IF YOU SAY A LIE LONG ENOUGH IT WILL
BECOME TRUE.
> People writing to Beal saying they hadn't personally seen that
> exact conjecture, is not too surprising. It does not, however, rise
> to the level of a confirmation that the work is "unknown" or
> "unique". For that one would need to search the literature, and it is
> *extremely* unlikely that any of those well regarded number
> theorists would characterize Beal's work as "unknown" or
> "unique" if also shown the prior work and publications
> of Tijdeman, Granville etc discussed in these threads.
MISREPRESENTATIONS AGAIN -- Earlier you deny hat Beal received such
responses - Now you say that you are not surprised by them. Everyone is
aware that many, many, many people asked the questions, and that
Granville speculated on an answer subsequently proven wrong, and that
Beal was the first to reason the correct answer.
>
> > Vanderpoorten's first confirmable date is the books publication in
1997.
>
> 1994 is on the record, verifiable, and at this point, you are well
> past the crackpot stage in trying to gainsay it.
Yes, June of 1994 is on the record as Beal's widespread disrtibution of
an answer to the question (please differentiate here between the
question and the answer, I know that is hard for you) and December 0f
1994 is suggested as Vanderpoorten's first confirmable reference date.
>
> Van der Poorten's article that you have been blithering about, is
> REPRINTED as Appendix A of his 1997 book. It was ORIGINALLY
> published in 1994, in the Australian Mathematical Society Gazette,
> 21, no. 5, pp. 150-159. The reprint is a DUPLICATE of the original,
> including the margination and including the explicit statement of
> the "Beal" conjecture. This is all stated in the footnote to Appendix
A
> in the book, and Chip Eastham has done the homework for you by
> posting it in this thread, and I have also brought these facts to your
> attention in both this discussion and its August 2000 predecessor.
AND THERE IS NO DISAGREEMENT ABOUT IT!!!! BEAL ANNOUNCED WIDELY IN JUNE
OF 1994 AND VANDERPOORTEN (who you say didn't even "propose" it anyway -
- see above) first announced in Dec. 1994 (probably as a result of
beal's announcements of the answer.)
Boaz Ben-David
Hull Loss Incident <x...@y.z.com> wrote in message
news:3A4B833B...@y.z.com...
> It seems others not only made the conjecture, but offered money
> for resolving it, prior to Beal! See quotation below...
>
> sel...@my-deja.com wrote:
>> > >
> > > [Da2] Darmon, Henri. The equations x^n+y^n=z 2 and x^n+y^n=z^3.
> > > Internat. Math. Res. Notices 1993, no. 10, 263--274. "
Hi,
I am interested in x^n + y^n = z^2
Much more interested in x^2 + y^n = z^(2n)
for odd n >=3
Any guid, reference, direct mail, is very welcom
Boaz
Hull Loss Incident
> > It is on record that Darmon gave conference lectures about
> > his work (with Granville) [...] in July 1993,
> He did not know or state beal's conjecture in the talks.
If he stated some form of the 1/a + 1/b + 1/c < 1 problem below,
that includes Beal's conjecture, and predates it.
> Darmon himself agrees that he was unaware of no solutions to beal's
> conjecture.
We can rely on his published, verifiable statements rather than Beal's
selective memories. In his Aisenstadt Prize lecture quoted below,
Darmon mentions a specific conjecture subsuming Beal's, and states
that he made it prior to Beukers and Zagier computer searches (= 1993).
"CITE A SINGLE WRITTEN REFERENCE!!!!! -- not your memory
of some old conversation." (andy...@my-deja.com, Aug 28 2000).
> > Meanwhile, quoting from the transcript of Darmon's
> > Aisenstadt prize lecture (C.R. Math Rep Acad Sci
> > Canada vol 19 (1) 1997 pp. 3-14):
> >
> > " In [DG], Andrew Granville and I made the following
> > conjecture:
> > GENERALIZED FERMAT CONJECTURE: If
> > 1/p + 1/q + 1/r < 1 then [x^p + y^q = z^r] has no
> > non-trivial primitive solutions except the following:
> > [gives list of 10 known solutions including the 5 large
> > solutions of Beukers and Zagier].
>
> This is not beal's conjecture
It obviously includes Beal's conjecture. You are invited
to ask any of your 30-40 number theorist correspondents
whether there is any relevant difference (for purposes of
assessing priority, uniqueness, and novelty) between your
conjecture and generalized FLT as stated above.
> and Darmon himself agrees he was unaware
> of no solutions for beal's form. Darmon say's he was simply trying to
> find additional solutions, not asserting that none existed.
Darmon, speaking for himself and on public record, states the
opposite: "I had conjectured that they [larger solutions] did not
exist". This subsumes and predates the Beal problem
> > This conjecture is really more of a "provocation" to
> > borrow a term from Barry Mazur. (The five larger
> > solutions were found by a computer search by Beukers
> > and Zagier, after I had conjectured that they did not
> > exist!) But as a measure of the stock I now place in the
> > conjecture, I will offer a reward of
> > 300 ( 1/(1/p + 1/q + 1/r -1) - 1)
> > (Canadian) dollars for a non-trivial primitive solution
> > to x^p + y^q = z^r which does not appear in the
> > above list."
> >
> There probably exist larger 2nd power solutions which will prove the
> assertion wrong.
That's a remarkable suggestion. Please explain why 2nd power
solutions are likely but not 3rd,4th,... solutions that would also
prove Beal's assertion incorrect.
> In any event this expanded 1997 assertion by Darmon is
> well after beal's 1994 correct assertion. Darmon and Granville's 1994
> speculation that only 5 solutions existed to their conjecture was
> subsequently proven incorrect.
So what? Correct or not it nullifies Beal's priority claims.
> > Van der Poorten's book dates Beukers' computer
> > searches as happening not later than November 1993,
> > and Darmon's stating the conjecture happened before
> > that (probably it was at the July 1993 conference, where
> > both Beukers and Zagier are also listed as speakers).
> > This all precedes Beal, but the most amusing part is
> > that Darmon in his prize lecture of March 1997 offered
> > prize money for the problem before Beal's Dec 1 1997
> > prize!
>
> Darmon and Granville's 1993 conjecture of five 2nd power solutions was
> subsequently proven incorrect.
First, this is irrelevant. That they publicized a problem in 1993,
subsuming Beal's conjecture, nullifies Beal's claims of a "unique,
unknown and original" discovery. (Others had publicized such
problems earlier, including Tijdeman 1988 and Granville 1992,
and we are discussing Darmon and Granville's problem simply
because their version explicitly states "no solutions" in cases
covering Beal's variant of the problem.)
Second, Darmon and Granville's statement is robust, because it
is supported by a lot of theoretical evidence. Finding a few more
solutions won't change that, the conjecture would just be amended
slightly. It would take more than a few solutions to challenge the
ideas their conjecture is built upon. Beal's version was derived
from computer searches and some half-baked reasoning by someone
who does not appear to fully understand exponentiation in arithmetic --
a lucky guess.
Third, you seem to think that a conjecture is cancelled or withdrawn
from circulation when a counterexample is found. It isn't, especially
when it comes to matters of assessing priority. If the idea was out
there before Beal, that kills his priority claims regardless of other
details.
> Beal and Darmon and Granville were not
> even aware of each others work during 93. Darmon and Granville
> speculated and derived an incorrect conjecture. Beal, independently,
> and unaware of Darmon's and Granville's work, derived a conjecture that
> has withstood the test of time (so far).
Counterexamples are not what determines whether a conjecture has
value or "stands the test of time". There is a $1000000 prize offered
for the Hodge conjecture, which has stood the test of time although
proved FALSE by Grothendieck sometime after Hodge posed it.
The ideas behind the conjecture were important, and after amending
it to take account of Grothendieck's work, the conjecture survived
as one of the major open problems in mathematics.
Beal's conjecture is not based on any significant ideas, so if a
counterexample is found, his "contribution" withers and dies.
Darmon and Granville's version with its more natural condition
1/a + 1/b + 1/c < 1, *is* linked to important mathematics,
and is not particularly threatened if other solutions are found.
> After Beal's widespread
> disemination of his conjecture in 1994, Darmon and Grandville
> subsequently ammended their conjecture to include 10 known solutions..
Their paper was available as a UGA preprint not later than March 1994,
before Beal's correspondence. Whether they listed 3 or 5 or 10
solutions is irrelevant.
> Beal already knew of some of the larger 2nd power solutions that
> disproved Darmon and Granville's conjecture in 1993 at the time he was
> formulating his own correct (so far) conjecture.
Please state how and when Beal knew this.
Hull Loss Incident
> > > > What I don't fully buy is selivan's idea that van der
> > > > Poorten, by stating his conjecture, is also "claiming
> > > > priority" for it.
> > >
> > > By claiming to "propose" it, rather than refering to another
> > > source, it
> > > is reasonable to conclude that Vanderpoorten thought the conjecture
> > > new and interesting and original.
> >
> > Ridiculous. First, as he states, Van der Poorten's article was written
> > for publication in a newspaper(!), so there is no pretense of making
> > any contribution to mathematical research.
>
> ABSURD - Vanderpoorten clearly says he is "proposing" the conjecture,
> and even discusses what "led" him to propose it.
As I posted back in August, the original 1994 publication of the article did
not involve the word "propose", so you are raving about nullities once
again.
Here it is, reposted below. Notice how Van der Poorten does not try
and take credit for anything, does not promote his name in connection
with any conjecture, and does not present his remark as anything but
a trivial comment on work done by others. Beal is certifiably crackpot
raving about this nonsense. Anyway, here is the quotation, from
Australian Math Society Gazette 21 no 5 (Dec 1994) pp. 150-159:
"Darmon and Granville (1993) suggest Fermat might have
chosen a different generalization. Say, that a^t + b^u = c^v
^^^^^^^
has no solution in integers greater than 1 if all of t,u,v are at
least 3. If one exponent is allowed to be 2, things are
different. For example, in the cases (t,u,v) = (3,3,2) and (4,3,2)
there are infinitely many solutions. In general, if 1/t+1/u+1/v < 1
we have grounds for believing that there are just finitely many
solutions for which a and b have no common factor. The
largest known is 43^8 + 96222^3 + 30042907^2.
All nine solutions known have one or other of the exponents
equal to 2."
> You cannot tell a lie long enough that it becomes true. Vanderpoorten
> is clearly proposing beal's conjecture years after beal's widespread
> disemination of it.
You have been corrected so often about this "years after" business,
that it is pure crackpottery to keep reposting it. He first published
the generalized Fermat conjecture in December 1994, not 1997.
sel...@my-deja.com
>
> > > > > What I don't fully buy is selivan's idea that van der
> > > > > Poorten, by stating his conjecture, is also "claiming
> > > > > priority" for it.
> > > >
> > > > By claiming to "propose" it, rather than refering to another
> > > > source, it
> > > > is reasonable to conclude that Vanderpoorten thought the
conjecture
> > > > new and interesting and original.
> > >
> > > Ridiculous. First, as he states, Van der Poorten's article was
written
> > > for publication in a newspaper(!), so there is no pretense of
making
> > > any contribution to mathematical research.
> >
> > ABSURD - Vanderpoorten clearly says he is "proposing" the
conjecture,
> > and even discusses what "led" him to propose it.
>
> As I posted back in August, the original 1994 publication of the
article did not involve the word "propose", so you are raving about
nullities once
> again.
Who cares what his 1994 paper says, (coming six months after beal's
widespread disemination of the conjecture), I am refering to his 1996
book wherein he says "led by this, I propose". Can you you get that
through your thick skull?????? Beal originated the conjecture in 1993,
wrote widely about it in june 1994, received knowledgeable responses
from number theorists in June and July 1994, confirming it was unknown
and "remarkable". Whatever Vanderpoorten did or didn't write in
December 1994 is meaningless. Even from your text below, one could
easily conclude that Vanderpoorten mistakenly thought he was
originating the conjecture, but that doesn't even matter. His 1996 book
clearly says he is "proposing" beal's conjecture. HOW MANY TIMES DO I
NEED TO SAY THIS?? Why don't you tell us all again about how you,
Andrew Granville, asked a class of students to look for solutions. Are
you so ignorant that you cannot understand simple sentences, or is it
the English language that you have a hard time with?????????
> Anyway, here is the quotation, from
> Australian Math Society Gazette 21 no 5 (Dec 1994) pp. 150-159:
>
> "Darmon and Granville (1993) suggest Fermat might have
> chosen a different generalization. Say, that a^t + b^u = c^v
> ^^^^^^^
> has no solution in integers greater than 1 if all of t,u,v are at
> least 3. If one exponent is allowed to be 2, things are
> different. For example, in the cases (t,u,v) = (3,3,2) and
(4,3,2)
> there are infinitely many solutions. In general, if
1/t+1/u+1/v < 1
> we have grounds for believing that there are just finitely many
> solutions for which a and b have no common factor. The
> largest known is 43^8 + 96222^3 + 30042907^2.
> All nine solutions known have one or other of the exponents
> equal to 2."
>
> > You cannot tell a lie long enough that it becomes true.
> > Vanderpoorten is clearly proposing beal's conjecture years after
beal's widespread
> > disemination of it.
>
> You have been corrected so often about this "years after" business,
> that it is pure crackpottery to keep reposting it. He first published
> the generalized Fermat conjecture in December 1994, not 1997.
NO - You have continued to lie about the truth, or perhaps you simply
can't subtract large integers. Let me repeat for you for about the
100th time: Vanderpoorten's first clear claim to have "proposed" Beal's
conjecture was his 1996 book published in 1997. This is 2 or 3 years
afters Beal's widespread disemination of the conjecture in 1994. What
part of this do you not understand??? Is the diffenence between 1994
and either 1996 or 1997 not "years". Do you understand what the english
word "years" means?? Do you understand the concept of "plurality". Can
I refer you to a remedial reading and writing program, Andrew
Granville??
sel...@my-deja.com
>
> > > It is on record that Darmon gave conference lectures about
> > > his work (with Granville) [...] in July 1993,
> > He did not know or state beal's conjecture in the talks.
>
> If he stated some form of the 1/a + 1/b + 1/c < 1 problem below,
> that includes Beal's conjecture, and predates it.
WRONG - He made a broader conjecture that was subsequently proven wrong.
He speculated that five second power solutions were the only ones for a
broader version of beal's conjecture. A simple computer search turned
up more solutions.
>
> > Darmon himself agrees that he was unaware of no solutions to beal's
> > conjecture.
>
> We can rely on his published, verifiable statements rather than Beal's
> selective memories. In his Aisenstadt Prize lecture quoted below,
> Darmon mentions a specific conjecture subsuming Beal's, and states
> that he made it prior to Beukers and Zagier computer searches (=
1993).
>
Yes, and it was subsequently proven incorrect.
> "CITE A SINGLE WRITTEN REFERENCE!!!!! -- not your memory
> of some old conversation." (andy...@my-deja.com, Aug 28 2000).
We're still waiting for a single reference prior to beal
still waiting--
still waiting ---
>
> > > Meanwhile, quoting from the transcript of Darmon's
> > > Aisenstadt prize lecture (C.R. Math Rep Acad Sci
> > > Canada vol 19 (1) 1997 pp. 3-14):
> > >
> > > " In [DG], Andrew Granville and I made the following
> > > conjecture:
> > > GENERALIZED FERMAT CONJECTURE: If
> > > 1/p + 1/q + 1/r < 1 then [x^p + y^q = z^r] has no
> > > non-trivial primitive solutions except the following:
> > > [gives list of 10 known solutions including the 5 large
> > > solutions of Beukers and Zagier].
> >
> > This is not beal's conjecture
>
> It obviously includes Beal's conjecture. You are invited
> to ask any of your 30-40 number theorist correspondents
> whether there is any relevant difference (for purposes of
> assessing priority, uniqueness, and novelty) between your
> conjecture and generalized FLT as stated above.
There are a number of important differences - first, it is probably
incorrect and more second power solutions will be found by a simple
computer search. Secondly, it came after beal's conjecture anyway. You
are correct that a broad incorrect conjecture can include a more
refined correct conjecture, but what is your point??? The only
conjecture (Incorrect, incidentally) that MAY have preceded beal was
the rank assertion by Granville that there were only five second power
solutions to a broader form.
>
> > and Darmon himself agrees he was unaware
> > of no solutions for beal's form. Darmon say's he was simply trying
to
> > find additional solutions, not asserting that none existed.
>
> Darmon, speaking for himself and on public record, states the
> opposite: "I had conjectured that they [larger solutions] did not
> exist". This subsumes and predates the Beal problem
>
This was said in the context of an incorrect conjecture where he was
subsequently proven incorrect (ie: larger solutions were found). It
does not subsume beal's conjecture and the date of the incorrect
assertion is unclear, not that it even matters anyway.
> > > This conjecture is really more of a "provocation" to
> > > borrow a term from Barry Mazur. (The five larger
> > > solutions were found by a computer search by Beukers
> > > and Zagier, after I had conjectured that they did not
> > > exist!) But as a measure of the stock I now place in the
> > > conjecture, I will offer a reward of
> > > 300 ( 1/(1/p + 1/q + 1/r -1) - 1)
> > > (Canadian) dollars for a non-trivial primitive solution
> > > to x^p + y^q = z^r which does not appear in the
> > > above list."
> > >
> > There probably exist larger 2nd power solutions which will prove the
> > assertion wrong.
>
> That's a remarkable suggestion. Please explain why 2nd power
> solutions are likely but not 3rd,4th,... solutions that would also
> prove Beal's assertion incorrect.
>
For the exact reasons that 10 second power solutions already exist but
no higher power solutions exist. Squares have many different properties
not shared by higher powers. I would explain this to you further but I
am not sure that you are capable of understanding these simple concepts
given your ignorant statements to date.
> > In any event this expanded 1997 assertion by Darmon is
> > well after beal's 1994 correct assertion. Darmon and Granville's
1994
> > speculation that only 5 solutions existed to their conjecture was
> > subsequently proven incorrect.
>
> So what? Correct or not it nullifies Beal's priority claims.
>
WRONG AGAIN -- An incorrect broad rank assertion easily proven
incorrect does not affect a more refined correct conjecture. Unless of
course you are Andrew Granville, in which case truth doesn't matter and
all forms of distortion become the truth.
> > > Van der Poorten's book dates Beukers' computer
> > > searches as happening not later than November 1993,
> > > and Darmon's stating the conjecture happened before
> > > that (probably it was at the July 1993 conference, where
> > > both Beukers and Zagier are also listed as speakers).
> > > This all precedes Beal, but the most amusing part is
> > > that Darmon in his prize lecture of March 1997 offered
> > > prize money for the problem before Beal's Dec 1 1997
> > > prize!
> >
> > Darmon and Granville's 1993 conjecture of five 2nd power solutions
was
> > subsequently proven incorrect.
>
> First, this is irrelevant. That they publicized a problem in 1993,
> subsuming Beal's conjecture, nullifies Beal's claims of a "unique,
> unknown and original" discovery. (Others had publicized such
> problems earlier, including Tijdeman 1988 and Granville 1992,
> and we are discussing Darmon and Granville's problem simply
> because their version explicitly states "no solutions" in cases
> covering Beal's variant of the problem.)
Andrew Granville, you are again confusing the asking of a question
(Granville, Tidjeman, Brun etc. etc.) with a reasoned correct (so far)
answer (Beal's conjecture) to the question.
We are still waiting for any written confirmable prior reference to
Beal's Conjecture, not someone asking a related question or speculating
on an incorrect answer
>
> Second, Darmon and Granville's statement is robust, because it
> is supported by a lot of theoretical evidence. Finding a few more
> solutions won't change that, the conjecture would just be amended
> slightly. It would take more than a few solutions to challenge the
> ideas their conjecture is built upon. Beal's version was derived
> from computer searches and some half-baked reasoning by someone
> who does not appear to fully understand exponentiation in arithmetic -
-
> a lucky guess.
That is a very interesting statement by someone who has no clue what
Beal's work included. Beal has not shared the bulk of his work with
anyone yet and certaintly not with Andrew Granville. Besides,
Granvilles conjecture is the one based on Rank Unreasoned Speculation
that was easily disproven. Beal's logic (that you have no knowledge of
but love to criticize) for his more refined conjecture predates
Granville anyway and appears much more solid.
Here come's Andrew Granville again -- Only Granville could claim that
his WRONG conjecture is more robust, and that his WRONG conjecture can
simply be changed again as it continues to be proven incorrect by
elementary computer searches. That HIS (Granvilles)incorrect conjecture
somehow subsumes a reasoned and so far correct conjecture (Beal's).
>
> Third, you seem to think that a conjecture is cancelled or withdrawn
> from circulation when a counterexample is found. It isn't, especially
> when it comes to matters of assessing priority. If the idea was out
> there before Beal, that kills his priority claims regardless of other
> details.
That's right, It's no longer a valid conjecture once a counterexample
is found. I'm sure that is also very hard for you to understand. The
fact that the counterexample might lead someone to a new conjecture
doesn't vindicate the old disproven conjecture, or extend its life.
Beal was the first to propose the scope an his conjecture in a correct
manner. THis remains undisputed despite your constant bullshit.
>
> > Beal and Darmon and Granville were not
> > even aware of each others work during 93. Darmon and Granville
> > speculated and derived an incorrect conjecture. Beal, independently,
> > and unaware of Darmon's and Granville's work, derived a conjecture
that
> > has withstood the test of time (so far).
>
> Counterexamples are not what determines whether a conjecture has
> value or "stands the test of time". There is a $1000000 prize
offered
> for the Hodge conjecture, which has stood the test of time although
> proved FALSE by Grothendieck sometime after Hodge posed it.
> The ideas behind the conjecture were important, and after amending
> it to take account of Grothendieck's work, the conjecture survived
> as one of the major open problems in mathematics.
>
It survived as a new conjecture, not as the old one. You are correct
that reasoning is important - that is why Granvilles assertion is not
even a true conjecture, it was rank speculation easily disproven by any
JUNIOR high school student with a computer. The fact that Granville has
done some work on related subjects does not give him priority over
Beal's reasoned and correct (so far) conjecture. I know this will be
hard for Granville to understand as well.
> Beal's conjecture is not based on any significant ideas,
Actually it is based on thousands of hours of work that inspired an
impiricle computer search. Besides the proof is in the pudding. Beal's
conjecture was well enough reasoned that it survives. GRanvilles
kindergarden assertion was disproved by junior high school methods.
so if a
> counterexample is found, his "contribution" withers and dies.
> Darmon and Granville's version with its more natural condition
> 1/a + 1/b + 1/c < 1, *is* linked to important mathematics,
> and is not particularly threatened if other solutions are found.
GRanville's version is not only threatened, it is already dead: A
victim of high school thought processes that proved it wrong.
>
> > After Beal's widespread
> > disemination of his conjecture in 1994, Darmon and Grandville
> > subsequently ammended their conjecture to include 10 known
solutions..
>
> Their paper was available as a UGA preprint not later than March 1994,
> before Beal's correspondence. Whether they listed 3 or 5 or 10
> solutions is irrelevant.
IT'S TOTALLY RELEVANT!!! It so clearly demonstrates GRanvilles lack of
a JUNIOR high school approach to reasoning. IT WAS ELEMENTARILY
WRONG!!! Is this reasoning too complicated for you?? In contrast,
Beal's reasoned conjecture still stands.
>
> > Beal already knew of some of the larger 2nd power solutions that
> > disproved Darmon and Granville's conjecture in 1993 at the time he
was
> > formulating his own correct (so far) conjecture.
>
> Please state how and when Beal knew this.
Beal's work in 1993 with variations of Pell's equation led him to some
of these solutions.
Hull Loss Incident
> > > > GENERALIZED FERMAT CONJECTURE: If
> > > > 1/p + 1/q + 1/r < 1 then [x^p + y^q = z^r] has no
> > > > non-trivial primitive solutions except the following:
> > > > [gives list of 10 known solutions...].
> > > >
> > > There probably exist larger 2nd power solutions which will prove
> > > the assertion wrong.
> >
> > That's a remarkable suggestion. Please explain why 2nd power
> > solutions are likely but not 3rd,4th,... solutions that would also
> > prove Beal's assertion incorrect.
> >
> For the exact reasons that 10 second power solutions already exist but
> no higher power solutions exist.
What are these exact reasons, exactly?
In the range containing the known solutions, there are about 10 times
as many potential solutions x,y,z for the problem with 1/a+1/b+1/c < 1,
as compared to the problem with higher powers. So finding 10
solutions of one type and none of the other is not an unusual
phenomenon; the chances of it happening at random are about
(9/10)^10, or better than 1 in 3.
> Squares have many different properties not shared by higher powers.
Identify any of these many properties that disfavors solutions in
powers higher than 2. The most obvious one, squares being
more common, is covered above and doesn't appear to support your
expectations.
> I would explain this to you further but I am not sure that you are capable
> of understanding these simple concepts given your ignorant statements to
> date.
Go ahead, embarrass us with your conceptual superiority. After stating
that 100^100 is "millions of orders of magnitude" larger than 10^15, your
credibility could use the boost.
> > > Beal already knew of some of the larger 2nd power solutions that
> > > disproved Darmon and Granville's conjecture in 1993 at the time he
> > > was formulating his own correct (so far) conjecture.
> >
> > Please state how and when Beal knew this.
>
> Beal's work in 1993 with variations of Pell's equation led him to some
> of these solutions.
Please elaborate. Which solutions, and how did they arise from Pell
equations? A way of getting from Pell equations to some of the
Beukers/Zagier solutions would be *much* more interesting (to
mathematicians) than merely stating some trivial conjecture.
sel...@my-deja.com
conjecture. Everyone has asked repeatedly for any prior reference.
There appear to be none. Everyone knowledgeable at the time beal
proposed the conjecture apparently either agrees that it was unknown or
has subsequently claimed it for themselves (ie: Granville &
Vanderpoorten). Please don't continue ranting about how many people
were thinkinmg about possible answers to various questions, please
simply cite A SINGLE previous confirmable reference. I repeat : not a
reference to A+B=C or 8+8=16 or a^x + b^y =c^z, a reference to anyone
ever proposing a conjecture prior to beal that precede's his
conjecture. (No, please don't repeat Granville's incorrect assertion
that a broader version had but five solutions.)
In article <3A527104...@y.z.com>,
Hull Loss Incident <x...@y.z.com> wrote:
Hull Loss Incident
> There are a number of elementary ways that Granville could appear to
> post from other isp's and university LAN's.
More certifiable lunacy. The LAN in question does not support
remote connections. Antonio Ramirez confirmed this for you
repeatedly. And you have ducked his direct question:
Hull Loss Incident
> Better yet, let's just stick with the subject: Beal's proposal of his
> conjecture.
You mean, let's change the subject now that Beal's
mathematical claims wither under scrutiny.
> Everyone has asked repeatedly for any prior reference.
Mr Beal, you are lying. Again. NOBODY has questioned
the (obvious) sufficiency of the many prior references posted,
other than Andy Beal posting under a string of aliases -- all
from Dallas, all through the @Home Network, all via Deja News,
all using the same software, the very same machines, the
same odd spelling errors and turns of phrase (such as the "impiricle study"
[sic] described by both andybeal@my-deja and selivan@my-deja),
and the same detailed knowledge of information about Beal and
his private communications not available from the public record.
Clearly all these are the very same andy...@my-deja.com
from the August 2000 discussions = the real-life Andrew Beal.
Meanwhile, ALL of the dozen or so non-Beal posters to these threads
have agreed that Beal's claims are bogus. There is a consensus,
and it is that Beal is full of shit.
> There appear to be none.
There appear to be many, and they have been posted here only
to be answered by Beal evasions. Below is another, from your friend
Granville,
posted 28 January 1994 to the NMBRTHRY email list read by hundreds
of mathematicians. This predates by 5 months Beal's correspondence
about the problem, which began in June 1994.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Date: Fri, 28 Jan 1994 21:19:27 -0500
Reply-To: Andrew Granville <and...@sophie.math.uga.edu>
Sender: Number Theory List <NMBR...@NDSUVM1.BITNET>
From: Andrew Granville <and...@sophie.math.uga.edu>
Subject: x^p+y^q=z^r
In reply to a question of Dave Davis on x^p+y^q=z^r:
Henri Darmon and I have been looking at integer solutions to
the above equations. It is trivial to find lots for many
different p,q,r. For example, the following parametric
solution exists for exponents p,p,p+1:
(ac)^p+(bc)^p = c^(p+1) where c = a^p+b^p.
To rid us of such upstart solutions, let us restrict
ourselves to solutions where x and y are coprime -- what we
will call `proper solutions'. It is `well-known'(see Dickson) that
1) The above equation has inf many proper solns whenever 1/p+1/q+1/r>1.
2) The above equation has no proper solns whenever 1/p+1/q+1/r=1 except
3^2-2^3=1^6
What Darmon and I have proved is:
If 1/p+1/q+1/r < 1 then there are only finitely many proper solutions
to x^p+y^q=z^r. The main tool we use is Faltings' theorem (nee Mordell's
conjecture); which we apply via an appropriate descent argument.
A preprint will soon be available (send email to me for this preprint).
Small examples of proper solutions to x^p+y^q=z^r with 1/p+1/q+1/r < 1
are: 1+2^3=3^2, \ \ 2^5+7^2=3^4, \ \ 7^3 + 13^2 = 2^9, \ \
2^7+17^3=71^2, \ \ 3^5+11^4=122^2
Extraordinarily large solutions have been found recently by
Beukers and Zagier:
17^7 + 76271^3 = 21063928^2, \ \ 1414^3 + 2213459^2 = 65^7, \ \
9262^3 + 15312283^2 = 113^7, \ \ 3^8 + 96222^3 = 30042907^2, \ \
33^8 + 1549034^2 = 15613^3.
It amazes me that there is such a gap between the two sets of solutions.
It may be that these are all of the solutions to the above, but I
thought that before Beukers and Zagier got involved, so maybe I am
wrong again. Can anyone compute some new examples ? That would be
very interesting.
Andrew Granville and...@sophie.math.uga.edu
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
> Everyone knowledgeable at the time beal
> proposed the conjecture apparently either agrees that it was unknown or
> has subsequently claimed it for themselves (ie: Granville &
> Vanderpoorten).
Name any number theorist who, when shown the above e-mail,
and Tijdeman's 1989 paper, and Granville's 1992 problem proposal,
Brun's 1914 paper, Darmon's work starting 1993 on generalized FLT,
etc etc --- would agree that Beal's problem is "unknown, unique and
original" as asserted by Beal.
sel...@my-deja.com
>
> > Better yet, let's just stick with the subject: Beal's proposal of
his
> > conjecture.
>
> You mean, let's change the subject now that Beal's
> mathematical claims wither under scrutiny.
>
posts using various pen names and repeated lies simply aren't enough to
make something true. You simply cannot tell a lie long enough that it
becomes true., Everyone including Ron Graham, Henri Darmon, Dan
Mauldin, Jarell Tunnell, Harold Edwards, Earl Taft, etc, etc.,
disagrees with you and agrees that they had no prior knowledge of
Beal's conjecture. The only people who claim otherwise are you and
Vanderpoorten, but neither of you have any evidence of prior knowledge
and Vanderpooretn claims the conjecture for himself years after Beal's
conjecture originated.
> > Everyone has asked repeatedly for any prior reference.
>
> Mr Beal, you are lying. Again. NOBODY has questioned
> the (obvious) sufficiency of the many prior references posted,
WRONG AGAIN - I am not Andrew Beal and there have been no references
posted of prior knowledge.
> Meanwhile, ALL of the dozen or so non-Beal posters to these threads
The Majority of whom are actually Andrew Granville as is Hull Loss
Incident. Those who are not pen names for Andrew Granville clearly see
the truth through all of Granvilles bullshit and lies and distortions.
Thanks (not really) for posting another IRRELEVANT reference. So
What!!!! Granville asserted that there were only five solutions and
then when proven wrong asked about more solutions. Who gives a shit
about Granville and his rank, speculative, (and incorrect) assertions
about second powers???????
>
> Andrew Granville and...@sophie.math.uga.edu
> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>
> > Everyone knowledgeable at the time beal
> > proposed the conjecture apparently either agrees that it was
unknown or
> > has subsequently claimed it for themselves (ie: Granville &
> > Vanderpoorten).
Henri Darmon himself (who worked closely with Granville) , along with
all those first listed above acknowledge the originality of Beal's
conjecture. Granville is the only one who disagrees and who constantly
references some previous irrelevant bullshit such as that referenced
above. Vanderpoorten apparently agrees that it was unknown because he
claims in his 1997 book (page 194) that he is "proposing" the
conjecture years after Beal did so. Granville claims he once asked
about more solutions after he was proven wrong about a prior
conjecture, therefore (he claims) he "inherently knew" Beal's
conjecture (but simply failed to ever tell anyone including his
collegue Henri Darmon). As Beal usually says, Bullshit and Talk are
Cheap, Andrew Granville.
Antonio Ramirez
> Andrew Granville, aka Hull Loss Incident, can simply modem by telephone
> long distance to other cities and overseas to other service providers.
> Computer cookies can demonstrate this most clearly.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Man, do you have any idea of how ignorant this sounds? There is
nothing pertaining to Usenet that is called "computer cookie".
> [...]
Hull Loss Incident
> > > Better yet, let's just stick with the subject: Beal's proposal of
> > > his conjecture.
> >
> > You mean, let's change the subject now that Beal's
> > mathematical claims wither under scrutiny.
> >
> You must have been dreaming again,
It is public record, not "dreaming", that you made a series of
remarkable mathematical assertions, and changed the subject
when called on them. For example, you say that there
are numerous fundamental reasons why further solutions of
X^a + Y^b = Z^c are expected if squares are allowed
(1/a+1/b+1/c <1) and unlikely when a,b,c>2. Other than
squares being more common, there are no such fundamental
reasons known to the number theory community, and (given
your history of mistaken assertions about matters of basic
arithmetic, let alone number theory) you are almost certainly
bluffing about material beyond your grasp.
> Everyone including Ron Graham, Henri Darmon, Dan
> Mauldin, Jarell Tunnell, Harold Edwards, Earl Taft, etc, etc.,
> disagrees with you and agrees that they had no prior knowledge of
> Beal's conjecture.
Whether or not "they had no prior knowledge" is irrelevant, even
if your paraphrase of their statements were accurate or honest.
What matters, of course, is whether any number theorist would agree
with your position, that the documentation of prior art posted in this
newsgroup, fails to destroy Beal's claims of an "unknown, unique
and original" discovery. You have been dodging that question in
favor of nebulous claims about apocryphal conversations.
Just to remind readers, the posted documentation of prior art includes:
Silverman's recollections from the 1985 Arcata conference;
Tijdeman's 1989 paper; Granville's 1992 problem proposal;
Granville's January 1994 email posted here; the Darmon/Granville
paper available as a preprint dated March 1994; the Beukers/Zagier
computer searches being dated prior to November 1993 (see Van
der Poorten's book); Darmon's published statements about
having made a certain conjecture (subsuming Beal's) prior to the
Beukers/Zagier searches; and Bremner's MathSciNet review tracing
the problem as far back as Brun's paper of 1914.
> > > Everyone has asked repeatedly for any prior reference.
> >
> > Mr Beal, you are lying. Again. NOBODY has questioned
> > the (obvious) sufficiency of the many prior references posted,
>
> WRONG AGAIN - I am not Andrew Beal and there have been no references
> posted of prior knowledge.
Dear Liar: the assertion was that nobody other than you ( = Beal) has
"repeatedly asked for any prior reference", and nobody other than
you (=Beal) has even suggested that the references that were
posted are insufficient to nullify Beal's priority claims. Regardless of
who is correct about the origin of the conjecture, those are
facts on the record concerning this newsgroup discussion, and you
are lying in representing "everyone" as asking for documentation,
"everyone" as agreeing with your claims, etc. In fact you have
received no support whatsoever, except from yourself posting under
various Deja News aliases.
> > Meanwhile, ALL of the dozen or so non-Beal posters to these threads
>
> The Majority of whom are actually Andrew Granville as is Hull Loss
> Incident. Those who are not pen names for Andrew Granville clearly see
> the truth through all of Granvilles bullshit and lies and distortions.
Pure lies from Beal. Back to facts on the record:
Bob Silverman, Denis Feldmann, Gerry Myerson, Dave Rusin, Severian,
Chip Eastham, Richard Tobin, Boudewijn Moonen, Bill Taylor, Derek Holt, and
Antonio Ramirez are examples of people who are neither me nor Granville,
and who have identified the "bullshit" as coming from Beal's side of the
discussion. Other people such as Fred Helenius, David Radcliffe, Christian
Bau
and Jan-Christoph Puchta made postings supporting my assertions and/or
disputing Beal's, but did not yet take a position in the dispute about the
naming of the conjecture, as far as I can tell.
Needless to say, there are no examples of pro-Beal postings except
the Beal sock puppets using DejaNews accounts from @Home
connections in Dallas.
Hull Loss Incident
sel...@my-deja.com wrote:
The original wording makes it clear that Van der Poorten does not
claim credit for the problem, defining the conjecture as contained or
implicit in Darmon and Granville's work. The change of wording to
"I propose" is apparently a matter of professional courtesy, because
the discussion of the problem in the Darmon/Granville article bears
some slight differences from Van der Poorten's comments (which
he states were written before he had seen their paper, based only
on reports thereof), so it was necessary to clearly indicate that
those comments were his not theirs. As further indication that
Van der Poorten treats the conjecture as known due to Darmon
and Granville's work, here is an excerpt from his email to the
NMBRTHRY list in 1996:
######################################################
Date: Thu, 29 Aug 1996 08:27:07 -0400
Sender: Number Theory List <NMBR...@LISTSERV.NODAK.EDU>
From: Alf van der Poorten <a...@mpce.mq.edu.au>
Subject: Re: x^a + y^b = z^c
[...regarding a sci.math query about the] Conjecture: X^a + Y^b = Z^c
has no solutions for coprime naturals X,Y,Z when each exponent a,b,c > 2.
----------
This conjecture, which I call the Generalized Fermat Conjecture in my book
`Notes on Fermat's Last Theorem' (Wiley--Interscience, 1996), surfaced in
the context of Henri Darmon and Andrew Granville, `On the equation
$z^m=F(x,y)$ and $Ax^p+By^q=Cz^r$', to appear, or recently appeared, in
{\it Bull.\ London Math.\ Soc.\/}).
It's easy to concoct seemingly nontrivial solutions with $X$, $Y$ and $Z$
sharing a common factor; so they're coprime from hereon: Even then there
are paramtrised solutions (so infinitely many) if $1/a+1/b+1/c>1$, but then
of course at least one of the exponents is $2$.
There are only finitely many solutions if $1/a+1/b+1/c\le1$. There are $10$
such interesting solutions known:
It's not too hard to notice the solutions $13^2+7^3=2^9$, $2^7+17^3=71^2$,
$2^5+7^2=3^4$ and $3^5+11^4=122^2$. I suppose one might include
$1+2^3=3^2$,
if only out of respect for history, for it provides the only known solution
to
Catalan's problem of finding all solutions to $z^t-y^s=1$. We'll deem that
$1=1^7$, say.
One's computer will probably get tired before finding any
solutions beyond these five. Yet five more solutions are now known (by
courtesy of the computers of Frits Beukers and of Don Zagier), a severe
blow for the Law of Small Numbers:
$17^7+76271^3&=21063928^2$,
$1414^3+2213459^2&=65^7$,
$33^8+1549034^2&=15613^3$,
$9262^3+15312283^2&=113^7$,
$43^8+96222^3&=30042907^2$.
Of course all these cases have an exponent $2$, so the GFC may well be
true.
------------------------
Alf van der Poorten
ceNTRe for Number Theory Research [...]
########################################################
> > Anyway, here is the quotation, from
> > Australian Math Society Gazette 21 no 5 (Dec 1994) pp. 150-159:
> >
> > "Darmon and Granville (1993) suggest Fermat might have
> > chosen a different generalization. Say, that a^t + b^u = c^v
> > has no solution in integers greater than 1 if all of t,u,v are at
> > least 3. If one exponent is allowed to be 2, things are
> > different. [...] All nine solutions known have one or other of
> the > exponents equal to 2."
>
> NO - You have continued to lie about the truth, or perhaps you simply
> can't subtract large integers. Let me repeat for you for about the
> 100th time: Vanderpoorten's first clear claim to have "proposed" Beal's
> conjecture was his 1996 book published in 1997.
It is extremely unlikely he claimed to be "proposing" an original
conjecture, because as his own writing makes clear he considered
the ideas to be already known. I suppose one could email him at
the address above to find out directly.
> Do you understand what the english word "years" means??
Let us remember that both Beal (andybeal@my-deja) and
sel...@my-deja.com misspell a certain common word
as "impiricle". Of course they are not only two different
entities but experts on the English language.
> Do you understand the concept of "plurality". Can
> I refer you to a remedial reading and writing program, Andrew
> Granville??
The term you are looking for is "plural" or "pluralization".
"Plurality" means something altogether different, so you
are self-revealed as an ignoramus once again.
EXCELLENT JOB MISTER BEAL!!!
Hull Loss Incident
> > Below is another, from your friend Granville,
> > posted 28 January 1994 to the NMBRTHRY email list read by hundreds
> > of mathematicians. This predates by 5 months Beal's correspondence
> > about the problem, which began in June 1994. [...]
>
> Thanks (not really) for posting another IRRELEVANT reference. So
> What!!!!
The "so what" is that months before Beal's (limited, private) circulation
of his conjecture, Granville published the problem in an email list read
by hundreds of mathematicians.
That Beal proclaimed NO SOLUTIONS rather than leaving it
open-ended as Granville (and others before him) did, in no way
affects the priority issue. The problem was published before Beal.
> Granville asserted that there were only five solutions and
> then when proven wrong asked about more solutions.
The email states that Granville "thought", rather than "asserted", that
there were only five solutions. "Asserted" would be more damaging
to Beal's priority claims, since that would be an earlier instance
of the "Beal" problem being raised before Beal. So if you have evidence
of Granville making that wrong wrong wrong public Assertion, by all
means go ahead and share it.
> Who gives a shit about Granville
Granville must have really traumatized you. Do you need a hug?
> and his rank, speculative, (and incorrect) assertions
> about second powers???????
What is rank and speculative is to proclaim NO SOLUTIONS without
any serious evidence, and what is stupid is to cite such a proclamation as
an insight not a mistake. "Second powers" is another advantage of
Granville's formulation over Beal's -- the a,b,c>2 restriction is ad hoc,
whereas several independent theoretical arguments support
1/a+1/b+1/c < 1 as the right set of exponents.
> Henri Darmon himself (who worked closely with Granville) , along with
> all those first listed above acknowledge the originality of Beal's
> conjecture.
It is extremely unlikely Darmon would support Beal's claim to an
"unknown, unique and original" discovery in light of Tijdeman's
article, Granville's 1992 proposal, etc etc referenced in the thread.
He is anyway on record claiming to have made the more general
5-solutions-only conjecture in 1993 well before Beal's correspondence about
a special case of the problem. More solutions found later doesn't affect
the
questions of priority and novelty.
Hull Loss Incident
> Andrew Granville can indeed be Hull Loss Incident - There are a number
> of elementary ways for Granville to appear to post from other isp's and
> from university LAN's.
Since you know the Usenet so well, could you actually answer the
questions how 3 supposedly different people posting from the same ISP,
same machines, etc can be credibly asserted to be anything other than
Beal aliases, just as "phil_r...@my-deja.com" in the August discussion?
Thanks in advance. Note Mr. Ramirez' observations, retained below.
sel...@my-deja.com
including Harold Edwards, Earl Taft, Jarell Tunnell, Ron Graham, Henri
Darmon, etc, etc, all agree that the conjecture was unknown prior to
Beal. Alf Vanderpoorten himself claims (on page 194 of his 1997 book)to
have "proposed" the conjecture in 1997, years after Beal. While many of
your numerous postings reference questions about and issues related to
A^X + B^Y = C^Z: NONE, I repeat, NONE, indicate any knowledge of Beal's
conjecture prior to Beal's widespread dissemination of it in 1994. A
number of writings AFTER 1994 reference Beal's conjecture. Those are
the facts.
The fact that Andrew Granville feels some need to post numerous
contrary messages under various pen names does not change the facts.
Granville apparently believes that if enough people tell a lie long
enough that it will become true. No-one cares how many people or
aliases post whatever on this message board. The truth is still the
truth.
In article <3A5E4937...@y.z.com>,
Hull Loss Incident <x...@y.z.com> wrote:
> sel...@my-deja.com wrote:
>
> > > > Better yet, let's just stick with the subject: Beal's proposal
of
> > > > his conjecture.
> > >
> > > You mean, let's change the subject now that Beal's
> > > mathematical claims wither under scrutiny.
> > >
> > You must have been dreaming again,
>
> It is public record, not "dreaming", that you made a series of
> remarkable mathematical assertions, and changed the subject
> when called on them. For example, you say that there
> are numerous fundamental reasons why further solutions of
> X^a + Y^b = Z^c are expected if squares are allowed
> (1/a+1/b+1/c <1) and unlikely when a,b,c>2. Other than
> squares being more common, there are no such fundamental
> reasons known to the number theory community, and (given
> your history of mistaken assertions about matters of basic
> arithmetic, let alone number theory) you are almost certainly
> bluffing about material beyond your grasp.
You must mean no reasons are known to you, Andrew Granville
>
> > Everyone including Ron Graham, Henri Darmon, Dan
> > Mauldin, Jarell Tunnell, Harold Edwards, Earl Taft, etc, etc.,
> > disagrees with you and agrees that they had no prior knowledge of
> > Beal's conjecture.
>
> Whether or not "they had no prior knowledge" is irrelevant, even
> if your paraphrase of their statements were accurate or honest.
>
> What matters, of course, is whether any number theorist would agree
> with your position, that the documentation of prior art posted in this
> newsgroup, fails to destroy Beal's claims of an "unknown, unique
> and original" discovery. You have been dodging that question in
> favor of nebulous claims about apocryphal conversations.
>
> Just to remind readers, the posted documentation of prior art
includes:
> Silverman's recollections from the 1985 Arcata conference;
> Tijdeman's 1989 paper; Granville's 1992 problem proposal;
> Granville's January 1994 email posted here; the Darmon/Granville
> paper available as a preprint dated March 1994; the Beukers/Zagier
> computer searches being dated prior to November 1993 (see Van
> der Poorten's book); Darmon's published statements about
> having made a certain conjecture (subsuming Beal's) prior to the
> Beukers/Zagier searches; and Bremner's MathSciNet review tracing
> the problem as far back as Brun's paper of 1914.
I could list 100 more irrelevant references - What's your point? - None
that predate Beal disclose his conjecture.
Beal doesn't need Granville's support - the facts speak loud and clear
for themselves.
sel...@my-deja.com
including Harold Edwards, Earl Taft, Jarell Tunnell, Ron Graham, Henri
Darmon, etc, etc, all agree that the conjecture was unknown prior to
Beal. Alf Vanderpoorten himself claims (on page 194 of his 1997 book)
dissemination of it. While many of your numerous postings reference
questions and issues related to A^X + B^Y = C^Z: NONE, I repeat, NONE
indicate any knowledge of Beal's conjecture prior to Beal's reasoning
it in 1993 and widely disseminating it in 1994. A number of writings
after 1994 reference Beal's conjecture. Those are the facts.
The fact that Andrew Granville feels some need to post numerous
contrary messages under various pen names does not change the facts.
Granville apparently believes that if enough people or aliases tell a
lie long enough and often enough that it will become true.
Incidentally, Granville's OWN continued arguments (see below) that his
assertion that a broader form of the equation had only five second
power solutions (which was rank speculation and subsequently easily
proven incorrect) somehow "subsumes" Beal's correct (so far) conjecture
is the most compelling evidence that I can offer of Granville's
nonsense.
In article <3A5E6055...@y.z.com>,
Hull Loss Incident <x...@y.z.com> wrote:
sel...@my-deja.com
including Harold Edwards, Earl Taft, Jarell Tunnell, Ron Graham, Henri
Beal. Alf Vanderpoorten himself claims (on page 194 of his 1997 book)
While many of your numerous postings reference questions and issues
knowledge of Beal's conjecture. A number of writings after 1994
reference Beal's conjecture. Those are the facts.
The fact that Andrew Granville feels some need to post numerous
contrary messages under various pen names does not change the facts.
Granville apparently believes that if enough people (or aliases) tell a
lie long enough that it will become true. Unfortunately for Granville,
the facts are still the facts.
In article <3A5E6517...@y.z.com>,
Hull Loss Incident <x...@y.z.com> wrote:
> sel...@my-deja.com wrote:
>
> > Andrew Granville can indeed be Hull Loss Incident - There are a
number
> > of elementary ways for Granville to appear to post from other isp's
and
> > from university LAN's.
>
> Since you know the Usenet so well, could you actually answer the
> questions how 3 supposedly different people posting from the same ISP,
> same machines, etc can be credibly asserted to be anything other than
> Beal aliases, just as "phil_r...@my-deja.com" in the August
discussion?
> Thanks in advance. Note Mr. Ramirez' observations, retained below.
Any kindergardener can tell you that IP addresses indentify service
providers, not individual machines. Therefore, you have, perhaps,
determined that some service providers have many customers.
> > > Do you know what this
> > > means? It means they were sent from the VERY SAME physical
> > > computer. It is simply not credible that they were sent by
different
> > > people.
>
>
sel...@my-deja.com
including Harold Edwards, Earl Taft, Jarell Tunnell, Ron Graham, Henri
Beal. Alf Vanderpoorten himself claims (on page 194 of his 1997 book)
of your numerous postings reference questions and issues related to A^X
+ B^Y = C^Z: NONE, I repeat, NONE, indicate any prior knowledge of
1994. A number of writings AFTER 1994 reference Beal's conjecture.
Those are the facts.
The fact that Andrew Granville feels some need to post numerous
contrary messages under various pen names does not change the facts.
Granville apparently believes that if enough people (or Aliases) tell a
lie long enough and often enough that it will become true.
Unfortunately for Granville, the facts remain the same.
Granvilles argument below regarding Vanderpoorten's use of the
word "propose" is incredibly disingenious, but nonetheless supports the
observation that Vanderpoorten didn't believe that Granville had made
the conjecture. We AGREE on that part. We also AGREE that Granville had
discussed the problem of A^X + B^Y = C^Z. SO WHAT!!! He didn't reason
the correct conjecture. We agree with Vanderpoorten (if Granvilles
comments below are to be believed) that he didn't want to lead the
reader to conclude that his remarks (ie: Beal's conjecture) were to be
attributed to Granville and therefore chose the phase "I propose".
Nowhere does Vanderpooretn suggest that the conjecture is "contained or
implicit" in any of Granvilles work. Darmon himself agrees that his
work never led him to Beal's conjecture prior to Beal's proposal of it.
article <3A5E5315...@y.z.com>,
denis-feldmann
<sel...@my-deja.com> wrote in message : 93m44m$jcp$1...@nnrp1.deja.com...>
>
>
> [Some funny lies about telling lies]
>
>
then
>
>
> In article <3A5E6517...@y.z.com>,
> Hull Loss Incident <x...@y.z.com> wrote:
> > sel...@my-deja.com wrote:
> >
> > > Andrew Granville can indeed be Hull Loss Incident - There are a
> number
> > > of elementary ways for Granville to appear to post from other isp's
> and
> > > from university LAN's.
> >
> > Since you know the Usenet so well, could you actually answer the
> > questions how 3 supposedly different people posting from the same ISP,
> > same machines, etc can be credibly asserted to be anything other than
> > Beal aliases, just as "phil_r...@my-deja.com" in the August
> discussion?
> > Thanks in advance. Note Mr. Ramirez' observations, retained below.
>
> Any kindergardener can tell you that IP addresses indentify service
> providers, not individual machines. Therefore, you have, perhaps,
> determined that some service providers have many customers
Kindergardener? Is there such a word? Or is this sentence synonymous for
"any boojum can tell you that..."?
Anyway, I dare you to prove any of those stupid assertions. Just for a
start, show us how you can send a message from France, which is what I am
presently doing. Then, I will admit I am Granville ;-)
sel...@my-deja.com
including Harold Edwards, Earl Taft, Jarell Tunnell, Ron Graham, Henri
Beal. Alf Vanderpoorten himself claims (on page 194 of his 1997 book)
what led him to "propose" it. While many of Andrew Granville's numerous
postings reference questions about and issues related to A^X + B^Y =
C^Z: NONE, I repeat, NONE indicate any knowledge of Beal's conjecture
prior to Beal's widespread dissemination of it in 1994. A number of
The fact that Andrew Granville feels some need to post numerous
contrary messages under various pen names does not change the facts.
Granville apparently believes that if enough people or aliases tell a
lie long enough and often enough that it will become true. Fortunately,
the truth remains the truth and is easily determined by anyone seeking
it.
As for your question below, anyone can telephone a dial up service
provider in France or anywhere in the world from the United States and
their message will originate from an IP address in France. I would be
happy to demonstrate this for you but I simply don't want to expend the
effort of opening an account with a French ISP and my service provider
does not support France. You can easily do it yourself if you truly
want it demonstrated. You can similarly dial up AOL or any large
service provider in the U.S. with a telephone modem and your posting
will list an IP address from any state you choose to connect through.
Perhaps your U.S. ISP will even have a dial up connection in France and
an additional account will not be needed. Virtually all university LAN
systems offer dial up modem access that is routinely used by students
and faculty. One of the significant drawbacks of the usenet system is
that anyone can post as many messages as they like from anywhere in the
world using any name they select.
It would seem that you, Andrew Granville, are making the most of that
capability. Thankyou for admiting below that you are indeed Andrew
Granville.
In article <93n7t8$9gp$1...@wanadoo.fr>,
Severian
>
> Alf Vanderpoorten himself claims (on page 194 of his 1997 book)
Alf van der Poorten, 1996.
--
Severian
---------------------------------------------------------------
Victor Meldrew: "The police can use sperm now as
a way of fingerprinting people."
Mrs Warboys: "I don't see what was wrong with the old inkpads."
---------------------------------------------------------------
David Renwick, _One Foot in the Grave_
Hull Loss Incident
Big signatures are enough for all the other crackpots, but Mr Beal
has his own ideas. Continuing his display of Usenet virtuosity,
Mr Beal has decided to post the same 16-line polemic at the *top*
of all his postings.
Other KOTM-worthy Beal contributions include:
--> set up web domain (www.bealconjecture.com) to defend
against criticisms made in Usenet discussion threads;
--> post in ALL CAPS, "to better distinguish" his replies;
--> post from 5 different DejaNews usernames (all through same
IP address, same software, same writing style and peculiar
spelling errors, etc) to create appearance of public support;
--> claim that at least 3, and possibly as many as 11 or 15, other posters
who criticized him in the threads are "pen names" for University
of Georgia mathematician Andrew Granville (who is uninvolved
in the discussion and probably doesn't even read Usenet).
--> accuse imaginary nemesis Prof. Granville of trying to slander
Beal and deny him credit for a scientific discovery
--> claim that Prof Granville and another mathematician (Prof Van der
Poorten from Australia), have tried to falsely take credit for
Beal's alleged discovery.
--> claim to have made an "unknown, unique and original" mathematical
discovery generalizing Fermat's Last Theorem. (Beal is a Fermatist
searching for an elementary proof, though to be fair he does not
claim to have proved either FLT or "his" generalization.
Mathematicians consider his alleged discovery to be valid but
somewhat trivial and known earlier.)
--> claim credit for new mathematical discovery while blundering with
basic arithmetic, e.g. statement that 100^100 is "millions of
orders of magnitude" larger than 10^15.
--> dismiss related work by mathematicians predating his "discovery" as
amateurish, mistaken, junior high school level and (yes!) crackpot.
--> claim to have written support from 30-40 mathematical experts,
but unable to give any details
This is just touching the surface. Beal is an eccentric millionaire
who funded an aerospace company to accelerate colonization of
other planets (in case an asteroid threatens life on earth -- search
WWW for Beal Aerospace), and established a $100000 prize to
promote his name in connection with "his" mathematical discovery.
Other Beal insights include:
> > Any kindergardener can tell you that IP addresses indentify service
> > providers, not individual machines.
References:
"Beal's conjecture" discussion thread in sci.math (Dec 2000 - present)
"Against the term "Beal conjecture" (sci.math thread, August 2000)
"A generalization of FLT" (sci.math thread, August 2000)
(Beal postings are under andy...@my-deja.com, phil_rogowski@my-deja,
selivan@my-deja, bob_paulson@my-deja, jim...@my-deja.com).
Enjoy. A sample posting is enclosed below.
================================================
Hull Loss Incident
> [16-line Beal manifesto, deleted]
> > It is public record, not "dreaming", that you made a series of
> > remarkable mathematical assertions, and changed the subject
> > when called on them. For example, you say that there
> > are numerous fundamental reasons why further solutions of
> > X^a + Y^b = Z^c are expected if squares are allowed
> > (1/a+1/b+1/c <1) and unlikely when a,b,c>2. Other than
> > squares being more common, there are no such fundamental
> > reasons known to the number theory community, and (given
> > your history of mistaken assertions about matters of basic
> > arithmetic, let alone number theory) you are almost certainly
> > bluffing about material beyond your grasp.
>
> You must mean no reasons are known to you, Andrew Granville
No such reasons are known, period. Since you claim to have
many fundamental reasons backing your assertion, you may post
them now or prove yourself a dunce bluffing about material beyond
your grasp.
> > > Everyone including Ron Graham, Henri Darmon, Dan
> > > Mauldin, Jarell Tunnell, Harold Edwards, Earl Taft, etc, etc.,
> > > disagrees with you and agrees that they had no prior knowledge of
> > > Beal's conjecture.
> >
> > Whether or not "they had no prior knowledge" is irrelevant, even
> > if your paraphrase of their statements were accurate or honest.
> >
> > What matters, of course, is whether any number theorist would agree
> > with your position, that the documentation of prior art posted in this
> > newsgroup, fails to destroy Beal's claims of an "unknown, unique
> > and original" discovery. You have been dodging that question in
> > favor of nebulous claims about apocryphal conversations.
> >
> > Just to remind readers, the posted documentation of prior art
> includes:
> > Silverman's recollections from the 1985 Arcata conference;
> > Tijdeman's 1989 paper; Granville's 1992 problem proposal;
> > Granville's January 1994 email posted here; the Darmon/Granville
> > paper available as a preprint dated March 1994; the Beukers/Zagier
> > computer searches being dated prior to November 1993 (see Van
> > der Poorten's book); Darmon's published statements about
> > having made a certain conjecture (subsuming Beal's) prior to the
> > Beukers/Zagier searches; and Bremner's MathSciNet review tracing
> > the problem as far back as Brun's paper of 1914.
>
> I could list 100 more irrelevant references - What's your point? -
That Beal is bluffing and lying about his level of support from various
experts (and some non-experts he represents as experts).
The given references would satisfy anyone knowledgeable in number
theory, that Beal's "discovery" was known before Beal came along.
Beal would like to dismiss the references as irrelevant, but since he
makes assertions on behalf of numerous mathematicians the question is
whether THEY consider the references relevant. Dan Mauldin, for
example, considered a small subset of the references discussed here (and
not even the ones most damaging to Beal's priority claims) enough to
warrant a sheepish followup letter explaining his AMS Notices propaganda
piece about Beal. Any number theorist would consider Tijdeman's 1989
article, Granville's Jan 1994 e-mail, etc as evidence of prior art for
Beal's
conjecture.
Beal is challenged to identify *any* number theorist who, after
seeing the many references given in these newsgroup discussions,
endorses Beal's claim to an "unknown, unique and original" discovery.
> None that predate Beal disclose his conjecture.
Darmon states on the record, that in 1993 he made a conjecture
that clearly includes Beal's. Granville explicitly raises the same
question in a January 1994 email, in a form that is immune to Beal's
objections that the statement is "wrong". Their article, available
early in 1994 (Van der Poorten references it in March 1994, as being
available in the UGA math preprint series), specifically asks whether
the "Beal" version of the problem has solutions. Van der Poorten
in 1993 wrote down the exact statement of the "Beal" conjecture as
an obvious comment on (reports of) Darmon & Granville's article.
Also, his Dec 1994 article appears to be the first published appearance
of the conjecture in the form stated by Beal, 3 years before Mauldin's
article in AMS Notices.
sel...@my-deja.com
asked about A^X + B^Y = C^Z or 8 + 8 = 16 (many references including
himself), The facts are simple: A large number of knowledgaable number
theorists including Harold Edwards, Earl Taft, Jerell Tunnell, Ron
Graham, Henri Darmon, etc. etc, all agree that Beal's conjecture was
unknown prior to Beal's assertion that no solutions exited. Alf
Vanderpoorten himself claims (on page 194 of his 1996-1997 book) to
have "proposed" the conjecture himself, years after Beal. While Andrew
Granville's numerous postings reference many questions about A^X + B^Y
= C^Z (and A+B=C and 8+8=16), NONE of those numerous references
indicate any knowledge of Beal's conjecture prior to Beal's widespread
dissemination of it in 1994. A number of writings AFTER 1994 reference
the correspondence from Beal to some of the above number theorists who
unanimously agree that it was previously unknown. Those are the facts.
Granville will undoutably respond to this using his pen name Hull Loss
Incident (or one of his other many pen names) and claim many examples
of prior knowledge were posted (many with himself as author), change
the subject to unrelated issues, criticize, and ramble on and on
because he obviously has nothing better to do with his time. I will
keep responding to his posts with this summary of the facts so that
users get the straight story. I will no longer take the effort to
respond individually to Granville's large quantities of bullshit and
constant argumentative nonesense.
The fact that Granville feels some need to post numerous false and
contrary messages under various pen names will not change the facts.
Granville apparently believes that if enough people (or aliases) tell a
lie long enough and often enough that it will become true.
Mostly himself)In article <3A62AB86...@y.z.com>,
Hull Loss Incident <x...@y.z.com> wrote:
denis-feldmann
<sel...@my-deja.com> a écrit dans le message :
93ore7$sun$1...@nnrp1.deja.com...
> The facts are simple:
Yes, I do think so
A large number of knowledgeable number theorists
> including Harold Edwards, Earl Taft, Jarell Tunnell, Ron Graham, Henri
> Darmon, etc. etc, all agree that Beal's conjecture was unknown prior to
> Beal.
A lie, how often repeated, etc etc.
>Alf Vanderpoorten himself claims (on page 194 of his 1997 book)
1996, by the way...
>
>
> As for your question below,
It was not a question, but a request for a demonstration. You did not (could
not) provide it.
anyone can telephone a dial up service
> provider in France or anywhere in the world from the United States and
> their message will originate from an IP address in France.
If you say so...
I would be
> happy to demonstrate this for you
No; if you could, you would have. Same as your other boasts...
but I simply don't want to expend the
> effort of opening an account with a French ISP and my service provider
> does not support France. You can easily do it yourself if you truly
> want it demonstrated. You can similarly dial up AOL or any large
> service provider in the U.S. with a telephone modem and your posting
> will list an IP address from any state you choose to connect through.
> Perhaps your U.S. ISP will even have a dial up connection in France and
> an additional account will not be needed. Virtually all university LAN
> systems offer dial up modem access that is routinely used by students
> and faculty. One of the significant drawbacks of the usenet system is
> that anyone can post as many messages as they like from anywhere in the
> world using any name they select.
>
> It would seem that you, Andrew Granville, are making the most of that
> capability. Thankyou for admiting below that you are indeed Andrew
> Granville.
>
I did not admit it. Read my words again. Oh, and I am not , by the way.
Youn on the other hand, need psychiatric help. A case of split personalities
in reverse?
Keith Ramsay
It's spelled "kindergartner" or "kindergartener": a child attending
kindergarten, or of kindergarten age, or a kindergarten teacher.
Kindergarten is defined as "a school or divison of a school below the
first grade usu. serving pupils of the 4 to 6 age group and fostering
their natural growth and social development through constructive play
with blocks, clay, crayons and by group games, songs, and exercise"
[Webster's Third New International Dictionary].
Keith Ramsay
Chris Thompson
denis-feldmann <denis-f...@wanadoo.fr> wrote:
>
><sel...@my-deja.com> wrote in message : 93m44m$jcp$1...@nnrp1.deja.com...>
>> Any kindergardener can tell you that IP addresses indentify service
>> providers, not individual machines. Therefore, you have, perhaps,
>> determined that some service providers have many customers
>
>Kindergardener? Is there such a word? Or is this sentence synonymous for
>"any boojum can tell you that..."?
Perhaps someone could undertake to introduce sel...@my-deja.com, not to
mention his clones, to a boojum? The result, as first described by that
eminent mathematician C.L. Dodgson, would be greatly to the benefit of
this newsgroup...
Chris Thompson
Email: cet1 [at] cam.ac.uk
Hull Loss Incident
> sel...@my-deja.com wrote:
> >
> > Alf Vanderpoorten himself claims (on page 194 of his 1997 book)
>
> Alf van der Poorten, 1996.
By pure coincidence, this is exactly the same subliterate
spelling favored by andy...@my-deja.com. See also
the "impiricle" data at the end of this posting...
andy...@my-deja.com wrote, in the Aug 2000 thread:
>Vanderportens assertion in the first edition of
>Vanderporten changed the assertion in subsequent
>compelling that Vanderporten must
>Vanderportens text was clear and unambiguous
>Vanderpoortens text in his 1997 book was clear
>The fact is that Vanderpoorten claimed credit in his 1997 book
>Vanderpoorten stated in the first edition of his 1997 book that he
>On page 194 vanderpoorten writes, and I qoute "I propose
>vanderpoorten who proposed the conjecture in his 1997 book.
sel...@my-deja.com wrote, in this thread:
>Vanderpoorten claimed in his 1996 book
>DO YOU MEAN AS STUPID as you and Vanderpoorten
>Vanderpoorten thinks since he "proposed" beal's conjecture himself
>Vanderpoorten "proposed" it himself years after Beal,
>reference prior to Vanderpoortens "I propose" of Beal's
>Vanderpoorten's "proposal" of the
>Another lie: Vanderpooretn writes for all the world to see: "I propose
>Wrong again; Vanderpoorten claims he "proposed" it (as detailed
>Vanderpooten's 1996 book "proposes" Beal's conjecture as though
>Vanderpoorten originated it (so much for Vanderpooretn believing it
>look at Vanderpoortens book
>Vanderpoorten). Please don't continue ranting
>Alf Vanderpoorten himself claims (on page 194 of his 1997 book)
andy...@my-deja.com wrote:
>co-prime bases, impirically test a
>impirically tested the concept.
>and impirically tested a reasonable
>suspected conclusion and impirically tested it within reasonable
>the first (apparently) reasonable impiricle study of terms
sel...@my-deja.com wrote:
>impiricle computer search.
Hull Loss Incident
> [20-line manifesto, reposted at top of each message, snipped]
2 paragraphs of SPAM per message will really endear you
to the readers here. It also continues the supersavvy mastery of
Usenet displayed in your lectures about IP numbers identifying ISP's [sic]
not machines, "computer cookies" controlling the headers, etc.
> Granville will undoutably respond to this using his pen name Hull Loss
> Incident (or one of his other many pen names)
Undoutably.
> I will keep responding to his posts with this summary of the facts so that
>
> users get the straight story.
Good idea. Keep building crackpot credentials in a bid for KOTM.
> I will no longer take the effort to respond individually
Posting spam against facts is the crackpot method of conceding defeat.
Hull Loss Incident
> The facts are simple:
Yes. Simple facts that you are currently avoiding, include Granville's
January 1994 distribution of a problem that includes Beal's
later proposal. It has the nice aspect of sidestepping your (irrelevant)
cavils that some even earlier instances of the conjecture were "wrong".
> A large number of knowledgaable number theorists including Harold Edwards,
> Earl Taft, Jerell Tunnell, Ron Graham, Henri Darmon, etc. etc, all agree
> that Beal's conjecture was unknown prior to Beal's assertion that no
> solutions exited.
Let us count the lies in one Beal sentence.
1. Taft is not a number theorist, knowledgeable or otherwise.
2. Taft did not review Beal's work, and did not assess its originality.
3. Darmon's published statements clearly specify that he had made a
conjecture
subsuming Beal's, the year before Beal privately circulated his problem.
4. Edwards is not qualified to assess originality of Beal's work.
5. Edwards never claimed such qualifications, and has not claimed to
certify that "Beal's conjecture was unknown prior to Beal".
6. None of Beal's sources have ever provided what Beal claims: an
authoritative professional certification that his problem
was "unknown, unique and original". In particular none of the people
named above searched the literature, WWW, etc for relevant
prior references, and they would almost certainly agree that the
references posted here demolish Beal's priority claims. The reviewer
for MathSciNet (A. Bremner) traced the problem as far back as 1914.
> Vanderpoorten himself claims (on page 194 of his 1996-1997 book) to
> have "proposed" the conjecture himself, years after Beal.
He uses the word "propose", yes. Other than that, you are lying.
> While Andrew Granville's numerous postings reference many questions about
> A^X + B^Y
> = C^Z (and A+B=C and 8+8=16), NONE of those numerous references
> indicate any knowledge of Beal's conjecture prior to Beal's widespread
> dissemination of it in 1994.
Granville's email to NMBRTHRY list, Jan 28 1994, went out to hundreds
of recipients. It predates Beal by 5 months, and it includes Beal's
conjecture.
Deal with it.
> Granville will undoutably respond to this using his pen name Hull Loss
> Incident (or one of his other many pen names)
See a psychiatrist. Granville is not participating in these threads.
> change the subject to unrelated issues,
Pursuing your (Beal's) bogus mathematical claims is not "unrelated issues".
We are still waiting to hear your numerous basic reasons why the
Tijdeman/Darmon/Granville/Zagier/Brun/etc version of the problem
with 1/a+1/b+1/c < 1 should have additional counterexamples, but the
Beal version should not.
Also waiting for answer to some other facts quoted but not dealt
with in your article:
sel...@my-deja.com
> > > > None that predate Beal disclose his conjecture.
> > > question in a January 1994 email, in a form that is immune to
Beal's
> > > objections that the statement is "wrong". Their article,
available
> > > early in 1994 (Van der Poorten references it in March 1994, as
being
> > > available in the UGA math preprint series), specifically asks
whether
> > > the "Beal" version of the problem has solutions.
Oh, - But ...., Wait a minute -- I thought that everyone and their
mothers already knew there were no solutions, all the way back to
1914!!!!!!
Hmmmm. Let me think for a minute, Hmmmm. So why would the brilliant
and all knowing Andrew Granville so ignorantly ask if the Beal
conjecture has solutions in March of 1994, given that Granville (and as
Granville claims; every other mathematician in the world) already KNEW
THERE WERE NO SOLUTIONS??????
This is very interesting -- Hmmmmmmm. Andrew Granville claims he
already knew Beal's conjecture (and that everyone already previously
knew it). Hmmmmmmm. But in March of 1994, Granville asks in an email
for solutions to the equation.
I must just be toooo stuuuupid. I just don't get it. I guess I will ask
the all knowing Andrew Granville to explain.
Andrew Granville (aka Hull Loss Incident) - coud you pleeese help us
ignorent illitorate peeple out here anderstand this haere thang???
Hull Loss Incident
> >>>> None that predate Beal disclose his conjecture.
> >>> Granville explicitly raises the same
> >>> question in a January 1994 email, in a form that is immune to
> >>> Beal's objections that the statement is "wrong". Their article,
> >>> available early in 1994 (Van der Poorten references it in March 1994,
>
> >>> as being available in the UGA math preprint series), specifically
> asks
> >>> whether the "Beal" version of the problem has solutions.
>
> Oh, - But ...., Wait a minute -- I thought that everyone and their
> mothers already knew there were no solutions, all the way back to
> 1914!!!!!!
Just deal with the facts above, not your digressions.
You requested discussion on whether Beal's problem was known
before Beal (i.e. June 1994). When confronted with prior references
as above, you change the subject to what "everybody knew".
Above facts indicate that it was indeed publicized earlier in several
forms: by Darmon and Granville (1993-1994 circulation of their work,
including a preprint of their article); Granville (Jan 1994 email to
NMBRTHRY list); and Van der Poorten (lectures in 1993 or 1994
as documented in his book, prior to the March 1994 note). Not to
mention being obviously implicit in earlier references such
as Tijdeman's 1989 article and others.
> why would the brilliant and all knowing Andrew Granville so
> ignorantly ask if the Beal
> conjecture has solutions in March of 1994, given that Granville (and as
> Granville claims; every other mathematician in the world) already KNEW
> THERE WERE NO SOLUTIONS??????
Nobody, including Beal, knew that there are no solutions, and it
remains unknown today. The rarity of solutions, the likelihood
of no solutions existing, and the problem of ruling out further
solutions or finding new ones, were all publically documented
by various people before Beal's private correspondence in 1994.
With that history, there is no contribution whatsoever in someone
stating their personal expectation that the answer to the question
will indeed turn out to be "no solutions". As it is, both Darmon
(apparently prior to the 1993 searches for large solutions) and
Granville (in his Jan 1994 email) did publicize their opinions
about the likelihood of no solutions existing, so Beal doesn't
even contribute any minor novelty in that direction either.
None of this makes it less interesting or impressive that Beal
hit upon the problem on his own as an amateur. But his priority
claims are ridiculous.
> This is very interesting -- Hmmmmmmm. Andrew Granville claims he
> already knew Beal's conjecture (and that everyone already previously
> knew it). Hmmmmmmm. But in March of 1994, Granville asks in an email
> for solutions to the equation.
Actually, in January (not March) of 1994, he specifically mentions the
possibility of no more solutions, discusses (for whatever they are or
aren't worth) some of his personal opinions on the matter, and raises the
problem of finding
new solutions. The relevance of March 1994 is that by then, the
paper appears to have been available where Darmon and Granville
also call attention to the problem with all exponents > 2, and specifically
ask whether this constraint on the exponents rules out solutions. i.e. a
clear prior publication of the "Beal" problem.
> coud you pleeese help us
> ignorent illitorate peeple out here anderstand this haere thang???
So you admit the spelling pecularities reveal you as yet another
alias (there are 4 by now) for andy...@my-deja.com?
barr...@my-deja.com
sel...@my-deja.com wrote:
Please consult "History of the Theory of Numbers" Vol. 2 ( Diophantine
Analysis) 1920 ( reprinted by Chelsea in 1952 ) by L. E. Dickson
chapt. XXVI page 731 The statement: A(x^r) + B(y^s) = C(z^t) is present
in the heading. A comment on A(x^m) + B(y^m) = C(z^n) was made by
A.Desboves in 1879 ( Dickson, pg 749 )
C.M. Puima commented on A(x^p) + B(y^q) = 0(mod m) in 1882-3 ( dickson
pg 751
hope it helps
barry :-)
sel...@my-deja.com
question (you don't seem to understand that as you constantly confuse
the question with the answer), which certaintly dates back a long time,
the issue has always been who first reasoned that no solutions were
possible. Granville did indeed speculate rankly and incorrectly prior
to beal about only five solutions being possible for a broader form.
Granville was wrong and his guess was wrong. Beal was the first to
assert the conjecture in its correct form.
So why don't you tell us all again about how you, Andrew Granville,
once asked a class of students to look for solutions, or how you e-
mailed so and so in 1994 asking for solutions to Beal's conjecture.
These nonsense responses will certainly convince people that you really
knew it all along.
In article <3A6CB315...@y.z.com>,
Hull Loss Incident <x...@y.z.com> wrote:
Hull Loss Incident
sel...@my-deja.com wrote:
> Actually no one has ever been interested in who first asked the
> question
You (Beal) have the arrogant habit of speaking for everyone
else; the US corporate-tycoon equivalent of the Majestic Plural.
> (you don't seem to understand that as you constantly confuse
> the question with the answer), which certaintly dates back a long time,
> the issue has always been who first reasoned that no solutions were
> possible.
Both the question and the answer predate Beal.
Five months before Beal, in January 1994, Granville
wrote to hundreds of people on the NMBRTHRY list:
"It may be that these are all of the solutions to [FLT
with unequal exponent], but I thought that before
Beukers and Zagier got involved [in computing solutions],
so maybe I am wrong again."
As the last clause makes clear, this is an unambiguous
statement of the expectation that no more solutions
exist, which includes Beal's conjecture. (If it were
merely a reminder that some equation may turn out to
have no more solutions, it would be impossible to
be "wrong again" and the last clause would make no
sense.)
> Granville did indeed speculate rankly and incorrectly prior
> to beal about only five solutions being possible for a broader form.
> Granville was wrong and his guess was wrong. Beal was the first to
> assert the conjecture in its correct form.
Granville's Jan 1994 assertion has exactly the same status
as Beal's statement: correct as far as is currently known.
He lists all 10 solutions in the email, not "five solutions"
as you claim. Thus, he publically asserted the conjecture
5 months before Beal. Deal with it rather than continuing
to duck the issue.
Dave Rusin
>the issue has always been who first reasoned that no solutions were
>possible.
What's the difference between "reasoned" and "guessed"?
Hull Loss Incident
Some statements from Mr Beal are quoted below. See
http://x71.deja.com/[ST_rn=ps]/getdoc.xp?AN=708100483&CONTEXT=980234947.2048262182&hitnum=0
In that article, he asserts that 100^100 is "millions
of orders of magnitude" larger than 10^15. And
on the subject of conjectures...
1. "THAT'S ALL A CONJECTURE IS, A REASONED DECLARATION OF OPINION LACKING
PROOF"
2.
" >Asserting that the statement is "reasoned" is also just
> a comment about your own private thought processes.
THAT IS TRUE, IT IS ALSO TRUE OF ANY SIMILIAR STATEMENT THAT ANYONE MAKES.
WHETHER THE REASONING IS ADEQUETE OR NOT IS GENERALLY REVEALED BY THE
LIFESPAN OF THE CONJECTURE."
3. "BEAL DIDN'T CONSIDER ANY OF HIS COMPUTER
SEARCHES PARTICULARLY SIGNIFICANT AND HAS NEVER CLAIMED THAT THEY WERE
EARTH SHAKING. THEY WERE HOWEVER, THE MOST EXHAUSTIVE DONE AT THAT TIME AND
SUFFICIENT TO ALLOW BEAL TO REASON AN UNKNOWN AND INTERESTING CONJECTURE."
Hull Loss Incident
> Actually no one has ever been interested in who first asked the
> question [...] the issue has always been who first reasoned that no
> solutions were possible.
Earlier you apparently stated the opposite:
"WHETHER IT [Beal's conjecture] WAS A LUCKY ACCIDENT OR A REASONED (TO
WHATEVER STANDARD GRANVILLE BELIEVES THE TERM REQUIRES) CONCLUSION ISN'T
EVEN RELEVANT." --- sel...@my-deja.com, 23 Dec 2000.