Elegant 17th-Century Proof of Fermat's Last Theorem
David Fabian
any ideas about how I should capitalize on it?
(On another note, I wonder about the validity of Wiles' proof. As
complex as it is, it does not seen so safe to assume that there *are*
no more holes in it, just because the few mathematicians who under-
stand it *cannot find* any more holes in it.)
Dave
The text enclosed below is from:
http://www.nsf.gov/discoveries/disc_summ.jsp?cntn_id=100029&org=DMS
=============================================
The most famous note ever scribbled in a book may very well be,
"I have a truly marvelous demonstration of this proposition that this
margin is too narrow to contain."
In the 1630s, French mathematician Pierre de Fermat jotted that
unassuming statement and set a thorny challenge for three centuries'
of mathematicians. He was referring to the claim that there are no
positive integers for which x^n + y^n = z^n when n is greater than 2.
Fermat never got around to writing down his "marvelous" proof,
and the margin note wasn't discovered until after his death.
For 350 years, Fermat's statement was known in mathematical cir-
cles as Fermat's Last Theorem, despite remaining stubbornly un-
proved.
[Snipped story about Taniyama-Shimura conjecture & Wiles' proof,
using 20th-century math.]
And what of Fermat? Because of the complexity the final proof --
certainly too large to fit in a book margin -- and because many
techniques Wiles used had not been invented in Fermat's day, it's
been suggested that Fermat didn't really have a proof after all.
Even so, idealists, diehards and enthusiasts continue the quest for
the more elegant and "truly marvelous demonstration" that they
believe Fermat had in mind.
-- David Hart
=============================================
Gareth Erskine-Jones
<david.m...@sbcglobal.net> wrote:
>Assuming I have found Fermat's elegant proof, does anyone have
>any ideas about how I should capitalize on it?
Publish it?
GEJ
A N Niel
<david.m...@sbcglobal.net> wrote:
> Assuming I have found Fermat's elegant proof, does anyone have
> any ideas about how I should capitalize on it?
There is no money in it. If you are a mathematician, it would
add a certain amount to your reputation. That's it.
However, it is extremely likely that the proof is flawed. In which
case, there is still no money in it, but if you are a mathematician
it would decrease your reputation.
If you want advice of what to do ... Put the proof on the web, send
a link here. On occasion readers of sci.math have offered sensible
criticism for such posts.
Don Del Grande
>Assuming I have found Fermat's elegant proof, does anyone have
>any ideas about how I should capitalize on it?
Somebody claimed a few years ago that they had figured out what
"Fermat's marvelous proof" was, and offered the solution on eBay for
$1,000,000. (Presumably, there were no takers.)
-- Don
W. Dale Hall
> Assuming I have found Fermat's elegant proof, does anyone have any ideas
> about how I should capitalize on it?
>
... stuff deleted ...
>
> -- David Hart
> =============================================
>
>
>
I'd take the letter at the beginning of each sentence, including
those direct quotes that include the beginnings of sentences,
and the first letter of each proper name, and place it in upper
case. If you refer to days of the week, months of the year, and
any deity, I'd place the initial letter of each of these into
upper case as well. For all other letters, I'd use lower case.
howzat?
Dave Parker
David Fabian
And how does that make money?
David Fabian
Thank you for the advice; but I am interested in making money, not
improving my reputation.
David Fabian
That is right... so I pulled the offer. (However, I said that the proof
would take only one page, but it will actually take about ten pages.)
Information can be sold to multiple buyers via eBay (as soon as eBay
enhances their software). (A few years ago, I emailed a person at
eBay, whose job title was "Innovative Disruptor" [one who disrupts
the normal flow of business, in order to make an improvement], but
he never wrote back.)
For example, I would have paid at least one penny to find out how
the pyramids were built (i.e. they rolled the blocks of stone, by
strapping on curved pieces of wood, which effectively turned the
blocks into cylinders); so the person who actually found one of the
pieces of wood could have made a fortune.
An information auction would work like this: The seller states that
he will release his information for a certain amount of money. Each
buyer would state that he will buy the information for whatever it is
worth to him. Optionally, a buyer can stipulate that his offer is good
only if (1) each other buyer pays at least a certain amount, or (2)
there is a specific limited number of buyers. (Of course, the money
would stay in escrow until the information was delivered.)
Dave
Carl G.
"David Fabian" <david.m...@sbcglobal.net> wrote in message
news:JPC7l.12709$YU2....@nlpi066.nbdc.sbc.com...
> Assuming I have found Fermat's elegant proof, does anyone have any ideas
> about how I should capitalize on it?
>
been verified as authentic, it could likely be sold at auction for nice sum.
It would not have to be a valid proof. Indeed, many present-day
mathematicians would be relieved if Fermat made an error in his marginal
claim.
If there is no physical document, then the proof by itself may or may not be
profitable. For example, if the proof led to better cryptographic
algorithms, it might be profitable. It's unlikely that the proof would be
profitable to you, unless you developed the profitable algorithms.
Below is one way to capitalize on the theorem itself:
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
If an integer n is greater than 2,
then the equation a^n + b^n = c^n
has no solutions in non-zero
integers a, b, and c
Carl G.
David R Tribble
>> Assuming I have found Fermat's elegant proof, does anyone have
>> any ideas about how I should capitalize on it?
>
Gareth Erskine-Jones wrote:
>> Publish it?
>
David Fabian wrote:
> And how does that make money?
By cashing the royalty checks from the publisher, the same way
everyone else makes money by publishing books?
Eric Sosman
Keep control of the movie rights.
--
Eric Sosman
eso...@ieee-dot-org.invalid
Gareth Erskine-Jones
<david.m...@sbcglobal.net> wrote:
>"Gareth Erskine-Jones" <g...@uberdog.net> wrote in message news:piiul49qa27ms1ec5...@4ax.com...
>> On Fri, 2 Jan 2009 23:36:37 -0600, "David Fabian"
>> <david.m...@sbcglobal.net> wrote:
>>
>>>Assuming I have found Fermat's elegant proof, does anyone have
>>>any ideas about how I should capitalize on it?
>>
>> Publish it?
>>
>> GEJ
>
>And how does that make money?
If it was a much simpler proof than that of Wiles, you'd achieve
recognition (obviously amongst mathematicians, but also to a lesser
extent amongst the general public). I'd imagine it wouldn't do any
harm for your career as a professional mathematician, and you'd
probably get on a chat show or two.
Other than that, I don't see any way to profit from it...
GEJ
David Fabian
>
> By cashing the royalty checks from the publisher, the same way
> everyone else makes money by publishing books?
The proof will be only about ten pages, so it would have to be
published in a journal (unless someone has the time to expand it
into a book, by adding lots of fluff), which would require that I
(1) give up all copyrights, and (2) take what little money the
publisher decides to toss me.
Gareth Erskine-Jones
Then I suspect you're barking up the wrong tree. Proving a theorem
that has already been proved ... I don't see how you can make money
from that.
Of course, if you could figure a way of making a fortune from proving
theorems which had already been proved - you could possibly patent
that technique, and then make money from that...
Here's a more interesting question (IMHO) - you discover an algorithm
to factor large numbers very rapidly. How do you capitalize on that?
How would you even survive that? You publish on the net, and most of
the world's cryto systems are useless. You go to your government, and
... well, you don't come back.
GEJ
Kevin Stone
> about how I should capitalize on it?
By your subject are we to assume that you've unearthed an existing 350 year
old document with the proof?
A pretty valuable piece of parchment methinks.
--
Kev
David R Tribble
>> By cashing the royalty checks from the publisher, the same way
>> everyone else makes money by publishing books?
>
David Fabian wrote:
> The proof will be only about ten pages, so it would have to be
> published in a journal (unless someone has the time to expand it
> into a book, by adding lots of fluff), which would require that I
> (1) give up all copyrights, and (2) take what little money the
> publisher decides to toss me.
They can copyright the text of your proof article, but they
can't copyright the proof itself. You knew that, right?
So then you're free to write another whole book about your
discovery, how you came up with the idea, the history of
the problem, etc. Just like most pop-math authors do.
Marilyn vos Savant wrote a book about Wile's proof just
a few months after he published it, and she seems to be
doing okay.
spudnik
per gross; he didn't make a single mistake,
that has come down to us!
so, does it use "congruence surds?"
> It would not have to be a valid proof. Indeed, many present-day
thus:
isn't that an award for journalism,
not the "actual hyper-hype physics?"
Dick Hoagland is dumber than a pile of rocks,
just by comparison with the Face and Genitals
on Mars.
> Entity will say: the Angstrom Institude got it right, the Angstrom
> Hoagland got it right, too: won a prize for hyperdimensional
thus:
I will guess that Wookiepoopya has no rational explanation
for cropcircles, other than "Doug and Dave with 2by9s,"
the obviously fake Druids.
David Fabian
> On Sat, 3 Jan 2009 14:28:40 -0600, "David Fabian"
> <david.m...@sbcglobal.net> wrote:
> >
>>Thank you for the advice; but I am interested in making money, not
>>improving my reputation.
>
> Then I suspect you're barking up the wrong tree. Proving a theorem
> that has already been proved ... I don't see how you can make money
> from that.
There are many mathematicians who would like to see a proof (especially
one that Fermat himself probably had in mild) that is much simpler than
Wiles' proof... so I should be able to capitalize in some way.
> Of course, if you could figure a way of making a fortune from proving
> theorems which had already been proved - you could possibly patent
> that technique, and then make money from that...
You are being facetious and|or sarcastic.
> Here's a more interesting question (IMHO) - you discover an algorithm
> to factor large numbers very rapidly. How do you capitalize on that?
> How would you even survive that? You publish on the net, and most of
> the world's cryto systems are useless. You go to your government, and
> ... well, you don't come back.
You are right. There is not much point in pursuing a goal, when success
costs you your life.
Dave
> GEJ
David Fabian
>> Assuming I have found Fermat's elegant proof, does anyone have any ideas
>> about how I should capitalize on it?
>
> By your subject are we to assume that you've unearthed an existing 350 year
> old document with the proof?
No. I devised the proof using the math tools that were available to Fermat
in the 17th-century.
Dave
Matt
wrote:
> "Kevin Stone" <newsacco...@hotpop.com> wrote in messagenews:6sa9iiF...@mid.individual.net...
> >> Assuming I have found Fermat's elegant proof, does anyone have any ideas
> >> about how I should capitalize on it?
>
> > By your subject are we to assume that you've unearthed an existing 350 year
> > old document with the proof?
>
> No. I devised the proof using the math tools that were available to Fermat
> in the 17th-century.
Has it been checked by anyone else? The default position, until there
is evidence otherwise, has to be that your proof is wrong. I hope for
your sake it's correct, but realistically the chances are slim.
CBFalconer
>
... snip ...
>
> If the proof was written in Fermat's own hand, then once the
> document has been verified as authentic, it could likely be sold
> at auction for nice sum. It would not have to be a valid proof.
> Indeed, many present-day mathematicians would be relieved if
> Fermat made an error in his marginal claim.
Why not face it? It is IMPOSSIBLE to prove Fermat made a mistake.
It IS possible to prove he was correct. It hasn't been done.
--
[mail]: Chuck F (cbfalconer at maineline dot net)
[page]: <http://cbfalconer.home.att.net>
Try the download section.
Don Del Grande
> Don Del Grande wrote:
>
>> David Fabian wrote:
>>
>>>Assuming I have found Fermat's elegant proof, does anyone have
>>>any ideas about how I should capitalize on it?
>>
>> Somebody claimed a few years ago that they had figured out what
>> "Fermat's marvelous proof" was, and offered the solution on eBay for
>> $1,000,000. (Presumably, there were no takers.)
>
>That is right... so I pulled the offer. (However, I said that the proof
>would take only one page, but it will actually take about ten pages.)
Pardon me for asking, but (a) just how much money are you looking to
make from this proof, and (b) what guarantee does anybody have that,
if the proof is incorrect, they won't have to pay anything?
-- Don
David Fabian
> David Fabian wrote:
>
>> Don Del Grande wrote:
>>
>>> David Fabian wrote:
>>>
>>>>Assuming I have found Fermat's elegant proof, does anyone have
>>>>any ideas about how I should capitalize on it?
>>>
>>> Somebody claimed a few years ago that they had figured out what
>>> "Fermat's marvelous proof" was, and offered the solution on eBay for
>>> $1,000,000. (Presumably, there were no takers.)
>>
>>That is right... so I pulled the offer. (However, I said that the proof
>>would take only one page, but it will actually take about ten pages.)
>
> Pardon me for asking, but (a) just how much money are you looking to
> make from this proof, and
I don't know. If eBay enhances their software to sell information
(see other thread for details), I would probably come up with an
asking price. Every year or so, I would, of course, have to lower
my price. On the other hand, some auctions do not even require
the seller to commit to an asking price -- if no one bids what the
seller wants by a certain time, the auction is off until a later date.
But that strategy seems kind of cheesy to me.
> (b) what guarantee does anybody have that,
> if the proof is incorrect, they won't have to pay anything?
Please read the final sentence of my previous post.
Dave
> -- Don
Mensanator
You forgot to add "...despite being as stupid as JSH."
Mensanator
wrote:
> "A N Niel" <ann...@nym.alias.net.invalid> wrote in messagenews:030120090857076134%ann...@nym.alias.net.invalid...
>
>
>
>
>
> > <david.m.fab...@sbcglobal.net> wrote:
>
> >> Assuming I have found Fermat's elegant proof, does anyone have
> >> any ideas about how I should capitalize on it?
>
> > There is no money in it. �If you are a mathematician, it would
> > add a certain amount to your reputation. �That's it.
>
> > However, it is extremely likely that the proof is flawed. �In which
> > case, there is still no money in it, but if you are a mathematician
> > it would decrease your reputation.
>
> > If you want advice of what to do ... Put the proof on the web, send
> > a link here. �On occasion readers of sci.math have offered sensible
> > criticism for such posts.
>
> Thank you for the advice; but I am interested in making money, not
> improving my reputation.
Ask JSH, he knows all about such matters. He claimed to
have proved it also, demonstarted that Wiles did not prove it,
and his only motive was money and chicks. I'm sure he can
give you all kinds of good advice.
David Fabian
>
> Has it been checked by anyone else?
No one but myself.
> The default position, until there is evidence otherwise,
> has to be that your proof is wrong.
The fact that I have solved many difficult logic problems
(e.g. http://www.eskimo.com/~miyaguch/powerresults.html)
indicates that there is at least a better-than-average chance
that I have solved *this* problem (although it does not logic-
ally prove it [argumentum ad verecundiam]).
> I hope for your sake it's correct, but realistically the
> chances are slim.
The chances are slim from your point of view, because you
have not yet seen my work.
Dave
David Fabian
>
> They can copyright the text of your proof article, but they
> can't copyright the proof itself. You knew that, right?
No, I didn't. But the text is what sells...
> So then you're free to write another whole book about your
> discovery, how you came up with the idea, the history of
> the problem, etc. Just like most pop-math authors do.
> Marilyn vos Savant wrote a book about Wile's proof just
> a few months after he published it, and she seems to be
> doing okay.
She is married to a famous heart surgeon... of course she
is doing well!
(Just teasing, Marilyn!)
Let me rephrase that... "Marilyn Savant is brilliant... of
course she is doing well."
Dave
Christopher Henrich
<16cc27b7-3c57-4139...@40g2000prx.googlegroups.com>,
Matt <matt271...@yahoo.co.uk> wrote:
Getting it checked is possible, but would be expensive. Mr. Fabian could
get a professional mathematician to check his work, for a fee, with a
non-disclosure agreement. I think it would take a lawyer to draft the
non-disclosure agreement. There's another fee, up front. Mr. F. is
going to have to spend a few thousand dollars, at least, to put himself
in position to even hope for earning anything directly from his proof.
So how does anybody ever get any benefit from doing pure mathematics?
Indirectly. One must "publish." If someone publishes good stuff, he
gains a reputation among the people whom he hopes to call his peers;
then he may get research grants or salaried positions.
--
Christopher J. Henrich
chen...@monmouth.com
http://www.mathinteract.com
Carl G.
"CBFalconer" <cbfal...@yahoo.com> wrote in message
news:49601D75...@yahoo.com...
> "Carl G." wrote:
>>
> ... snip ...
>>
>> If the proof was written in Fermat's own hand, then once the
>> document has been verified as authentic, it could likely be sold
>> at auction for nice sum. It would not have to be a valid proof.
>> Indeed, many present-day mathematicians would be relieved if
>> Fermat made an error in his marginal claim.
>
> Why not face it? It is IMPOSSIBLE to prove Fermat made a mistake.
> It IS possible to prove he was correct. It hasn't been done.
Why would a document, containing an invalid proof written by Fermat himself,
not be considered a reasonable proof that he made a mistake? Is it
impossible that such a document can exist? Is there a complete list of all
documents created by Fermat?
I agree with the following anagram (found by another):
FERMAT'S LAST THEOREM = REALM OF THE SMARTEST.
There _is_ a simple proof of the theorem that is based on the same
techniques used to prove Goldbach's conjecture, but I don't have enough ink
remaining to print it here. ;-)
Carl G.
Mark Galeck
Here is how.
Offer a bet to everybody that your proof is correct in really attractive odds. Say, if the proof is incorrect, you pay them x sum of US dollars. If correct, the person pays you 10x sum of US dollars.
Collect the bets over a certain period of time, say 2 months. The procedure to verify the proof, is for you to choose, any mathematician in the math department of any of the top 10 research universities in the US (as published by the US News and World Report), and ask to verify the proof, for a fee, say 10% of your winnings from the bet. That person's judgement would be final. Since you are sure the proof is correct, and you are sure it is done used only 17-th century methods, and it is only 10 pages, so any mathematician in a top research department, would have no problem verifying it, and you have the choice of whom to pick, then you should have no problem with this method of verification.
OK, with the general public, probably you will not get many bettors. However, I can guarantee you, that every research mathematician in the world (and there are thousands), will be ready to bet you any amount of money. Try and you will see. Of course you will not get that many bettors, probably, what would happen is you would need a lawyer, to guarantee your net worth, and then make sure you are not risking more than your net worth, and then to make sure the mathematicians are not risking more than theirs. I guarantee you, that after all this is in place, you will immediately get your whole entire net worth distributed in bets promises, among probably only a few mathematicians who will each bet for the maximal amount they can, and consider themselves lucky for getting in first on this opportunity.
Since you are sure you are correct, you will multiply your net worth by 10, minus attorneys fees and the verifier.
David Fabian
>
> Getting it checked is possible, but would be expensive. Mr. Fabian
> could get a professional mathematician to check his work, for a fee,
> with a non-disclosure agreement.
I already have a friend who agreed to check my proof for free. He has
a PhD in computer science, has almost enough credit for a PhD in math,
and he graduated from Harvard in three years. You appear to live in
the same region:
http://www.monmouth.com/~colonel/
> I think it would take a lawyer to draft the non-disclosure agreement.
> There's another fee, up front. Mr. F. is going to have to spend a few
> thousand dollars, at least, to put himself in position to even hope for
> earning anything directly from his proof.
Non-disclosure agreements are standard forms. They do not really
require a lawyer.
> So how does anybody ever get any benefit from doing pure mathematics?
> Indirectly. One must "publish." If someone publishes good stuff, he
> gains a reputation among the people whom he hopes to call his peers;
> then he may get research grants or salaried positions.
Pure mathematics is just a hobby for me (so I do not need to publish,
gain recognition, and obtain research grants or a job). But I am still
not convinced that it is impossible for a hobbyist to make money.
I have already gained a reputation in my profession (software develop-
ment) and already have a good-paying job. However, research grants
are totally out of the question, because I am self-taught and do not have
the time or inclination to obtain the required college degree (i.e. research
grants are awarded by and for academia).
By the way, here are two papers that *others* have published about
my work:
http://front.math.ucdavis.edu/0803.1245
http://adsabs.harvard.edu/abs/1987SPIE..755..114C
Dave
Mark Galeck
> Wiles' proof. As
> complex as it is, it does not seen so safe to assume
> that there *are*
> no more holes in it, just because the few
> mathematicians who under-
> stand it *cannot find* any more holes in it.)
>
Of course, there may be holes in it. However, in case you thought that "proof" meant - "absolute proof beyond any doubt - the chance of being wrong is precisely 0" - that is not what "proof" means. Such "absolute proofs" are not possible in principle, in math or any other science.
Instead, the definition of "proof", is : an argument, that convinces the established top authorities on the subject. So, Wiles's argument is a proof. In general science, it sometimes happens, that "proof" at one time, has a fault discovered later and it is not longer considered a proof by the top authorities. This also happens in math, but very very rarely. That is why math is considered a much more precise science, than other sciences.
David Fabian
Mark, your ideas are excellent!!! Give me some time to think about how I can pull this off... I must at least cut you in on my
winnings!
Dave
David Fabian
I agree with you absolutely -- my statement was ignorant.
I just wish I had the time to study higher math... then I could at least understand and appreciate Wiles' proof.
Dave
David Fabian
>
> You forgot to add "...despite being as stupid as JSH."
I do not know much about JSH's knowledge or abilities,
but you should not attack him, because he is at least trying.
Dave
mike3
Movie?
mike3
> "David Fabian" <david.m.fab...@sbcglobal.net> wrote in message
>
> news:JPC7l.12709$YU2....@nlpi066.nbdc.sbc.com...> Assuming I have found Fermat's elegant proof, does anyone have any ideas
> > about how I should capitalize on it?
>
> been verified as authentic, it could likely be sold at auction for nice sum.
> It would not have to be a valid proof. Indeed, many present-day
> mathematicians would be relieved if Fermat made an error in his marginal
> claim.
>
This I am curious about. How would the proof being valid be so bad for
mathematics,
anyway?
> If there is no physical document, then the proof by itself may or may not be
> profitable. For example, if the proof led to better cryptographic
> algorithms, it might be profitable. It's unlikely that the proof would be
> profitable to you, unless you developed the profitable algorithms.
>
> Below is one way to capitalize on the theorem itself:
>
> IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
> If an integer n is greater than 2,
> then the equation a^n + b^n = c^n
> has no solutions in non-zero
> integers a, b, and c
>
> Carl G.
Angus Rodgers
<mark_...@pacbell.net> wrote:
>>On another note, I wonder about the validity of
>> Wiles' proof. As
>> complex as it is, it does not seen so safe to assume
>> that there *are*
>> no more holes in it, just because the few
>> mathematicians who under-
>> stand it *cannot find* any more holes in it.)
>>
>
>Of course, there may be holes in it. However, in case you thought
>that "proof" meant - "absolute proof beyond any doubt - the chance
>of being wrong is precisely 0" - that is not what "proof" means.
>Such "absolute proofs" are not possible in principle, in math or
>any other science.
True.
>Instead, the definition of "proof", is : an argument, that convinces
>the established top authorities on the subject. So, Wiles's argument
>is a proof. In general science, it sometimes happens, that "proof"
>at one time, has a fault discovered later and it is not longer
>considered a proof by the top authorities. This also happens in math,
>but very very rarely. That is why math is considered a much more
>precise science, than other sciences.
But that's not quite true. If an argument convinces the top
authorities, what they are convinced of is not the fact that
the argument is convincing to them (!), but that it is valid!
Of course, they may be wrongly convinced, and this has indeed
been known to happen in some cases; however, this cannot mean
that a proof makes no absolute claim to validity, and that a
sociological definition must be used. Absolute claims do not
imply infallibility - indeed, the boot is on the other foot,
and if the top authorities in mathematics believed that all
that a proof has to do is to convince them, they would indeed
believe themselves to be infallible! Also, what would happen
if one "top authority" were convinced by a proof, and another
wasn't? Would they have to wrestle for it? :-)
Your error here (or what seems to me to be an error, because I
am certainly not infallible!) seems to be an odd inversion of
James Harris's error in defining a mathematical proof in such
a way that it /cannot/ be fallacious.
Perhaps it would be clearer if I said that your argument is
analogous to claiming that for a person to be guilty of a
crime is equivalent to them being found guilty of it in a
court of law - making this claim on the reasonable grounds
that no court of law is infallible, which in fact supports
the opposite conclusion! I think the fallacy is easier to
see here, where the degree of certainty is less than it is
in mathematics.
(I need to clarify my own thinking about this, but even if I
have not identified your error correctly, I am pretty sure
there is something amiss in your argument, as with James's.)
--
Angus Rodgers
Mike Williams
>>
>> By cashing the royalty checks from the publisher, the same way
>> everyone else makes money by publishing books?
>
>published in a journal (unless someone has the time to expand it into a
>book, by adding lots of fluff), which would require that I (1) give up
>all copyrights, and (2) take what little money the publisher decides to
>toss me.
It wouldn't be possible to get it published in a professional journal,
because they receive so many erroneous proofs that they no longer
consider such submissions. It can take a lot of effort to spot a subtle
error in 10 pages of equations, and the likelihood of an unknown
mathematician coming up with a valid proof isn't worth the effort.
--
Mike Williams
Gentleman of Leisure
N. Silver
> Pure mathematics is just a hobby for me (so I do not need to publish, gain
> recognition, and obtain research grants or a job). But I am still not
> convinced that it is impossible for a hobbyist to make money.
It's close to impossible.
> I have already gained a reputation in my profession (software develop-
> ment) and already have a good-paying job. However, research grants are
> totally out of the question, because I am self-taught and do not have the
> time or inclination to obtain the required college degree (i.e. research
> grants are awarded by and for academia).
>
> By the way, here are two papers that *others* have published about my
> work:
> http://front.math.ucdavis.edu/0803.1245
> http://adsabs.harvard.edu/abs/1987SPIE..755..114C
The papers are irrelevant to your claim. Moreover, one of the papers you
cite
is close to 30 years old. It all adds up to you being a crank and getting
crankier.
Richard Heathfield
> On Jan 3, 1:56 pm, "Carl G." <cgin...@socal.rr.com> wrote:
<snip>
>> Indeed, many present-day mathematicians would be relieved if
>> Fermat made an error in his marginal claim.
>>
>
> This I am curious about. How would the proof being valid be so bad
> for mathematics,
> anyway?
It would actually be very /good/ for mathematics, if it contained
some "OH! OF COURSE!" insight that everyone's just failed to spot
in the last 350 years. It might, however, be considered bad for
matheticians! At least, bad for those who had tried to prove FLT.
As Euler famously pointed out, V + F = E + 2 - where V is the
mathematician, F is the number of faces he has, and E is the egg.
--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999
Angus Rodgers
<mike...@yahoo.com> wrote:
>On Jan 3, 1:56 pm, "Carl G." <cgin...@socal.rr.com> wrote:
>> "David Fabian" <david.m.fab...@sbcglobal.net> wrote in message
>> news:JPC7l.12709$YU2....@nlpi066.nbdc.sbc.com...
>>
>> > Assuming I have
>> > found Fermat's elegant proof, does anyone have any ideas
>> > about how I should capitalize on it?
>>
>> If the proof was written in Fermat's own hand, then once the document has
>> been verified as authentic, it could likely be sold at auction for nice sum.
>> It would not have to be a valid proof. Indeed, many present-day
>> mathematicians would be relieved if Fermat made an error in his marginal
>> claim.
>
>This I am curious about. How would the proof being valid be so bad for
>mathematics, anyway?
It seemed a curious judgement to me, too. Of course, I'm no
professional mathematician, but, for what it's worth, I would
be delighted if Fabian's (or anyone else's) claimed elementary
proof of FLT were valid; and my feeling is that most professional
mathematicians would be even more delighted than me. (OK, perhaps
Andrew Wiles wouldn't, but that would be perfectly understandable!)
--
Angus Rodgers
Angus Rodgers
Very. :-)
--
Angus Rodgers
Marc 'BlackJack' Rintsch
Yep. And merchandising of course!
Ciao,
Marc 'BlackJack' Rintsch
Aatu Koskensilta
> Also, what would happen if one "top authority" were convinced by a
> proof, and another wasn't? Would they have to wrestle for it? :-)
Many top authorities in set theory are convinced that determinacy
holds in L(R) (the universe constructible sets relative to the reals),
on basis of a proof of that fact from large cardinal axioms. Others do
not accept these axioms. The two cordially agree to disagree, one
party interpreting the proof as establishing determinacy in L(R), the
other party as establishing merely that if large cardinals exist[1]
then determinacy holds in L(R).
Some intuitionists hold that classical mathematics is unjustified,
theological, metaphysical, and so on, and consequently refuse to
accept as proven theorems that rely on principles that are justified
on the classical understanding of mathematics but not on the
intuitionistic. And so on. What one thinks of this disagreement is a
matter of personal taste, mostly, and it is entirely possible to
happily agree that something is justified on the classical
understanding of the mathematical notions involved, but not on the
intuitionistic, finding this discovery in itself highly interesting,
without committing to any implicit or explicit criticism of classical
reasoning. (This eclectic "Kreiselian" attitude is of course
profoundly unsatisfying to the thoroughgoing intuitionist.)
Not much can be made of such disagreements, however -- they are indeed
mostly a matter of personal inclinations, preferences, what one finds
intellectually pleasing and what not; we have no theoretical account
of what makes some mathematical principles acceptable and others
unacceptable, so we can in the abstract really do not much more than
note that this is so.
These disagreements are no doubt familiar to many, so why bring them
up? While there is a disagreement over whether e.g. classical logic is
applicable for infinite domains, whether large cardinal axioms are to
be accepted in the same sense that, say, the induction principle or
choice is, there is no disagreement over what counts, in an idealised
sense, as a correct classical or intuitionistic proof from these or
those principles. Thus the disagreement is, so to speak, localised in
the question of acceptability of this or that -- it indeed has not
much to do with proofs at all! So, to answer the question that began
this paragraph, the reason for introducing these disagreements is to
brush them off as irrelevant to the issue at hand. (For otherwise
someone would surely blather about them in an even more tedious manner
than I have.)
The issue was the acceptability of /proofs/, and possible disagreement
over the correctness of a proof. This question arises whatever
conception of mathematics one adopts, whatever mathematical principles
one accepts (or refuses to accept). Indeed, even though pondering
mind-bogglingly large cardinals or the justification of the law of
excluded middle might be very exciting, most disagreements over
correctness of proofs we actually encounter have absolutely nothing to
do with such issues. Rather, they concern whether or not the proof in
question adheres to the idealised criteria of correctness, in deriving
the result by means of logical steps from accepted principles (in the
relevant community of mathematicians, whatever those principles
are). A proof might be byzantine, opaque, poorly written, it might
rely on unpublished results, folk-lore, a lemma in the 1924 issue of
the Wallachian Annals of Mathematics no-one's ever read, and so on. In
practical terms, what is to be done in such cases is clear: the
unpublished results must be scrutinised, the missing steps filled in,
obscure passages clarified, telegraphic remarks elaborated, and so
on. However difficult this might be, it is nevertheless clear what we
are to do, and why: we must show to our satisfaction that the proof is
indeed correct, in the sense of being a presentation of logically
correct reasoning. And, given that we are not infallible, we might be
satisfied even if we shouldn't be. What is important is that there are
criteria, criteria we ourselves recognise, on which this would count
as a mistake; that in this sense a proof being correct is not merely a
matter of our finding it so. This is borne out by the fact that when
there is disagreement over the correctness of proofs, the debate does
not end by the two sides merely agreeing that for some the proof is
correct while for others it is not.
To proceed beyond these general reflections, it would be necessary to
consider cases of actual disagreement, e.g. the four-colour theorem,
Poincare conjecture, and so on, and to see how we -- or, rather, the
relevant experts -- in fact react in face of disagreement over
correctness of proofs. But I'm off for my morning tea so I'll leave
that for others.
> Perhaps it would be clearer if I said that your argument is
> analogous to claiming that for a person to be guilty of a crime is
> equivalent to them being found guilty of it in a court of law -
> making this claim on the reasonable grounds that no court of law is
> infallible, which in fact supports the opposite conclusion! I think
> the fallacy is easier to see here, where the degree of certainty is
> less than it is in mathematics.
Quite so. The problem with all sorts of naive instrumentalist accounts
of notions such as truth or guilt is that they make it entirely
unintelligible how or why methods for finding out truth or guilt could
be assessed. Less naive accounts exist, of course, and it is possible
to make a philosophical career out of studying them, whatever good
that does to anyone.
Footnotes:
[1] We don't actually need existence here, merely "moral"
existence. That is, if determinacy holds in L(R) there are inner
models of set theory with all sorts of nice properties in which there
are cardinals satisfying the relevant largeness conditions -- even if
these cardinals do not actually satisfy the conditions outside the
inner model. Sometimes this observation is put in terms of
equi-consistency, but that results in ridiculous understatement.
--
Aatu Koskensilta (aatu.kos...@uta.fi)
"Wovon man nicht sprechen kann, darüber muss man schweigen"
- Ludwig Wittgenstein, Tractatus Logico-Philosophicus
Kevin Stone
> about how I should capitalize on it?
How about a wager with someone?
You each stake a million dollars and if your 'proof' is flawed, then you
lose your million.
Sound like an idea?
Actually, surely someone clever enough to find a proof doesn't need our
help? The interviews, on radio and TV, along with the books will make you a
wealthy man.
--
Kev
Mike Williams
>> Assuming I have found Fermat's elegant proof, does anyone have any ideas
>> about how I should capitalize on it?
>
>How about a wager with someone?
>
>You each stake a million dollars and if your 'proof' is flawed, then you
>lose your million.
>
>Sound like an idea?
It sounds like an idea to me. I don't have a million to bet against you,
but I'd be in for ten thousand. All you need now is to find another 99
people like me, and an a procedure for deciding whether the proof is
flawed that we can all agree on.
Nick
If I had any confidence he could find the million he'd need I'd be in
for it - put me down for 10000 quid (which I don't have, but which I
could find if I absolutely had to).
--
Online waterways route planner: http://canalplan.org.uk
development version: http://canalplan.eu
Denis Feldmann
Denis Feldmann
> On Jan 3, 1:56 pm, "Carl G." <cgin...@socal.rr.com> wrote:
>> "David Fabian" <david.m.fab...@sbcglobal.net> wrote in message
>>
>> news:JPC7l.12709$YU2....@nlpi066.nbdc.sbc.com...> Assuming I have found Fermat's elegant proof, does anyone have any ideas
>>> about how I should capitalize on it?
>> If the proof was written in Fermat's own hand, then once the document has
>> been verified as authentic, it could likely be sold at auction for nice sum.
>> It would not have to be a valid proof. Indeed, many present-day
>> mathematicians would be relieved if Fermat made an error in his marginal
>> claim.
>>
>
> This I am curious about. How would the proof being valid be so bad for
> mathematics,
> anyway?
1) Because it would show 350 years efforts of the best minds missed a
simple proof 2) because it would show that our proofs that such a thing
is impossible were wrong 3) because it would show that the very strong
arguments we have (i.e. the letter to Freniscle) showing Fermat was
aware of his mistake are somehow wrong...
Denis Feldmann
trying has *no* value by itself. See "Darwin prize" to illustrate what
I mean...
amy666
> David Fabian a écrit :
> > "Mensanator" <mensa...@aol.com> wrote in message
> >
> news:8c05e202-b3c8-4fe0-87a5-aedfc8f93d3f@w1g2000prm.g
> ooglegroups.com...
> >>
> >> You forgot to add "...despite being as stupid as
> JSH."
> >
> > I do not know much about JSH's knowledge or
> abilities, but you should
> > not attack him, because he is at least trying.
> >
> > Dave
> >
> This is enough to prove you are a crank...
i dont agree.
he might not know who JSH is.
( or did he say he does or read his stuff ? in that case your correct of course )
he might have gotten the idea that JSH is trying.
and thats not cranky but ...
but the thing is , JSH isnt even trying.
so , i would wait to call him a crank before he leaves sci.math or presents his FLT math.
however when the waiting is over you will probably be correct :)
regards
tommy1729
--CELKO--
These days, you put the ten pages into a theorem proving software
package and push a button. If you solved Fermat with just algebra and
a little calculus, this will be fairly quick work.
Angus Rodgers
A point of English usage: if I say that James is "very trying",
it's not a compliment!
--
Angus Rodgers
Angus Rodgers
<denis.feldm...@neuf.fr> wrote:
>mike3 a écrit :
>
>> This I am curious about. How would the proof being valid be so bad for
>> mathematics,
>> anyway?
>
>1) Because it would show 350 years efforts of the best minds missed a
>simple proof
That would be humiliating, but not bad for mathematics.
However ...
>2) because it would show that our proofs that such a thing
>is impossible were wrong
Oops! I didn't know about this. I thought the only argument against
there being an elementary proof was (1) above (which is heuristically
quite strong, but not a proof). Can you give a reference to an actual
proof of the impossibility?
>3) because it would show that the very strong
>arguments we have (i.e. the letter to Freniscle) showing Fermat was
>aware of his mistake are somehow wrong...
That would be confusing, but not bad for mathematics.
--
Angus Rodgers
Aatu Koskensilta
> On Sun, 04 Jan 2009 13:16:46 +0100, Denis Feldmann
> <denis.feldm...@neuf.fr> wrote:
>
> >2) because it would show that our proofs that such a thing
> >is impossible were wrong
>
> Oops! I didn't know about this.
Don't worry about it. There is no mathematical proof of the
impossibility of proving Fermat's last theorem by elementary means. It
would be very exciting, at least for logicians, if there were. I don't
know what Denis had in mind with his comment.
Denis Feldmann
> Angus Rodgers <twi...@bigfoot.com> writes:
>
>> On Sun, 04 Jan 2009 13:16:46 +0100, Denis Feldmann
>> <denis.feldm...@neuf.fr> wrote:
>>
>>> 2) because it would show that our proofs that such a thing
>>> is impossible were wrong
>> Oops! I didn't know about this.
>
> Don't worry about it. There is no mathematical proof of the
> impossibility of proving Fermat's last theorem by elementary means. It
> would be very exciting, at least for logicians, if there were. I don't
> know what Denis had in mind with his comment.
Well, mostly that a lot of elementary approaches are doomed (like the
fact there are solutions in Z_p, but no lifting from local to global,
, or the impossibility of using infinite descent, etc. See Hellgouach's
book, for instance) Of course, a real proof is indeed impossible (or at
least would come as a complete surprise...°
David Bernier
The December 2008 issue of the Notices of the AMS is about formal proofs and proof assistants,
which assist in developing formal proofs. There's an article by Thomas Hales,
who submitted a proof to Annals of Math. on the Kepler Conjecture.
After a year, the referees couldn't certify the proof, but had checked
sub-claims. Later, Hale started project Flyspeck (k is for Kepler),
whose aim is to arrive at a formal proof of the Kepler Conjecture.
So based on what's already been formalized, 10 pages at the undergraduate
level seems formalizable by "experts" in a reasonable amount of time.
AMS Notices, 12/2008:
http://www.ams.org/notices/200811/index.html
David Bernier
hagman
> On Sat, 3 Jan 2009 14:28:40 -0600, "David Fabian"
>
>
>
> <david.m.fab...@sbcglobal.net> wrote:
> >"A N Niel" <ann...@nym.alias.net.invalid> wrote in messagenews:030120090857076134%ann...@nym.alias.net.invalid...
> >> In article <JPC7l.12709$YU2.9...@nlpi066.nbdc.sbc.com>, David Fabian
> >> <david.m.fab...@sbcglobal.net> wrote:
>
> >>> Assuming I have found Fermat's elegant proof, does anyone have
> >>> any ideas about how I should capitalize on it?
>
> >> add a certain amount to your reputation. That's it.
>
> >> However, it is extremely likely that the proof is flawed. In which
> >> case, there is still no money in it, but if you are a mathematician
> >> it would decrease your reputation.
>
> >> If you want advice of what to do ... Put the proof on the web, send
> >> a link here. On occasion readers of sci.math have offered sensible
> >> criticism for such posts.
>
> >Thank you for the advice; but I am interested in making money, not
> >improving my reputation.
>
> Then I suspect you're barking up the wrong tree. Proving a theorem
> that has already been proved ... I don't see how you can make money
> from that.
>
> Of course, if you could figure a way of making a fortune from proving
> theorems which had already been proved - you could possibly patent
> that technique, and then make money from that...
>
> Here's a more interesting question (IMHO) - you discover an algorithm
> to factor large numbers very rapidly. How do you capitalize on that?
> How would you even survive that? You publish on the net, and most of
> the world's cryto systems are useless. You go to your government, and
> ... well, you don't come back.
>
> GEJ
Some of such factoring experts just keep coming back *sigh*
quasi
<david.m...@sbcglobal.net> wrote:
Trying to deceive.
quasi
hagman
> "Don Del Grande" <del_grande_n...@earthlink.net> wrote in messagenews:1b70m4lddfa8aojo7...@4ax.com...
>
>
>
> > David Fabian wrote:
>
> >> Don Del Grande wrote:
>
> >>> David Fabian wrote:
>
> >>>>Assuming I have found Fermat's elegant proof, does anyone have
> >>>>any ideas about how I should capitalize on it?
>
> >>> "Fermat's marvelous proof" was, and offered the solution on eBay for
> >>> $1,000,000. (Presumably, there were no takers.)
>
> >>That is right... so I pulled the offer. (However, I said that the proof
> >>would take only one page, but it will actually take about ten pages.)
>
> > Pardon me for asking, but (a) just how much money are you looking to
> > make from this proof, and
>
> I don't know. If eBay enhances their software to sell information
> (see other thread for details), I would probably come up with an
> asking price. Every year or so, I would, of course, have to lower
> my price. On the other hand, some auctions do not even require
> the seller to commit to an asking price -- if no one bids what the
> seller wants by a certain time, the auction is off until a later date.
> But that strategy seems kind of cheesy to me.
>
> > (b) what guarantee does anybody have that,
> > if the proof is incorrect, they won't have to pay anything?
>
> Please read the final sentence of my previous post.
>
> Dave
>
> > -- Don
The final sentence of your previous post says
>(Of course, the money
> would stay in escrow until the information was delivered.)
You do not mention it, but should that mean that the information
(here: your proof) has to be *correct*? In what sense?
Achava Nakhash, the Loving Snake
wrote:
> "Mark Galeck" <mark_gal...@pacbell.net> wrote in messagenews:22063179.1231045670...@nitrogen.mathforum.org...
> > David, it is very simple to make your money from your proof, assuming of course that the proof is correct - and from your
> > discussion I understand that you are positively sure it is correct.
>
> > Here is how.
>
> > Offer a bet to everybody that your proof is correct in really attractive odds. Say, if the proof is incorrect, you pay them x sum
> > of US dollars. If correct, the person pays you 10x sum of US dollars.
>
> > Collect the bets over a certain period of time, say 2 months. The procedure to verify the proof, is for you to choose, any
> > mathematician in the math department of any of the top 10 research universities in the US (as published by the US News and World
> > Report), and ask to verify the proof, for a fee, say 10% of your winnings from the bet. That person's judgement would be final.
> > Since you are sure the proof is correct, and you are sure it is done used only 17-th century methods, and it is only 10 pages, so
> > any mathematician in a top research department, would have no problem verifying it, and you have the choice of whom to pick, then
> > you should have no problem with this method of verification.
>
> > OK, with the general public, probably you will not get many bettors. However, I can guarantee you, that every research
> > mathematician in the world (and there are thousands), will be ready to bet you any amount of money. Try and you will see. Of
> > course you will not get that many bettors, probably, what would happen is you would need a lawyer, to guarantee your net worth,
> > and then make sure you are not risking more than your net worth, and then to make sure the mathematicians are not risking more
> > than theirs. I guarantee you, that after all this is in place, you will immediately get your whole entire net worth distributed
> > in bets promises, among probably only a few mathematicians who will each bet for the maximal amount they can, and consider
> > themselves lucky for getting in first on this opportunity.
>
> > Since you are sure you are correct, you will multiply your net worth by 10, minus attorneys fees and the verifier.
>
> Mark, your ideas are excellent!!! Give me some time to think about how I can pull this off... I must at least cut you in on my
> winnings!
>
> Dave- Hide quoted text -
>
> - Show quoted text -
David,
When I was young, I dreamed of proving Fermat's last theorem and was
stunned to find out that mathematicians were not payed for their
journal articles. I came up witgh the idea of embedding the proof in
a novel. I would then get royalties from the sales of the book. Of
course it would fly off the shelves, as everybody would either want to
buy the crazy novel that had a proof of Fermat's last theorem in it
even they were not capable of understanding the proof. When you bet
as Mark has suggested, you are risking a huge amount of money. With
the novel, you risk only failing to make money.
Whatever technique you use, I wish you the best of luck. I will ask
you how you did it after I have proved the Riemann hypothesis. Of
course it is correct.
Regards,
Achava
hagman
> Mike Williams <nos...@econym.demon.co.uk> writes:
> > Wasn't it Kevin Stone who wrote:
> >>> Assuming I have found Fermat's elegant proof, does anyone have any ideas
> >>> about how I should capitalize on it?
>
> >>How about a wager with someone?
>
> >>You each stake a million dollars and if your 'proof' is flawed, then you
> >>lose your million.
>
> >>Sound like an idea?
>
> > It sounds like an idea to me. I don't have a million to bet against
> > you, but I'd be in for ten thousand. All you need now is to find
> > another 99 people like me, and an a procedure for deciding whether the
> > proof is flawed that we can all agree on.
>
> If I had any confidence he could find the million he'd need I'd be in
> for it - put me down for 10000 quid (which I don't have, but which I
> could find if I absolutely had to).
Yep, if necessary you could get your 10000$ share from selling flying
pigs :)
Mensanator
wrote:
> "Mensanator" <mensana...@aol.com> wrote in messagenews:8c05e202-b3c8-4fe0...@w1g2000prm.googlegroups.com...
>
> > You forgot to add "...despite being as stupid as JSH."
>
> I do not know much about JSH's knowledge or abilities,
> but you should not attack him, because he is at least trying.
Ignorance is only skin deep,
but stupid goes to the bone.
>
> Dave
mike3
> David Fabian wrote:
> > Pure mathematics is just a hobby for me (so I do not need to publish, gain
> > recognition, and obtain research grants or a job). But I am still not
> > convinced that it is impossible for a hobbyist to make money.
>
> It's close to impossible.
>
Does this mean they could not attempt to publish the proof, at all?
mike3
wrote:
> "Kevin Stone" <newsacco...@hotpop.com> wrote in messagenews:6sa9iiF...@mid.individual.net...
> >> Assuming I have found Fermat's elegant proof, does anyone have any ideas
> >> about how I should capitalize on it?
>
> > old document with the proof?
>
> No. I devised the proof using the math tools that were available to Fermat
> in the 17th-century.
>
So then even if your proof is right, you cannot assume it must be the
one that Fermat
had. The only way to know what Fermat had would be to unearth a 350
year old document
that could be verified to have been penned by Fermat's own hand.
Please, you should post the proof. You would not be able to make much
money on it if it
was right (you are probably making more in your current profession
right now than you could
off this proof), and if it was wrong, you could save yourself a lot of
grief that could come about
by betting lots of money on it being right. So I would not see how
posting it would be a big loss
for you.
Bill Dubuque
>"Matt" <matt271...@yahoo.co.uk> wrote:
>>
>> Has it been checked by anyone else?
>
> No one but myself.
>
>> The default position, until there is evidence otherwise,
>> has to be that your proof is wrong.
>
> The fact that I have solved many difficult logic problems
> (e.g. http://www.eskimo.com/~miyaguch/powerresults.html) indicates
> that there is at least a better-than-average chance that I have solved
> *this* problem (although it does not logic-
> ally prove it [argumentum ad verecundiam]).
Certainly not. Your performance on some random "IQ test" says
absolutely nothing at all about your higher mathematical skills.
Marilyn vos Savant is a prime example. The woman who supposedly
has the "world's highest IQ" published a Parade magazine column and
a book about Wiles proof of FLT. Her nonsensical arguments proved
beyond a doubt that she (and her advisors) has no clue about higher
mathematics and, worse, doesn't have the intelligence to realize
that she's completely clueless on such matters (even after many
experts pointed out gaping flaws in her extremely naive arguments).
Even more mathematical tests (IMO, Putnam, etc) are not necessarily
good measures of ability to solve longstanding problems such as
FLT since such tests merely measure the ability to _quickly_ solve
problems that are _explicitly constructed_ for such purposes.
>> I hope for your sake it's correct, but realistically the chances are slim.
>
> The chances are slim from your point of view, because you have not yet
> seen my work.
There is no chance involved. Your proof is surely wrong.
I'm so sure of this I'll bet you 10-1 odds. I'll pay you
$1000 if your proof is correct, you pay me $100 if it is
wrong (or incomprehensible). So here's your sought chance
to "capitalize on the proof". Most likely other sci.math
folks would happily join in at those odds. Even more likely
is that you will never reveal any such elementary FLT proof.
If you don't accept it'll be clear you're just blowing smoke.
Robert Israel
Probably, but I think it would be a lot harder than just "pushing a button".
Translating a human-written proof into something like HOL Light is not a
trivial task. It requires careful attention to each step. I suspect it
would be easier to spot the error "by hand".
--
Robert Israel isr...@math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
Gareth Erskine-Jones
wrote:
Yeah, but no-one's ever succeeded yet.... but if someone did, what
could they do? If they reveal to the whole world at once, then they'd
cause chaos, but might escape with their lives. If they revealed it to
their own nation's security services - well, would the NSA or GCHQ
hesitate to grab the solution for themselves and to eliminate any
potential leaks?
GEJ
Richard Heathfield
> On Sun, 4 Jan 2009 08:30:31 -0800 (PST), hagman
> <goo...@von-eitzen.de> wrote:
>
>>On 3 Jan., 23:27, Gareth Erskine-Jones <g...@uberdog.net> wrote:
>
>>> Here's a more interesting question (IMHO) - you discover an
>>> algorithm to factor large numbers very rapidly. How do you
>>> capitalize on that? How would you even survive that? You publish
>>> on the net, and most of the world's cryto systems are useless.
>>> You go to your government, and ... well, you don't come back.
>>>
>>> GEJ
>>
>>Some of such factoring experts just keep coming back *sigh*
>
> Yeah, but no-one's ever succeeded yet....
How do you know?
> but if someone did, what
> could they do? If they reveal to the whole world at once, then
> they'd cause chaos, but might escape with their lives. If they
> revealed it to their own nation's security services - well, would
> the NSA or GCHQ hesitate to grab the solution for themselves and
> to eliminate any potential leaks?
What makes you believe this hasn't already happened?
No, I don't have inside information. Contrary to unpopular belief, I
really don't work for the British intelligence services. (But I
would say that, wouldn't I?)
--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999
CBFalconer
>
... snip ...
>
> Here's a more interesting question (IMHO) - you discover an
> algorithm to factor large numbers very rapidly. How do you
> capitalize on that? How would you even survive that? You publish
> on the net, and most of the world's cryto systems are useless.
> You go to your government, and ... well, you don't come back.
No, you keep it to yourself and set yourself up as a master invader
of secrecy systems. I am sure you will find something that you can
blow up into a lot of money.
That way you get rich, not famous. You also eventually get
forgotten.
--
[mail]: Chuck F (cbfalconer at maineline dot net)
[page]: <http://cbfalconer.home.att.net>
Try the download section.
Nick Wedd
<david.m...@sbcglobal.net> writes
>Assuming I have found Fermat's elegant proof, does anyone have any
>ideas about how I should capitalize on it?
In case you have not already learned the answer from other replies -
You publicise the fact that you have a proof. You also publicise the
fact that you are willing to accept bets against the validity of your
proof. There are enough cynical people in the world that you should be
able to get very good odds. Once you have accepted bets against all the
capital you can raise, you publish your proof and collect your winnings.
Nick
--
Nick Wedd ni...@maproom.co.uk
tc...@lsa.umich.edu
Robert Israel <isr...@math.MyUniversitysInitials.ca> wrote:
>Probably, but I think it would be a lot harder than just "pushing a button".
>Translating a human-written proof into something like HOL Light is not a
>trivial task. It requires careful attention to each step. I suspect it
>would be easier to spot the error "by hand".
Yes, of course, but I think the point was that *if* the proof is correct,
then an unknown author has a chance of getting people to take him or her
seriously by producing a machine-checked version. In principle, this is
one nice thing about machine-checkable proofs.
In practice, unfortunately, the most likely outcome is that even if a crank
succeeds in learning some HOL Light (say), the crank will produce a proof
of something that isn't actually Fermat's Last Theorem, and it may be
even harder to decipher what HOL Light theorem the crank has proved than
to decipher a conventional handwritten proof. And then, of course, one
will get into interminable arguments with the crank of the form "What
you've proved isn't Fermat's Last Theorem...Yes it is!...No it isn't!"
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
junoexpress
wrote:
> "Matt" <matt271829-n...@yahoo.co.uk> wrote in messagenews:16cc27b7-3c57-4139...@40g2000prx.googlegroups.com...
>
>
> > The default position, until there is evidence otherwise,
> > has to be that your proof is wrong.
>
> The fact that I have solved many difficult logic problems
> indicates that there is at least a better-than-average chance
> that I have solved *this* problem
>
Well, I wouldn't rate your ability at probability too highly. There
have been a large number of mathematicians unable to solve FLT who
were bone fide geniuses and had the knowledge and experience which you
admittedly lack. In light of that fact, for you to say that you have
"at least a better-than average chance" of solving FLT (on the basis
of a high score on a problem in an IQ test and two papers published),
seems to me, to be on the contrary unlikely.
M
Matthew Russotto
Gareth Erskine-Jones <g...@uberdog.net> wrote:
>
>Here's a more interesting question (IMHO) - you discover an algorithm
>to factor large numbers very rapidly. How do you capitalize on that?
I think there's a few factoring contests still out there. Aside from
that, there's crime.
--
It's times like these which make me glad my bank is Dial-a-Mattress
G. A. Edgar
<a6c39bc9-d872-4e77...@r15g2000prh.googlegroups.com>,
mike3 <mike...@yahoo.com> wrote:
Mathematics research journals do not pay their authors, so that would
not be a way to make money.
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
David Bernier
> In article <rbisrael.20090104203548$5c...@news.acm.uiuc.edu>,
> Robert Israel <isr...@math.MyUniversitysInitials.ca> wrote:
>> Probably, but I think it would be a lot harder than just "pushing a button".
>> Translating a human-written proof into something like HOL Light is not a
>> trivial task. It requires careful attention to each step. I suspect it
>> would be easier to spot the error "by hand".
>
> Yes, of course, but I think the point was that *if* the proof is correct,
> then an unknown author has a chance of getting people to take him or her
> seriously by producing a machine-checked version. In principle, this is
> one nice thing about machine-checkable proofs.
>
> In practice, unfortunately, the most likely outcome is that even if a crank
> succeeds in learning some HOL Light (say), the crank will produce a proof
> of something that isn't actually Fermat's Last Theorem, and it may be
> even harder to decipher what HOL Light theorem the crank has proved than
> to decipher a conventional handwritten proof. And then, of course, one
> will get into interminable arguments with the crank of the form "What
> you've proved isn't Fermat's Last Theorem...Yes it is!...No it isn't!"
Of course, it's best to have the supposed proof hand-checked first.
I was thinking of HOL Light as a Gold Standard (if it passes
hand-checking and formalization, it's very likely right).
I was imagining the proof proposer protesting that "HOL is wrong!"
if it didn't accept the proposed proof.
David Bernier
Phuong Tri Nguyen
Recapitulating the important points in the proof:
Suppose that a^n + b^n = c^n, where a, b, c are nonzero integers and pairwise relatively prime.
It is clear that we are only necessary to prove the theorem for two cases:
Case 1: n is an odd number greater than 2.
Case 2: n = 4
If the numbers a, b are both odd, then A = B, where A = 4g + 2, B = 4h and g, h are nonzero integers.
Therefore, the numbers a, b are of different parity (one is odd, one is even).
If the number n is odd, then 2 is a divisor of the odd number n. This is a contradiction.
If n = 4, then a^2 + b^2 is a divisor of GCD (a^4 - b^4, a^4 + b^4).
Since GCD (a^4, b^4) =1, we have GCD (a^4 - b^4, a^4 + b^4) =1. It follows that a^2 + b^2 = 1. This is a contradiction.
The theorem is proved.
David Fabian
news:d953c849-937f-4e67...@v39g2000pro.googlegroups.com...
>
> The final sentence of your previous post says
> >(Of course, the money
> > would stay in escrow until the information was delivered.)
> You do not mention it, but should that mean that the information
> (here: your proof) has to be *correct*? In what sense?
Of course it would have to be correct. Otherwise, it would not
be the information that the seller claimed he would produce. It
would legally fall under "implied warranty".
David Fabian
news:wdSjqnZJ...@maproom.demon.co.uk...
| In message <JPC7l.12709$YU2....@nlpi066.nbdc.sbc.com>, David Fabian
| <david.m...@sbcglobal.net> writes
| >Assuming I have found Fermat's elegant proof, does anyone have
| >any ideas about how I should capitalize on it?
|
| In case you have not already learned the answer from other replies -
|
| You publicise the fact that you have a proof. You also publicise
| the fact that you are willing to accept bets against the validity of
| your proof. There are enough cynical people in the world that
| cepted bets against all the capital you can raise, you publish your
| proof and collect your winnings.
Here is one strategy that might work (after I have verified the
legality of making Internet bets [which, if illegal {e.g. it might
be illegal to accept a bet from a person under 18 in Morocco},
might mean that our whole discussion here constitutes "con-
spiracy to commit a crime"]):
(1) I put $10,000 in escrow (since I do not have $1,000,000).
(2) I accept bets for any amount, with the stipulation that, if I
lose, my opponents divvy up my $10,000 in proportion to
the amounts they each bet, and if I win, I receive everything
my opponents bet. (However, I would require that the bet-
ting period ends when both (a) six months have transpired
since the opening bet, and (b) my opponents' bets total to
at least $1,000,000.)
(I am pretty sure I can find enough skeptics who will settle for
100:1 odds.)
Dave
David Fabian
news:6sbgh5F...@mid.individual.net...
|> Assuming I have found Fermat's elegant proof, does anyone
| > have any ideas about how I should capitalize on it?
|
|
| You each stake a million dollars and if your 'proof' is flawed,
| then you lose your million.
|
| Sound like an idea?
First, I do not have a million dollars. Second, I do not think
any single person would risk one million dollars.
| Actually, surely someone clever enough to find a proof
| doesn't need our help?
No, I do not think that I am God, just because I believe I
solved a difficult problem. Posters have already given me
much help.
| The interviews, on radio and TV, along with the books
| will make you a wealthy man.
What makes you so sure? I don't think anyone would pay
me for an interview or for book rights. (CNN once asked
to interview me, but they did not mention any money, so I
immediately declined.)
Dave
| --
| Kev
anonymous....@yahoo.com
wrote:
> "Nick Wedd" <n...@maproom.co.uk> wrote in message
>
> news:wdSjqnZJ...@maproom.demon.co.uk...
> | In message <JPC7l.12709$YU2.9...@nlpi066.nbdc.sbc.com>, David Fabian
> | <david.m.fab...@sbcglobal.net> writes
100:1 odds might be too extreme--I don't have more than a few thousand
dollars I could put into something like this, and at 100:1 odds, the
$20 or $30 I would make from winning wouldn't be worth the few hours
it would take to verify that you had some kind of legitimate setup and
jump through the logistics hoops to actually put down the money. The
problem of finding an escrow service that is so obviously reliable
that your audience won't think they're being scammed, and which would
streamline the betting process enough that it wouldn't be too big a
hassle to even get involved--that is a significant problem.
Have you looked into the 19th century attacks on FLT? Are you sure
that your putative proof isn't one of the (failed, but for subtle
reasons) 19th century ones? The reason that Kummer's proof of FLT for
regular prime exponents isn't a proof for ALL exponents are subtle,
and many people stumble there, thinking they have a proof because they
have assumed a certain class group is trivial (or something equivalent
to this), when it is not.
David Fabian
news:7c86d71f-7368-42c8...@m22g2000vbp.googlegroups.com...
>
>100:1 odds might be too extreme--I don't have more than a few thousand
>dollars I could put into something like this, and at 100:1 odds, the
>$20 or $30 I would make from winning wouldn't be worth the few hours
>it would take to verify that you had some kind of legitimate setup and
>jump through the logistics hoops to actually put down the money. The
>problem of finding an escrow service that is so obviously reliable
>that your audience won't think they're being scammed, and which would
>streamline the betting process enough that it wouldn't be too big a
>hassle to even get involved--that is a significant problem.
Good points. I will have to sleep on this...
>Have you looked into the 19th century attacks on FLT? Are you sure
>that your putative proof isn't one of the (failed, but for subtle reasons)
>19th century ones? The reason that Kummer's proof of FLT for
>regular prime exponents isn't a proof for ALL exponents are subtle,
>and many people stumble there, thinking they have a proof because they
>have assumed a certain class group is trivial (or something equivalent
>to this), when it is not.
No, I have not seen any of those flawed proofs.
quasi
It's a very naive plan.
(1) Not many people, if any, would be willing place a large amount of
money in escrow, then have to wait possibly as much as 6 months in
order to complete the transaction.
(2) Not many people, if any will offer 100-1 odds. It's not that the
odds are unfair -- in fact, the true odds, given your background, are
probably at least 10,000-1. Still, the reason people will not offer
100-1 is because the potential profit is simply not worth the trouble.
Would I bet $10,000 against your $100? Why should I bother? I would
have to wait possibly 6 months, all the time worrying about possible
fraud. Is the escrow service legitimate? Is the referee secretly in
collusion with you? Etc.
(3) You haven't specified how the referees would be selected. I
suspect that most bettors would insist on more than one referee, and
that the referees be world class mathematicians, widely regarded as
Number Theory gurus. What makes you think any such mathematicians
would agree to be a referee for your scheme? It seems pretty unlikely.
In my opinion, your betting idea is just a foolish fantasy -- it will
never get off the ground. Forget it.
However, it is true that if you publish your proof (on the web, for
example), and if it magically survives public criticism, you _will_
become famous, and at that point, you would be widely sought after for
interviews, tv appearances, guest talks at colleges, etc. Appearance
fees would definitely be offered.
And has been suggested, you could write a book describing the problem,
some of its history, your quest for the proof, the actual proof
together with expanded explanations of the key ideas, your struggle to
convince the skeptics, your attempts to capitalize on your discovery,
and finally, the eventual worldwide recognition.
Fees and royalties -- it's a more standard approach, and while not
guaranteed to make you millions, it might reach $100,000 over time.
In any case, regardless of how you proceed, you are not going to make
a million dollars. Unless ... Unless you can also prove that Wiles'
proof is invalid. In that case, your fame escalates, and so does the
money.
But my gut sense is that it's all just an ego trip on your part. The
more you talk about selling your proof on eBay, or your ultra-naive
100-1 escrow-based betting scheme, the more I'm convinced that in
essence, you're just another JSH-like troll, and that your true goal
is just to be a center of attention for awhile.
quasi
Phil Carmody
By offering such odds, he's saying that he believes that there's
a 99% chance of him being wrong.
I think we can at that point, to 1 significant figure, simply
agree with him.
Phil
--
I tried the Vista speech recognition by running the tutorial. I was
amazed, it was awesome, recognised every word I said. Then I said the
wrong word ... and it typed the right one. It was actually just
detecting a sound and printing the expected word! -- pbhj on /.
Gareth Erskine-Jones
<r...@see.sig.invalid> wrote:
>Gareth Erskine-Jones said:
>
>> On Sun, 4 Jan 2009 08:30:31 -0800 (PST), hagman
>> <goo...@von-eitzen.de> wrote:
>>
>>>On 3 Jan., 23:27, Gareth Erskine-Jones <g...@uberdog.net> wrote:
>>
>>>> Here's a more interesting question (IMHO) - you discover an
>>>> algorithm to factor large numbers very rapidly. How do you
>>>> capitalize on that? How would you even survive that? You publish
>>>> on the net, and most of the world's cryto systems are useless.
>>>> You go to your government, and ... well, you don't come back.
>>>>
>>>> GEJ
>>>
>>>Some of such factoring experts just keep coming back *sigh*
>>
>> Yeah, but no-one's ever succeeded yet....
>
>How do you know?
True - I don't know.
>> but if someone did, what
>> could they do? If they reveal to the whole world at once, then
>> they'd cause chaos, but might escape with their lives. If they
>> revealed it to their own nation's security services - well, would
>> the NSA or GCHQ hesitate to grab the solution for themselves and
>> to eliminate any potential leaks?
>
>What makes you believe this hasn't already happened?
>
>No, I don't have inside information. Contrary to unpopular belief, I
>really don't work for the British intelligence services. (But I
>would say that, wouldn't I?)
I don't either. See you in the office tomorrow btw. :-)
GEJ
Gareth Erskine-Jones
(Matthew Russotto) wrote:
>In article <c7pvl41i4mjfdjvq2...@4ax.com>,
>Gareth Erskine-Jones <g...@uberdog.net> wrote:
>>
>>Here's a more interesting question (IMHO) - you discover an algorithm
>>to factor large numbers very rapidly. How do you capitalize on that?
>
>I think there's a few factoring contests still out there.
Sure, but if you've really got an efficient algorithm, your problem
remains - you reveal it (even in the context of a contest) and you
could cause chaos around the world as trusted cryptographic systems
become useless.
> Aside from
>that, there's crime.
That's the only thing I can think of to capitalize on a discovery like
that. Not quite so nice as being known as the one who solved a very
difficult and important problem though.
GEJ
Jasen Betts
> "Gareth Erskine-Jones" <g...@uberdog.net> wrote in message news:c7pvl41i4mjfdjvq2...@4ax.com...
>> On Sat, 3 Jan 2009 14:28:40 -0600, "David Fabian"
>> <david.m...@sbcglobal.net> wrote:
>> >
>>>Thank you for the advice; but I am interested in making money, not
>>>improving my reputation.
>>
>> Then I suspect you're barking up the wrong tree. Proving a theorem
>> that has already been proved ... I don't see how you can make money
>> from that.
>
> There are many mathematicians who would like to see a proof (especially
> one that Fermat himself probably had in mild) that is much simpler than
> Wiles' proof... so I should be able to capitalize in some way.
>
write an E-book sell it through clickbank (or similar)
put signed copies on e-bay ?
try and sell it to a math journal? or Nature?
sell movie rights?
Han de Bruijn
Sure. Why not do it the typical American way ? Sell before you have !
Han de Bruijn
Tim Smith
Gareth Erskine-Jones <g...@uberdog.net> wrote:
> >>Here's a more interesting question (IMHO) - you discover an algorithm
> >>to factor large numbers very rapidly. How do you capitalize on that?
> >
> >I think there's a few factoring contests still out there.
>
> Sure, but if you've really got an efficient algorithm, your problem
> remains - you reveal it (even in the context of a contest) and you
> could cause chaos around the world as trusted cryptographic systems
> become useless.
The factoring contests don't require you to reveal your methods, I
believe. What you could do is skip some of the challenge numbers, and
hint that you skipped them because you do NOT have a factoring
breakthrough--you found a flaw in how they generated the challenge
numbers and were able to exploit it for some of them.
>
> > Aside from
> >that, there's crime.
>
> That's the only thing I can think of to capitalize on a discovery
> like that. Not quite so nice as being known as the one who solved a
> very difficult and important problem though.
Anti-crime would also be a possibility. Start a data recovery service,
specializing in recovering incriminating evidence for police from
alleged criminal's computers.
--
--Tim Smith
Tim Smith
quasi <qu...@null.set> wrote:
> (2) Not many people, if any will offer 100-1 odds. It's not that the
> odds are unfair -- in fact, the true odds, given your background, are
> probably at least 10,000-1. Still, the reason people will not offer
> 100-1 is because the potential profit is simply not worth the trouble.
> Would I bet $10,000 against your $100? Why should I bother? I would
> have to wait possibly 6 months, all the time worrying about possible
> fraud. Is the escrow service legitimate? Is the referee secretly in
> collusion with you? Etc.
If the escrow is with someone trustworthy, I don't think there would be
that much problem finding people willing to bet. Looking at how my
investments have performed over the last year, putting money up on a bet
against a 17th-century technology proof of FLT looks like a better
investment than what I've got now. :-(
--
--Tim Smith
Tim Smith
Gareth Erskine-Jones <g...@uberdog.net> wrote:
[How to proceed if you have a factoring breakthrough?]
> Yeah, but no-one's ever succeeded yet.... but if someone did, what
> could they do? If they reveal to the whole world at once, then they'd
> cause chaos, but might escape with their lives. If they revealed it to
> their own nation's security services - well, would the NSA or GCHQ
> hesitate to grab the solution for themselves and to eliminate any
> potential leaks?
That's overly dramatic. The NSA supposedly is the world's largest
employer of mathematicians. You go to them and show them a significant
factoring breakthrough, then they will indeed take steps to eliminate
leaks--by showing you to your new office, and putting you on the payroll
with a good salary and benefits.
--
--Tim Smith
G. A. Edgar
Tim Smith <reply_i...@mouse-potato.com> wrote:
> The NSA supposedly is the world's largest
> employer of mathematicians.
The version I heard said "largest non-academic employer of
mathematicians"
quasi
But note the bars on the windows, and the lack of a handle on the
inside of the door.
Still, it sounds like an offer that you just can't refuse.
quasi
Angus Rodgers
"And now it's time to meet your line manager, Mr. Harris."
--
Angus Rodgers
junoexpress
> It's a very naive plan.
>
>
> never get off the ground. Forget it.
>
> However, it is true that if you publish your proof (on the web, for
> example), and if it magically survives public criticism, you _will_
> become famous, and at that point, you would be widely sought after for
> interviews, tv appearances, guest talks at colleges, etc. Appearance
> fees would definitely be offered.
>
>
Quasi is right: the betting is pie-in-the-sky stuff. IF you publish
and IF you are correct, you'll get your 15 minutes of fame. Milk it
for all it's worth (ain't that the American way?) It might help if you
had some sort of human interest angle that the general public would
eat up. Maybe you had a battle with the bottle or an abusive family,
or a drug dependency, and yet you overcame it to come back and solve
the world's hardest problem. That sort of thing always seems to keep
people glued to their TV sets, fat and happy. But I'm no expert in
such matters, so besides an attorney, you might want to hire a PR firm
too.
However, you might be a bit short-sighted on this one David. You want
one big payout, but if you did publish wouldn't your reputation among
your peers now go from impressively smart guy who scores high on those
IQ tests, to super-genius? Maybe the publicity would get you a better
paying job, lucrative jobs as a consultant to solve difficult
problems, which in the *long-term* might be worth more than the short-
term pay-off (not to mention the enhanced, long-term prestige and
security vs the 15 minute "flash-in the pan" routine).
HTH,
M
Dave L. Renfro
http://groups.google.com/group/sci.math/msg/0d4d7d1571209bc4
>> Thank you for the advice; but I am interested in making money,
>> not improving my reputation.
quasi wrote (in part):
http://groups.google.com/group/sci.math/msg/1ed5d11ad39f5eaa
> However, it is true that if you publish your proof (on the web,
> for example), and if it magically survives public criticism,
> you _will_ become famous, and at that point, you would be
> widely sought after for interviews, tv appearances, guest
> talks at colleges, etc. Appearance fees would definitely
> be offered.
>
> And has been suggested, you could write a book describing
> the problem, some of its history, your quest for the proof,
> the actual proof together with expanded explanations of the
> key ideas, your struggle to convince the skeptics, your
> attempts to capitalize on your discovery, and finally,
> the eventual worldwide recognition.
>
> Fees and royalties -- it's a more standard approach, and
> while not guaranteed to make you millions, it might reach
> $100,000 over time.
I was going to write something similar to what quasi wrote
in response to David Fabian's comment above, but decided to
first scan through the posts in this thread to see if anyone
commented on the obvious, which quasi did.
David Fabian -- If you truly want to make money off this,
then you need to realize that what will be valuable is _you_,
not the proof. Most of the public probably won't even be
interested in trying to read the proof and most mathematicians
won't be interested in buying the proof (not when, after it's
available, they can just look at it). What people will be
interested in is _you_ and thus it's _you_ that will be
marketable, not the proof. And I disagree with quasi about
"might reach $100,000 over time", because I have little doubt
that you could easily get several million in marketing yourself
after you become world famous.
Again, there is little chance of making money directly from
the proof itself. The money will come from the fame and human
interest that the proof will generate for _you_.
Dave L. Renfro
junoexpress
>
> Most of the public probably won't even be
> interested in trying to read the proof and most mathematicians
> won't be interested in buying the proof (not when, after it's
> available, they can just look at it).
> Dave L. Renfro
Because by definition the proof involves elementary methods,
mathematicians might not have much interest in it. A good deal of the
interest in FLT was not from the solution itself (which from past work
and simulations people pretty much a good idea which way things would
go), but rather from the *new* math it generated. Math people might
regard your clever soln more as you being more of a "one-trick" pony.
To reiterate what I said in my previous post, use your publicity to
enhance your career. If you're as smart as you think you are, you have
more than the soln of just one tough problem in you. People pay very
good $$ for such people. (Of course, the obvious rebuttal is "Well, I
want to get rich quick and retire to the Bahamas with a boatful of
babes". Well, we all do, but it ain't happening, so get real and think
of a practical soln.)
HTH,
M
tc...@lsa.umich.edu
junoexpress <MTBre...@gmail.com> wrote:
>Because by definition the proof involves elementary methods,
>mathematicians might not have much interest in it. A good deal of the
>interest in FLT was not from the solution itself (which from past work
>and simulations people pretty much a good idea which way things would
>go), but rather from the *new* math it generated. Math people might
>regard your clever soln more as you being more of a "one-trick" pony.
I don't believe this for a second. A (correct) elementary proof of FLT
would be enormously interesting to mathematicians. They would certainly
study it very carefully, and *if* they were certain it was correct,
some would even pay to see it. The reason is that there has been a lot
of effort expended trying to prove the theorem by elementary means, and
so any correct elementary proof must involve some highly original ideas.
Furthermore, mathematicians are human beings. Because of the history and
human interest angle, FLT fascinates mathematicians. They may *say* that
what's "really" interesting about the papers by Wiles and Taylor-Wiles is
that they established the semistable case of the Shimura-Taniyama-Weil
conjecture. But don't believe them. Yes, STW is more important
*theoretically* than FLT. But if there were no known connection between
STW and FLT, then for the most part, only number theorists would care
about the semistable case of STW. Even Wiles would probably not have
thrown himself so thoroughly into STW if FLT weren't part of the picture.
Compare, for example, Apery's elementary proof of the irrationality of
zeta(3). This did not generalize to zeta(2n+1), and while it has inspired
some further research, it has not been as theoretically fruitful as the
work of Wiles. Nevertheless, Apery's proof is very interesting to
mathematicians and has a permanent place in the history of mathematics,
because the problem was so famous.
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences