info
Google Groups no longer supports new Usenet posts or subscriptions. Historical content remains viewable.
Dismiss
Great theorems proved by elementary means?
29 views
Skip to first unread message
Paul
Jan 21, 2012, 12:16:46 PM1/21/12
to
Does anyone know any examples of any significant theorems whose first
proofs were elementary? By "elementary", I mean that they could be
read by a non-exceptional first-year undergraduate.
I have seen purely elementary proofs of deepish theorems but I would
guess that the first proofs were highly sophisticated and that much
work was done to translate the difficult technical proofs into
elementary notions.
Among the maths that I know, here are some of my favourite deep
theorems with elementary proofs.
Erdos -- Ko -- Rado: Suppose n >= 2r. Let S be a set of size n.
Suppose a family F of subsets of S is pairwise-intersecting, then F
must have <= n-1 C r-1 members.
This is a surprising result (I've become a convert to the use of the
word "surprising" to discuss maths), in my opinion, because the bound
above is the bound on the number of members of F if all the members of
F intersect at a common point. Pairwise-intersecting is much less
restrictive than the entire collection having non-empty intersection
so I would have thought the bound would have to be much larger.
The result that sum 1/p_i diverges where p_i denotes the ith prime.
If you partition the natural numbers into a finite collection of non-
overlapping sets, at least one of these sets contains arbitrarily long
arithmetical progressions.
I thought of this question of elementary proofs of deep theorems
because there was a recent elementary attempt to prove Goldbach's
conjecture. How plausible is it that some such elementary attempt
could work?
Paul Epstein
proofs were elementary? By "elementary", I mean that they could be
read by a non-exceptional first-year undergraduate.
I have seen purely elementary proofs of deepish theorems but I would
guess that the first proofs were highly sophisticated and that much
work was done to translate the difficult technical proofs into
elementary notions.
Among the maths that I know, here are some of my favourite deep
theorems with elementary proofs.
Erdos -- Ko -- Rado: Suppose n >= 2r. Let S be a set of size n.
Suppose a family F of subsets of S is pairwise-intersecting, then F
must have <= n-1 C r-1 members.
This is a surprising result (I've become a convert to the use of the
word "surprising" to discuss maths), in my opinion, because the bound
above is the bound on the number of members of F if all the members of
F intersect at a common point. Pairwise-intersecting is much less
restrictive than the entire collection having non-empty intersection
so I would have thought the bound would have to be much larger.
The result that sum 1/p_i diverges where p_i denotes the ith prime.
If you partition the natural numbers into a finite collection of non-
overlapping sets, at least one of these sets contains arbitrarily long
arithmetical progressions.
I thought of this question of elementary proofs of deep theorems
because there was a recent elementary attempt to prove Goldbach's
conjecture. How plausible is it that some such elementary attempt
could work?
Paul Epstein
Rupert
Jan 21, 2012, 12:28:13 PM1/21/12
to
algebraic number theory" is quite a nice proof due to Fermat that
every prime number of the form 4n+1 is a sum of two squares. Also in
Simon Singh's book is a discussion of the dot conjecture which
remained open for more than a century but was eventually resolved by
an elementary argument.
I don't think it is very likely that Goldbach's conjecture has an
elementary proof.
Gerry Myerson
Jan 22, 2012, 12:41:39 AM1/22/12
to
In article
<fb5f5c4f-a81f-4974...@o14g2000vbo.googlegroups.com>,
for a long time, and has attracted the attention of many
brilliant people. If they didn't find an elementary proof,
chances are there isn't one.
--
Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email)
<fb5f5c4f-a81f-4974...@o14g2000vbo.googlegroups.com>,
Paul <peps...@gmail.com> wrote:
> I thought of this question of elementary proofs of deep theorems
> because there was a recent elementary attempt to prove Goldbach's
> conjecture. How plausible is it that some such elementary attempt
> could work?
Plausibility = roughly zero. The problem has been around
> I thought of this question of elementary proofs of deep theorems
> because there was a recent elementary attempt to prove Goldbach's
> conjecture. How plausible is it that some such elementary attempt
> could work?
for a long time, and has attracted the attention of many
brilliant people. If they didn't find an elementary proof,
chances are there isn't one.
--
Gerry Myerson (ge...@maths.mq.edi.ai) (i -> u for email)
Gustavo Broos
Jan 22, 2012, 2:41:19 AM1/22/12
to
effort to make math more accessible to everybody (me included), but is
that even possible?
Tonico
Jan 22, 2012, 6:00:22 AM1/22/12
to
It all depends on what you call "maths" to. There've been several very
good "popularizers" of mathematics in particular, and of science in
general, Gardner and Asimov being two of them, which have done a very
nice job trying somehow to lure people in general towards stuff beyond
multiplication tables and linear equations.
The above efforts though have a rather low upper bound of
possibilities since very elementary mathematics, beyond high school or
at this level say, already require some machinery which is beyond the
capabilities/interest of most people, like limits and abstract
thinking in linear algebra andset theory.
Thus, it is possible to explain Fermat's Last Theorem, Cantor's
Theorem or Goldbach Conjecture to high schools students, but to
actually understand in a minimal way, and to be attracted to, Riemann
Hypothesis, say, is already way beyond most people's interest/
capabilities.
This is one of the main reasons why there are so many cranks and
trolls stinking around the web about Cantor's Theorem, FLT or Goldbach
Conj., but you can hardly find any of these beasts dealing with R.H.,
Poincare's Conjecture (already a Theorem) or other more advanced
stuff, as these last ones already require some deeper knowledge of
mathematics to deal with.
Tonio
Timothy Murphy
Jan 22, 2012, 8:11:55 AM1/22/12
to
Gerry Myerson wrote:
>> I thought of this question of elementary proofs of deep theorems
>> because there was a recent elementary attempt to prove Goldbach's
>> conjecture. How plausible is it that some such elementary attempt
>> could work?
>
> Plausibility = roughly zero. The problem has been around
> for a long time, and has attracted the attention of many
> brilliant people. If they didn't find an elementary proof,
> chances are there isn't one.
I'm not sure about that.
>> I thought of this question of elementary proofs of deep theorems
>> because there was a recent elementary attempt to prove Goldbach's
>> conjecture. How plausible is it that some such elementary attempt
>> could work?
>
> Plausibility = roughly zero. The problem has been around
> for a long time, and has attracted the attention of many
> brilliant people. If they didn't find an elementary proof,
> chances are there isn't one.
It depends of course on what you mean by "elementary".
But if one uses it in the sense of
the "elementary proof of the prime number theorem"
by Selberg, Erdos, etc
(which is much more difficult in my eyes than the standard proof),
then it seems to me the probability of such a proof of Goldbach
(or rather, the relative probability given that the result _is_ proved)
is > epsilon.
As an example of an elementary proof of a deep theorem
I'd suggest Roth's proof of his result
on rational approximations to algebraic numbers.
--
Timothy Murphy
e-mail: gayleard /at/ eircom.net
tel: +353-86-2336090, +353-1-2842366
s-mail: School of Mathematics, Trinity College Dublin
Pubkeybreaker
Jan 22, 2012, 9:38:17 AM1/22/12
to
On Jan 22, 8:11 am, Timothy Murphy <gayle...@eircom.net> wrote:
> Gerry Myerson wrote:
> >> I thought of this question of elementary proofs of deep theorems
> >> because there was a recent elementary attempt to prove Goldbach's
> >> conjecture. How plausible is it that some such elementary attempt
> >> could work?
>
> > Plausibility = roughly zero. The problem has been around
> > for a long time, and has attracted the attention of many
> > brilliant people. If they didn't find an elementary proof,
> > chances are there isn't one.
>
> I'm not sure about that.
> It depends of course on what you mean by "elementary".
> But if one uses it in the sense of
> the "elementary proof of the prime number theorem"
The OP defined it. "elementary" == accessible to an average
> Gerry Myerson wrote:
> >> I thought of this question of elementary proofs of deep theorems
> >> because there was a recent elementary attempt to prove Goldbach's
> >> conjecture. How plausible is it that some such elementary attempt
> >> could work?
>
> > Plausibility = roughly zero. The problem has been around
> > for a long time, and has attracted the attention of many
> > brilliant people. If they didn't find an elementary proof,
> > chances are there isn't one.
>
> I'm not sure about that.
> It depends of course on what you mean by "elementary".
> But if one uses it in the sense of
> the "elementary proof of the prime number theorem"
college freshman. And he does not mean students in Math 55.
Daryl McCullough
Jan 22, 2012, 10:17:55 AM1/22/12
to
On Sunday, January 22, 2012 6:00:22 AM UTC-5, Tonico wrote:
> This is one of the main reasons why there are so many cranks and
> trolls stinking around the web about Cantor's Theorem, FLT or Goldbach
> Conj., but you can hardly find any of these beasts dealing with R.H.,
> Poincare's Conjecture (already a Theorem)
So there's a niche waiting to be filled: We need a Riemann Hypothesis
> This is one of the main reasons why there are so many cranks and
> trolls stinking around the web about Cantor's Theorem, FLT or Goldbach
> Conj., but you can hardly find any of these beasts dealing with R.H.,
> Poincare's Conjecture (already a Theorem)
crank.
Timothy Murphy
Jan 22, 2012, 6:07:30 PM1/22/12
to
Even so, I would say that every step of the elementary proof
of the prime number theorem _is_ accessible to an average maths freshman,
in the sense that the way to multiply two 100 digit numbers is accessible.
It is just that the number of steps is very large,
and some of those steps are incredibly complicated.
Pubkeybreaker
Jan 22, 2012, 6:28:13 PM1/22/12
to
>
> - Show quoted text -
Hardy & Wright has a nice presentation.
Paul
Jan 23, 2012, 4:39:46 AM1/23/12
to
On Jan 22, 1:11 pm, Timothy Murphy <gayle...@eircom.net> wrote:
....
initial posting was to make a case against crankdom.
However, I wouldn't say "No significant deep theorem has been proved
by an amateur mathematician using elementary means" because I don't
know if that's true. Perhaps the dot conjecture is a counter-example
to the quoted statement above. By the way, after some casual
googling, I couldn't find a clear (to me) statement of the dot
conjecture, let alone a proof.
I read a proof of Roth's result in one of the Springer texts on
Diophantine equations. Although somewhat elementary, I think it's far
_less_ elementary than nearly all amateur attempts at FLT, Goldbach
conjecture etc.
For example, Roth's proof uses multivariable integration, I think.
Furthermore, even if my recollection is wrong and Roth's proof was
just as elementary as (for example) Hovdan's attempted proof, that
doesn't in any way make a case for amateur elementary attempts at
great theorems, because I would guess that Roth used highly
sophisticated techniques and machinery to bear in his thinking about
the result. While digesting the sophisticated results, he found a way
to translate the notions into elementary mathematics (I imagine).
In other words, even purely elementary results of deep theorems are
_not_ examples to show that deep maths can be produced with little
knowledge because the "elementary exposition" is only the end product
-- a lot of deep knowledge and cutting edge research was needed to
produce the ideas which could eventually be translated into elementary
form.
Paul Epstein
....
>
> As an example of an elementary proof of a deep theorem
> I'd suggest Roth's proof of his result
> on rational approximations to algebraic numbers.
>
I think that part of the (somewhat unconscious) motivation for my
> As an example of an elementary proof of a deep theorem
> I'd suggest Roth's proof of his result
> on rational approximations to algebraic numbers.
>
initial posting was to make a case against crankdom.
However, I wouldn't say "No significant deep theorem has been proved
by an amateur mathematician using elementary means" because I don't
know if that's true. Perhaps the dot conjecture is a counter-example
to the quoted statement above. By the way, after some casual
googling, I couldn't find a clear (to me) statement of the dot
conjecture, let alone a proof.
I read a proof of Roth's result in one of the Springer texts on
Diophantine equations. Although somewhat elementary, I think it's far
_less_ elementary than nearly all amateur attempts at FLT, Goldbach
conjecture etc.
For example, Roth's proof uses multivariable integration, I think.
Furthermore, even if my recollection is wrong and Roth's proof was
just as elementary as (for example) Hovdan's attempted proof, that
doesn't in any way make a case for amateur elementary attempts at
great theorems, because I would guess that Roth used highly
sophisticated techniques and machinery to bear in his thinking about
the result. While digesting the sophisticated results, he found a way
to translate the notions into elementary mathematics (I imagine).
In other words, even purely elementary results of deep theorems are
_not_ examples to show that deep maths can be produced with little
knowledge because the "elementary exposition" is only the end product
-- a lot of deep knowledge and cutting edge research was needed to
produce the ideas which could eventually be translated into elementary
form.
Paul Epstein
Tonico
Jan 23, 2012, 7:46:57 AM1/23/12
to
because it probably gave some insights to him or to some of the
readers, honest because it actually looked like a sincere effort.
Hovdan doesn't belong in the crankhood neighborhood, unlike many
others who not only announce pompously their "achievments" but also
will not pay any attention to critics to their work, many a time a
pretty lousy one.
Tonio
Paul
Jan 23, 2012, 11:25:17 AM1/23/12
to
On Jan 23, 12:46 pm, Tonico <Tonic...@yahoo.com> wrote:
...
Of course, it's a matter of definition whether Hovdan behaved like a
"mathematical crank".
From my understanding of the term, I would say "Yes, he was maths-
cranky."
He was maths-cranky because
1) His initial posts didn't show enough self-doubt. He never said
anything like "I'm sure the Goldbach conjecture can't be proved so
easily by elementary means, so I would like some help in finding the
mistake."
2) He was slow to accept Nordhaus's criticism even though a simple
google-search (like I did) shows Nordhaus to have a maths Ph.D from
the University of Utah. Presumably, credentials mean something.
3) He shows no signs of having done any study of any of the related
research.
But this is just a matter of semantics.
I guess maths-crankiness belongs on a scale.
If the only way to be a maths crank is to write unintelligible
gibberish and then blame the maths community for failing to
understand, then he's not a maths crank by that standard.
In the defence of the way I'm using the term. Consider the following:
In the pre-usenet era, suppose a famous number theorist said "Hell,
I'm being flooded with mail from cranks who are saying they've proved
the Goldbach conjecture!"
The Hovdan paper seems like an excellent example of the type of thing
we would expect the number theorist to be complaining about.
And if the famous number theorist did have the Hovdan paper in mind in
my hypothetical scenario, it would be most unlikely for another
mathematician to say "Wait a minute. I don't think Hovdan's a
crank." No, another mathematician would see Hovdan as cranky because
it's an attempt at an extremely elementary and extremely short proof
of one of the great unsolved problems.
Paul Epstein
...
> I think Hovdan's try to prove G.B. was a good, honest one: good
> because it probably gave some insights to him or to some of the
> readers, honest because it actually looked like a sincere effort.
>
> Hovdan doesn't belong in the crankhood neighborhood, unlike many
> others who not only announce pompously their "achievments" but also
> will not pay any attention to critics to their work, many a time a
> pretty lousy one.
>
Agree totally with your first para -- "I think ... effort".
> because it probably gave some insights to him or to some of the
> readers, honest because it actually looked like a sincere effort.
>
> Hovdan doesn't belong in the crankhood neighborhood, unlike many
> others who not only announce pompously their "achievments" but also
> will not pay any attention to critics to their work, many a time a
> pretty lousy one.
>
Of course, it's a matter of definition whether Hovdan behaved like a
"mathematical crank".
From my understanding of the term, I would say "Yes, he was maths-
cranky."
He was maths-cranky because
1) His initial posts didn't show enough self-doubt. He never said
anything like "I'm sure the Goldbach conjecture can't be proved so
easily by elementary means, so I would like some help in finding the
mistake."
2) He was slow to accept Nordhaus's criticism even though a simple
google-search (like I did) shows Nordhaus to have a maths Ph.D from
the University of Utah. Presumably, credentials mean something.
3) He shows no signs of having done any study of any of the related
research.
But this is just a matter of semantics.
I guess maths-crankiness belongs on a scale.
If the only way to be a maths crank is to write unintelligible
gibberish and then blame the maths community for failing to
understand, then he's not a maths crank by that standard.
In the defence of the way I'm using the term. Consider the following:
In the pre-usenet era, suppose a famous number theorist said "Hell,
I'm being flooded with mail from cranks who are saying they've proved
the Goldbach conjecture!"
The Hovdan paper seems like an excellent example of the type of thing
we would expect the number theorist to be complaining about.
And if the famous number theorist did have the Hovdan paper in mind in
my hypothetical scenario, it would be most unlikely for another
mathematician to say "Wait a minute. I don't think Hovdan's a
crank." No, another mathematician would see Hovdan as cranky because
it's an attempt at an extremely elementary and extremely short proof
of one of the great unsolved problems.
Paul Epstein
quasi
Jan 23, 2012, 5:56:46 PM1/23/12
to
On Mon, 23 Jan 2012 08:25:17 -0800 (PST), Paul <peps...@gmail.com>
wrote:
>On Jan 23, 12:46 pm, Tonico <Tonic...@yahoo.com> wrote:
>...
>> I think Hovdan's try to prove G.B. was a good, honest one:
>> good because it probably gave some insights to him or to
>> some of the readers, honest because it actually looked like
>> a sincere effort.
>>
>> Hovdan doesn't belong in the crankhood neighborhood, unlike
>> many others who not only announce pompously their
>> "achievments" but also will not pay any attention to critics
>> to their work, many a time a pretty lousy one.
>
>Agree totally with your first para -- "I think ... effort".
>
>Of course, it's a matter of definition whether Hovdan behaved
>like a "mathematical crank". From my understanding of the term,
>I would say "Yes, he was maths-cranky."
>
>He was maths-cranky because
>
>1) His initial posts didn't show enough self-doubt. He never
>said anything like "I'm sure the Goldbach conjecture can't be
>proved so easily by elementary means, so I would like some
>help in finding the mistake."
No, he doesn't have to say it in such a self-deprecating way.
You can have that point of view as reviewer of the proof, but
he doesn't have to assert in advance that his argument is
probably flawed.
Too much self-doubt and his idea for the proof never gets
acted on in the first place. I'm sure that his development of
the proof required a lot work. Why would he waste his time if
he truly believed that the conjecture _couldn't_ be proved by
elementary means.
Besides, he did ask politely for corrections.
>2) He was slow to accept Nordhaus's criticism
Not really. A few clarifications was all it took to dispel
his initial misunderstanding.
>even though a simple google-search (like I did) shows
>Nordhaus to have a maths Ph.D from the University of Utah.
>Presumably, credentials mean something.
I don't think one needs to check credentials as a criterion
for deciding whether a critique is valid or invalid. The
math of the critique stands for itself.
>3) He shows no signs of having done any study of any of
>the related research.
How do you know that he had done no such research?
And what signs were you looking for?
And why should he undertake what could easily be years of
study of prior research, if the idea for his proof is along
completely different lines.
That would have created quite a barrier to entry.
>But this is just a matter of semantics.
>
>I guess maths-crankiness belongs on a scale.
>
>If the only way to be a maths crank is to write
>unintelligible gibberish and then blame the maths community
>for failing to understand, then he's not a maths crank by
>that standard.
Throughout history, there have been many proofs submitted by
legitimate (non-crank) members of the mathematical community,
for which the author asserted the result as correct, only
for a flaw to be later discovered.
>In the defence of the way I'm using the term. Consider
>the following: In the pre-usenet era, suppose a famous number
>theorist said "Hell, I'm being flooded with mail from cranks
>who are saying they've proved the Goldbach conjecture!"
>
>The Hovdan paper seems like an excellent example of the type
>of thing we would expect the number theorist to be complaining
>about.
Straw-man argument.
Highly unlikely the fictitious number theorist is being flooded
with proposed proofs of the Goldbach conjecture written at a
level of rigor and mathematical maturity greater than or equal
to that of Hovdan's proof.
>And if the famous number theorist did have the Hovdan paper in
>mind in my hypothetical scenario,
Again, it's a straw-man argument.
>it would be most unlikely for another mathematician to say
>"Wait a minute. I don't think Hovdan's a crank." No,
>another mathematician would see Hovdan as cranky because
>it's an attempt at an extremely elementary and extremely
>short proof of one of the great unsolved problems.
So no one should even bother _trying_ to solve a famous
unsolved problem using an elementary (sub-graduate level)
approach? A total waste of time? No point? No chance of
success?
And if despite your pessimistic "don't bother" advice, they
try anyway, they shouldn't dare to post a proposed argument to
an informal discussion group such as sci.math, for fear of
being called a crank?
In my opinion, your point of view is oppressive and overly
aristocratic.
quasi
wrote:
>On Jan 23, 12:46 pm, Tonico <Tonic...@yahoo.com> wrote:
>...
>> I think Hovdan's try to prove G.B. was a good, honest one:
>> good because it probably gave some insights to him or to
>> some of the readers, honest because it actually looked like
>> a sincere effort.
>>
>> Hovdan doesn't belong in the crankhood neighborhood, unlike
>> many others who not only announce pompously their
>> "achievments" but also will not pay any attention to critics
>> to their work, many a time a pretty lousy one.
>
>Agree totally with your first para -- "I think ... effort".
>
>Of course, it's a matter of definition whether Hovdan behaved
>like a "mathematical crank". From my understanding of the term,
>I would say "Yes, he was maths-cranky."
>
>He was maths-cranky because
>
>1) His initial posts didn't show enough self-doubt. He never
>said anything like "I'm sure the Goldbach conjecture can't be
>proved so easily by elementary means, so I would like some
>help in finding the mistake."
You can have that point of view as reviewer of the proof, but
he doesn't have to assert in advance that his argument is
probably flawed.
Too much self-doubt and his idea for the proof never gets
acted on in the first place. I'm sure that his development of
the proof required a lot work. Why would he waste his time if
he truly believed that the conjecture _couldn't_ be proved by
elementary means.
Besides, he did ask politely for corrections.
>2) He was slow to accept Nordhaus's criticism
his initial misunderstanding.
>even though a simple google-search (like I did) shows
>Nordhaus to have a maths Ph.D from the University of Utah.
>Presumably, credentials mean something.
for deciding whether a critique is valid or invalid. The
math of the critique stands for itself.
>3) He shows no signs of having done any study of any of
>the related research.
And what signs were you looking for?
And why should he undertake what could easily be years of
study of prior research, if the idea for his proof is along
completely different lines.
That would have created quite a barrier to entry.
>But this is just a matter of semantics.
>
>I guess maths-crankiness belongs on a scale.
>
>If the only way to be a maths crank is to write
>unintelligible gibberish and then blame the maths community
>for failing to understand, then he's not a maths crank by
>that standard.
legitimate (non-crank) members of the mathematical community,
for which the author asserted the result as correct, only
for a flaw to be later discovered.
>In the defence of the way I'm using the term. Consider
>the following: In the pre-usenet era, suppose a famous number
>theorist said "Hell, I'm being flooded with mail from cranks
>who are saying they've proved the Goldbach conjecture!"
>
>The Hovdan paper seems like an excellent example of the type
>of thing we would expect the number theorist to be complaining
>about.
Highly unlikely the fictitious number theorist is being flooded
with proposed proofs of the Goldbach conjecture written at a
level of rigor and mathematical maturity greater than or equal
to that of Hovdan's proof.
>And if the famous number theorist did have the Hovdan paper in
>mind in my hypothetical scenario,
>it would be most unlikely for another mathematician to say
>"Wait a minute. I don't think Hovdan's a crank." No,
>another mathematician would see Hovdan as cranky because
>it's an attempt at an extremely elementary and extremely
>short proof of one of the great unsolved problems.
unsolved problem using an elementary (sub-graduate level)
approach? A total waste of time? No point? No chance of
success?
And if despite your pessimistic "don't bother" advice, they
try anyway, they shouldn't dare to post a proposed argument to
an informal discussion group such as sci.math, for fear of
being called a crank?
In my opinion, your point of view is oppressive and overly
aristocratic.
quasi
Transfer Principle
Jan 23, 2012, 6:24:11 PM1/23/12
to
On Jan 23, 8:25 am, Paul <pepste...@gmail.com> wrote:
> On Jan 23, 12:46 pm, Tonico <Tonic...@yahoo.com> wrote:
> ...
> > I think Hovdan's try to prove G.B. was a good, honest one: good
> > because it probably gave some insights to him or to some of the
> > readers, honest because it actually looked like a sincere effort.
> > Hovdan doesn't belong in the crankhood neighborhood, unlike many
> > others who not only announce pompously their "achievments" but also
> > will not pay any attention to critics to their work, many a time a
> > pretty lousy one.
> Agree totally with your first para -- "I think ... effort".
> Of course, it's a matter of definition whether Hovdan behaved like a
> "mathematical crank".
> From my understanding of the term, I would say "Yes, he was maths-
> cranky."
Disclaimer: I'm aware that Hovdan has not given a satisfactory proof
> On Jan 23, 12:46 pm, Tonico <Tonic...@yahoo.com> wrote:
> ...
> > I think Hovdan's try to prove G.B. was a good, honest one: good
> > because it probably gave some insights to him or to some of the
> > readers, honest because it actually looked like a sincere effort.
> > Hovdan doesn't belong in the crankhood neighborhood, unlike many
> > others who not only announce pompously their "achievments" but also
> > will not pay any attention to critics to their work, many a time a
> > pretty lousy one.
> Agree totally with your first para -- "I think ... effort".
> Of course, it's a matter of definition whether Hovdan behaved like a
> "mathematical crank".
> From my understanding of the term, I would say "Yes, he was maths-
> cranky."
of Goldbach's conjecture. I'm aware that many mathematicians are
skeptical that an elementary proof of Goldbach exists, since if it
did, it would have been found centuries, if not millennia ago.
That being said, this is No Name Calling Week, and I noticed that
Epstein just used the c-word insult to describe Hovdan.
Let's see what justification Epstein gives for using the c-word:
> He was maths-cranky because
> 1) His initial posts didn't show enough self-doubt. He never said
> anything like "I'm sure the Goldbach conjecture can't be proved so
> easily by elementary means, so I would like some help in finding the
> mistake."
> 2) He was slow to accept Nordhaus's criticism even though a simple
> google-search (like I did) shows Nordhaus to have a maths Ph.D from
> the University of Utah. Presumably, credentials mean something.
> 3) He shows no signs of having done any study of any of the related
> research.
> But this is just a matter of semantics.
an elementary proof of Goldbach is even possible. Unlike the other
insult threads which possibly involve some nonstandard theories of
infinite sets, Goldbach involves only standard theories. (That is to
say, since Goldbach has been verified up to around a quintillion, an
ultrafinitist claiming that 10^18 is the largest number and thus
Goldbach is proved in the ultrafinitist theory will not receive the
glory that a resolver of Goldbach in standard theory would.) Thus I
agree with 1) the most.
I partly agree with 2). Yes, credentials mean something, and it's
unlikely that an amateur will ever resolve Goldbach. It's just that
emphasizing credentials hints at the idea that non-professionals
have little, if anything to contribute to sci.math at all. I've
discussed this notion in previous threads (at least a year ago).
But 3) is one with which I disagree the most. "Study of the related
research" sounds as if it involves reading books that might not be
accessible to the OP.
> In the defence of the way I'm using the term. Consider the following:
> In the pre-usenet era, suppose a famous number theorist said "Hell,
> I'm being flooded with mail from cranks who are saying they've proved
> the Goldbach conjecture!"
is overused. Interesting point there about the pre-Usenet use of
that word, but it seems to be on Usenet where that word has been
overused -- and IMHO abused.
I'll admit, though, that Epstein's use of the c-word isn't as bad
as the typical use of that word at sci.math. I can't defend Hovdan,
since I can't argue that he really has a proof of Goldbach, which
is a significant conjecture about (finite-sized) natural numbers in
_standard_theory_ only. And I'm not sure which is worse -- calling
a poster the c-word directly, or starting a new thread to call a
poster the c-word, as Epstein has done.
But during this No Name Calling Week especially, I want to focus my
efforts on ways to reduce the use of that c-word at sci.math.
quasi
Jan 23, 2012, 7:10:45 PM1/23/12
to
On Mon, 23 Jan 2012 15:24:11 -0800 (PST), Transfer Principle
<david.l...@lausd.net> wrote:
... this is No Name Calling Week
Say's who?
And by what authority?
Your rantings have had little effect except to make you
look like a fool.
quasi
<david.l...@lausd.net> wrote:
... this is No Name Calling Week
Say's who?
And by what authority?
Your rantings have had little effect except to make you
look like a fool.
quasi
Tonico
Jan 23, 2012, 7:21:33 PM1/23/12
to
On Jan 24, 1:24 am, Transfer Principle <david.l.wal...@lausd.net>
wrote:
millenia ago...in fact, Goldbach and his conjecture have been around
less than 0.4 millenium, so it'd be highly impossible that something
inexistent 400 years ago could have been solved millenia ago.
Of course, perhaps you meant to say that if we mathematicians are
skeptical an elementary proof of G.B. exists since if G.B. was
elementarily provable then somebody would have given a proof some
thousands of year ago...but who can tell for sure?
Oh, and I'm a mathematician and I don't think anything even close to
what you think many mathematicians do, FYI. ***
>
> That being said, this is No Name Calling Week, and I noticed that
> Epstein just used the c-word insult to describe Hovdan.
>
> Let's see what justification Epstein gives for using the c-word:
>
> > He was maths-cranky because
> > 1) His initial posts didn't show enough self-doubt. He never said
> > anything like "I'm sure the Goldbach conjecture can't be proved so
> > easily by elementary means, so I would like some help in finding the
> > mistake."
> > 2) He was slow to accept Nordhaus's criticism even though a simple
> > google-search (like I did) shows Nordhaus to have a maths Ph.D from
> > the University of Utah. Presumably, credentials mean something.
> > 3) He shows no signs of having done any study of any of the related
> > research.
> > But this is just a matter of semantics.
>
> As I mentioned in the disclaimer, I understand the skepticism that
> an elementary proof of Goldbach is even possible. Unlike the other
> insult threads which possibly involve some nonstandard theories of
> infinite sets,
**** You don't learn , do you mom? The "insult threads" do not involve
"nonstandard theoreis of infinite sets" but nonsensical rubbish spat
by non-mathematician cranks, if you excuse my being subtle. ****
**** It's really heart-warming to observe your clarification about
natural numbers: finite sized.
Because, as we all know, infinite-sized natural num,bers can be eerie.
***
> But during this No Name Calling Week especially, I want to focus my
> efforts on ways to reduce the use of that c-word at sci.math.
***** Crank, crank, crank, crank, crank, crank, crank, crank,
crank...there, "no-name calling week" has been busted, so why won't
you better focus your efforts in some mathematical thing?
Also, don't be that prude, mom: the c-work is C-R-A-N-K...CRANK.
Nothing happens if you write it down.
Tonio
wrote:
> On Jan 23, 8:25 am, Paul <pepste...@gmail.com> wrote:
>
> > On Jan 23, 12:46 pm, Tonico <Tonic...@yahoo.com> wrote:
> > ...
> > > I think Hovdan's try to prove G.B. was a good, honest one: good
> > > because it probably gave some insights to him or to some of the
> > > readers, honest because it actually looked like a sincere effort.
> > > Hovdan doesn't belong in the crankhood neighborhood, unlike many
> > > others who not only announce pompously their "achievments" but also
> > > will not pay any attention to critics to their work, many a time a
> > > pretty lousy one.
> > Agree totally with your first para -- "I think ... effort".
> > Of course, it's a matter of definition whether Hovdan behaved like a
> > "mathematical crank".
> > From my understanding of the term, I would say "Yes, he was maths-
> > cranky."
>
> Disclaimer: I'm aware that Hovdan has not given a satisfactory proof
> of Goldbach's conjecture. I'm aware that many mathematicians are
> skeptical that an elementary proof of Goldbach exists, since if it
> did, it would have been found centuries, if not millennia ago.
*** Errm...mom, Goldbach and his conjecture were pretty inexistent
>
> > On Jan 23, 12:46 pm, Tonico <Tonic...@yahoo.com> wrote:
> > ...
> > > I think Hovdan's try to prove G.B. was a good, honest one: good
> > > because it probably gave some insights to him or to some of the
> > > readers, honest because it actually looked like a sincere effort.
> > > Hovdan doesn't belong in the crankhood neighborhood, unlike many
> > > others who not only announce pompously their "achievments" but also
> > > will not pay any attention to critics to their work, many a time a
> > > pretty lousy one.
> > Agree totally with your first para -- "I think ... effort".
> > Of course, it's a matter of definition whether Hovdan behaved like a
> > "mathematical crank".
> > From my understanding of the term, I would say "Yes, he was maths-
> > cranky."
>
> Disclaimer: I'm aware that Hovdan has not given a satisfactory proof
> of Goldbach's conjecture. I'm aware that many mathematicians are
> skeptical that an elementary proof of Goldbach exists, since if it
> did, it would have been found centuries, if not millennia ago.
millenia ago...in fact, Goldbach and his conjecture have been around
less than 0.4 millenium, so it'd be highly impossible that something
inexistent 400 years ago could have been solved millenia ago.
Of course, perhaps you meant to say that if we mathematicians are
skeptical an elementary proof of G.B. exists since if G.B. was
elementarily provable then somebody would have given a proof some
thousands of year ago...but who can tell for sure?
Oh, and I'm a mathematician and I don't think anything even close to
what you think many mathematicians do, FYI. ***
>
> That being said, this is No Name Calling Week, and I noticed that
> Epstein just used the c-word insult to describe Hovdan.
>
> Let's see what justification Epstein gives for using the c-word:
>
> > He was maths-cranky because
> > 1) His initial posts didn't show enough self-doubt. He never said
> > anything like "I'm sure the Goldbach conjecture can't be proved so
> > easily by elementary means, so I would like some help in finding the
> > mistake."
> > 2) He was slow to accept Nordhaus's criticism even though a simple
> > google-search (like I did) shows Nordhaus to have a maths Ph.D from
> > the University of Utah. Presumably, credentials mean something.
> > 3) He shows no signs of having done any study of any of the related
> > research.
> > But this is just a matter of semantics.
>
> As I mentioned in the disclaimer, I understand the skepticism that
> an elementary proof of Goldbach is even possible. Unlike the other
> insult threads which possibly involve some nonstandard theories of
> infinite sets,
"nonstandard theoreis of infinite sets" but nonsensical rubbish spat
by non-mathematician cranks, if you excuse my being subtle. ****
natural numbers: finite sized.
Because, as we all know, infinite-sized natural num,bers can be eerie.
***
> But during this No Name Calling Week especially, I want to focus my
> efforts on ways to reduce the use of that c-word at sci.math.
crank...there, "no-name calling week" has been busted, so why won't
you better focus your efforts in some mathematical thing?
Also, don't be that prude, mom: the c-work is C-R-A-N-K...CRANK.
Nothing happens if you write it down.
Tonio
Tonico
Jan 23, 2012, 7:22:43 PM1/23/12
to
On Jan 24, 2:10 am, quasi <qu...@null.set> wrote:
> On Mon, 23 Jan 2012 15:24:11 -0800 (PST), Transfer Principle
>
> On Mon, 23 Jan 2012 15:24:11 -0800 (PST), Transfer Principle
>
> <david.l.wal...@lausd.net> wrote:
>
> ... this is No Name Calling Week
>
> Say's who?
>
> And by what authority?
>
> Your rantings have had little effect except to make you
> look like a fool.
>
> quasi
Oops! Quasi didn't respect the no-name calling week...heresy!
>
> ... this is No Name Calling Week
>
> Say's who?
>
> And by what authority?
>
> Your rantings have had little effect except to make you
> look like a fool.
>
> quasi
Tonio
Transfer Principle
Jan 23, 2012, 11:41:27 PM1/23/12
to
On Jan 23, 4:21 pm, Tonico <Tonic...@yahoo.com> wrote:
> On Jan 24, 1:24 am, Transfer Principle <david.l.wal...@lausd.net>
> wrote:
> > Disclaimer: I'm aware that Hovdan has not given a satisfactory proof
> > of Goldbach's conjecture. I'm aware that many mathematicians are
> > skeptical that an elementary proof of Goldbach exists, since if it
> > did, it would have been found centuries, if not millennia ago.
> *** Errm...mom, Goldbach and his conjecture were pretty inexistent
> millenia ago...in fact, Goldbach and his conjecture have been around
> less than 0.4 millenium, so it'd be highly impossible that something
> inexistent 400 years ago could have been solved millenia ago.
The reason for my disclaimer is that I thought that defending
> On Jan 24, 1:24 am, Transfer Principle <david.l.wal...@lausd.net>
> wrote:
> > Disclaimer: I'm aware that Hovdan has not given a satisfactory proof
> > of Goldbach's conjecture. I'm aware that many mathematicians are
> > skeptical that an elementary proof of Goldbach exists, since if it
> > did, it would have been found centuries, if not millennia ago.
> *** Errm...mom, Goldbach and his conjecture were pretty inexistent
> millenia ago...in fact, Goldbach and his conjecture have been around
> less than 0.4 millenium, so it'd be highly impossible that something
> inexistent 400 years ago could have been solved millenia ago.
Hovdan from Epstein's insult was tantamount to claiming that
Hovdan actually had a completed correct proof of GB. But, as I
soon found out, it's possible to defend Hovdan without claiming
correctness of the proof.
> Of course, perhaps you meant to say that if we mathematicians are
> skeptical an elementary proof of G.B. exists since if G.B. was
> elementarily provable then somebody would have given a proof some
> thousands of year ago...but who can tell for sure?
Myerson, 22nd, approx. 6AM Greenwich:
"Plausibility = roughly zero. The problem has been around
for a long time, and has attracted the attention of many
brilliant people. If they didn't find an elementary proof,
chances are there isn't one."
for a long time, and has attracted the attention of many
brilliant people. If they didn't find an elementary proof,
chances are there isn't one."
> Oh, and I'm a mathematician and I don't think anything even close to
> what you think many mathematicians do, FYI. ***
And now I finally see what's going here, especially after seeing
> what you think many mathematicians do, FYI. ***
quasi's post to Epstein just before my own.
One thing that I said I'd do this week is make fewer groups,
especially if the words I used to describe the groups end up being
construed as insults. In this thread, I grouped all the previous
posters, and even though the word I used to describe the group was
definitely _not_ an insult ("mathematicians"), Tonio still catches
me grouping.
Now that the group is gone, I can see clearly what's happening in
this thread. Epstein insulted Hovdan, and quasi and Tonio are
actually defending _Hovdan_ as not deserving the c-word!
Note that I entered this thread wanting the defend Hovdan against
Epstein's use of the c-word. And as always, I ask myself, what can
I do to help out _Hovdan_ in this thread?
It appears that the correct answer is for me to leave the thread. I
see that there are already posters defending Hovdan, and they
already outnumber the insulter (one insulter vs. two defenders). In
addition, my presence here is distracting Hovdan's defenders from
defending Hovdan.
I won't leave completely, but I just won't _post_. I'll go watch to
see what a _real_ defense of a person called the c-word actually
looks like, and I'll use that knowledge to help defend insulted
posters in future threads.
> > But during this No Name Calling Week especially, I want to focus my
> > efforts on ways to reduce the use of that c-word at sci.math.
> ***** Crank, crank, crank, crank, crank, crank, crank, crank,
> crank...there, "no-name calling week" has been busted, so why won't
> you better focus your efforts in some mathematical thing?
thread (at sci.logic) do?
But I'll gladly forget that I ever saw those seven posts. All that
matters is that in the here and now, Tonio is defending Hovdan, and
I want to get out of the way so that he can keep on defending him.
> Also, don't be that prude, mom: the c-work is C-R-A-N-K...CRANK.
> Nothing happens if you write it down.
criticized me for using the word _more_often_ than those posters
whom I was criticizing. Thus, something _did_ happen when I wrote
it down, and I avoid writing it out so that the thing that's
already happened won't happen again.
> Oops! Quasi didn't respect the no-name calling week...heresy!
could've hoped for. He's defending Hovdan from being called names.
And so concludes my last post of the thread. I sincerely wish quasi
and Tonio good luck in convincing Epstein that Hovdan doesn't merit
the c-word, and eagerly await Epstein's response to quasi's post.
Tonico
Jan 24, 2012, 6:23:10 AM1/24/12
to
On Jan 24, 6:41 am, Transfer Principle <david.l.wal...@lausd.net>
*** As encouraging and exciting as your announce of no more
participating in this thread is mom, I'm afraid your watching
expectations of defence could be heartbreaking dissapointed, at least
from my side.
I certainly could add one post or two about this issue in this thread,
but I'd hardly go beyond that as my spirit isn't overwhelmed with
feelings of poetical justice and sword-drawing chivalry.
Sorry, no Don Quijote over here...at most a tired Sancho Panza. ***
>
> > > But during this No Name Calling Week especially, I want to focus my
> > > efforts on ways to reduce the use of that c-word at sci.math.
> > ***** Crank, crank, crank, crank, crank, crank, crank, crank,
> > crank...there, "no-name calling week" has been busted, so why won't
> > you better focus your efforts in some mathematical thing?
>
> Some mathematical thing, as the seven i-word posts back in the Herc
> thread (at sci.logic) do?
>
> But I'll gladly forget that I ever saw those seven posts. All that
> matters is that in the here and now, Tonio is defending Hovdan, and
> I want to get out of the way so that he can keep on defending him.
*** "Seven i=word...seven posts..."...mom, are you high or you've
taken on the number 7 as a religious mantra? What are you talking
about and who cares what happens in other forums?
Now, you can use any word (a c-word, an i-word, a k-word or a ж-word)
you want, just stick to maths more often than you do to knightly
efforts of defenceless princesses...I mean, participants in these
threads agains those awful c-word-using dragoons...I mean,
mathematicians. ***
>
> > Also, don't be that prude, mom: the c-work is C-R-A-N-K...CRANK.
> > Nothing happens if you write it down.
>
> I used to spell the c-word out all the time. But then others
> criticized me for using the word _more_often_ than those posters
> whom I was criticizing. Thus, something _did_ happen when I wrote
> it down, and I avoid writing it out so that the thing that's
> already happened won't happen again.
**** You shouldn't be so prone to give a damn about what others think/
say about you, in particular in these open-wide over-public forums,
lest your heart will get broken very often. ****
>
> > Oops! Quasi didn't respect the no-name calling week...heresy!
>
> Actually, quasi respected No Name Calling Week _better_ than I
> could've hoped for. He's defending Hovdan from being called names.
>
> And so concludes my last post of the thread. I sincerely wish quasi
> and Tonio good luck in convincing Epstein that Hovdan doesn't merit
> the c-word, and eagerly await Epstein's response to quasi's post.
I've no interest whatsoever in convincing Paul or anyone else that
somebody is or isn't something. All I was trying is to make a
mathematical point on some paper which, I believe, proves that some
serious work was done.
Yeah, I know: I'm not as good and spiritual as you are as I don't
defend people from being called names, but what to do: not all were
blessed with such a morally superior and brave soul as you were, mom.
Deal with it.
Tonio
participating in this thread is mom, I'm afraid your watching
expectations of defence could be heartbreaking dissapointed, at least
from my side.
I certainly could add one post or two about this issue in this thread,
but I'd hardly go beyond that as my spirit isn't overwhelmed with
feelings of poetical justice and sword-drawing chivalry.
Sorry, no Don Quijote over here...at most a tired Sancho Panza. ***
>
> > > But during this No Name Calling Week especially, I want to focus my
> > > efforts on ways to reduce the use of that c-word at sci.math.
> > ***** Crank, crank, crank, crank, crank, crank, crank, crank,
> > crank...there, "no-name calling week" has been busted, so why won't
> > you better focus your efforts in some mathematical thing?
>
> Some mathematical thing, as the seven i-word posts back in the Herc
> thread (at sci.logic) do?
>
> But I'll gladly forget that I ever saw those seven posts. All that
> matters is that in the here and now, Tonio is defending Hovdan, and
> I want to get out of the way so that he can keep on defending him.
taken on the number 7 as a religious mantra? What are you talking
about and who cares what happens in other forums?
Now, you can use any word (a c-word, an i-word, a k-word or a ж-word)
you want, just stick to maths more often than you do to knightly
efforts of defenceless princesses...I mean, participants in these
threads agains those awful c-word-using dragoons...I mean,
mathematicians. ***
>
> > Also, don't be that prude, mom: the c-work is C-R-A-N-K...CRANK.
> > Nothing happens if you write it down.
>
> I used to spell the c-word out all the time. But then others
> criticized me for using the word _more_often_ than those posters
> whom I was criticizing. Thus, something _did_ happen when I wrote
> it down, and I avoid writing it out so that the thing that's
> already happened won't happen again.
say about you, in particular in these open-wide over-public forums,
lest your heart will get broken very often. ****
>
> > Oops! Quasi didn't respect the no-name calling week...heresy!
>
> Actually, quasi respected No Name Calling Week _better_ than I
> could've hoped for. He's defending Hovdan from being called names.
>
> And so concludes my last post of the thread. I sincerely wish quasi
> and Tonio good luck in convincing Epstein that Hovdan doesn't merit
> the c-word, and eagerly await Epstein's response to quasi's post.
somebody is or isn't something. All I was trying is to make a
mathematical point on some paper which, I believe, proves that some
serious work was done.
Yeah, I know: I'm not as good and spiritual as you are as I don't
defend people from being called names, but what to do: not all were
blessed with such a morally superior and brave soul as you were, mom.
Deal with it.
Tonio
Jesse F. Hughes
Jan 24, 2012, 6:51:29 AM1/24/12
to
Transfer Principle <david.l...@lausd.net> writes:
> I used to spell the c-word out all the time. But then others
> criticized me for using the word _more_often_ than those posters
> whom I was criticizing. Thus, something _did_ happen when I wrote
> it down, and I avoid writing it out so that the thing that's
> already happened won't happen again.
Wow. Er. Just wow.
> I used to spell the c-word out all the time. But then others
> criticized me for using the word _more_often_ than those posters
> whom I was criticizing. Thus, something _did_ happen when I wrote
> it down, and I avoid writing it out so that the thing that's
> already happened won't happen again.
Your thought processes (if we can call it that) are really fascinating.
--
Jesse F. Hughes
"Wiles made somewhere around half a million dollars U.S. that I heard
about, and I know he didn't take major endorsements."
--JSH on the rewards of proving Fermat's last theorem.
Bill Taylor
Jan 24, 2012, 8:40:02 AM1/24/12
to
On Jan 23, 12:00 am, Tonico <Tonic...@yahoo.com> wrote:
> This is one of the main reasons why there are so many cranks and
> trolls stinking around the web about Cantor's Theorem, FLT or Goldbach
What puzzles me is that so many good chaps here, keep on trying to
> This is one of the main reasons why there are so many cranks and
> trolls stinking around the web about Cantor's Theorem, FLT or Goldbach
educate them long after it has become apparent that they're hopeless.
"stinking around the net" is a good term, BTW!
> but you can hardly find any of these beasts dealing with R.H.,
> Poincare's Conjecture (already a Theorem) or other more advanced
> stuff, as these last ones already require some deeper knowledge of
> mathematics to deal with.
of the fame that would attach to accidentally solving it;
but of course you provide the answer well.
Along with Cantor, FLT, 7 Goldbach, you failed to mention Godel,
which is perhaps the king area for crank-hood. This one even
attracts otherwise serious cranks like Penrose!
Another lack of crankdom that puzzles me is CH. Given that
the statement of CH is at least as easy as that of Cantor,
and the fact that it has no dis/proof, (or as a crank
would say "alLEGedly no dis/proof"), it would seem
to be an unfailing magnet for the aspiring crank.
Finally, where have all the angle trisectors gone?
They used to be so common in the old days!
-- Bulldozing Bill
Michael Stemper
Jan 24, 2012, 8:48:01 AM1/24/12
to
--
Michael F. Stemper
#include <Standard_Disclaimer>
Always remember that you are unique. Just like everyone else.
Bill Taylor
Jan 24, 2012, 8:52:44 AM1/24/12
to
On Jan 22, 8:41 pm, Gustavo Broos <gpu...@gmail.com> wrote:
> I wish there was a constant
> effort to make math more accessible to everybody (me included),
> but is that even possible?
I think there is such an effort, though it could always be bigger.
> I wish there was a constant
> effort to make math more accessible to everybody (me included),
> but is that even possible?
One of my favorite things I like to spring on everyday people
who appear to show a glimmering of interest or ability
in math, but never got into it, is the following:
(1 + 2 + 3 + 4)^2 = 1^3 + 2^3 + 3^3 + 4^3 .
I point out that this works "for any value of 4", and ask
them to take away the scrap of paper it's on, check it out
for several cases, and even see if they can prove it
(if they seem already quite good at math). They won't have
a hope of proving it, OC, but it may stir their interest more.
I have no idea whether any of my puzzlees has ever done more
math because of this (maybe I should get cards printed up?)
but the fascinated look they generally have on seeing it,
gives me a tiny hope.
I have even made a Haiku for it:-
** Sum the first few numbers,
** And square this. Now sum the cubes.
** Is it the same result?
-- Bashoan Bill
Jesse F. Hughes
Jan 24, 2012, 4:16:51 PM1/24/12
to
mste...@walkabout.empros.com (Michael Stemper) writes:
> In article <15726121.744.1327245475277.JavaMail.geo-discussion-forums@vbhn11>, Daryl McCullough <stevend...@yahoo.com> writes:
>>On Sunday, January 22, 2012 6:00:22 AM UTC-5, Tonico wrote:
>
>>> This is one of the main reasons why there are so many cranks and
>>> trolls stinking around the web about Cantor's Theorem, FLT or Goldbach
>>> Conj., but you can hardly find any of these beasts dealing with R.H.,
>>> Poincare's Conjecture (already a Theorem)
>>
>>So there's a niche waiting to be filled: We need a Riemann Hypothesis
>>crank.
>
> Haven't both AP and JSH claimed to have resolved it?
As far as I recall, JSH claimed that his "research" on prime counting
> In article <15726121.744.1327245475277.JavaMail.geo-discussion-forums@vbhn11>, Daryl McCullough <stevend...@yahoo.com> writes:
>>On Sunday, January 22, 2012 6:00:22 AM UTC-5, Tonico wrote:
>
>>> This is one of the main reasons why there are so many cranks and
>>> trolls stinking around the web about Cantor's Theorem, FLT or Goldbach
>>> Conj., but you can hardly find any of these beasts dealing with R.H.,
>>> Poincare's Conjecture (already a Theorem)
>>
>>So there's a niche waiting to be filled: We need a Riemann Hypothesis
>>crank.
>
> Haven't both AP and JSH claimed to have resolved it?
*might* prove that RH is false. I don't think he claimed to have a
proof of that.
--
Jesse F. Hughes
"Leaving things always seems to fix me,
Running seems to ease my worried mind."
-- Bad Livers, "Honey, I've Found a Brand New Way"
Tinus
Jan 24, 2012, 6:57:41 PM1/24/12
to
1) the increase of a square of size a by b increases it's area by bｲ+2ab
2) The sum of the first n-1 numbers equals 1/2 n (n-1).
3) Increasing the square of the size of the first n-1 numbers by the
number n results in an increase in area of bｲ+2ab. With b=n and a = 1/2
n (n-1) we get n^2 + n^2 (n-1) = n^3
4) The haiku is true for the first number.
5) induction leads to the haiku to be true for all numbers because of 3
Tonico
Jan 24, 2012, 10:25:59 PM1/24/12
to
On Jan 24, 3:48 pm, mstem...@walkabout.empros.com (Michael Stemper)
wrote:
cranks: I think they both, and perhaps AP even more, are (almost or
not) deranged individuals, edging on schizophrenia and suffering from
an almost complete loss of touch with anything ressembling reality,
whatever that might be for most of us.
But for some newbies and some rather earnest hunters, almost nobody
else dealt with AP a few years ago, and if I'm a regular sample of the
forum, I think the huge majority of us don't even open anything signed
by AP already a good ammount of time.
JSH, OTOH, as been away for quite a while now.
Tonio
wrote:
> In article <15726121.744.1327245475277.JavaMail.geo-discussion-forums@vbhn11>, Daryl McCullough <stevendaryl3...@yahoo.com> writes:
> >On Sunday, January 22, 2012 6:00:22 AM UTC-5, Tonico wrote:
> >> This is one of the main reasons why there are so many cranks and
> >> trolls stinking around the web about Cantor's Theorem, FLT or Goldbach
> >> Conj., but you can hardly find any of these beasts dealing with R.H.,
> >> Poincare's Conjecture (already a Theorem)
>
> >So there's a niche waiting to be filled: We need a Riemann Hypothesis
> >crank.
>
> Haven't both AP and JSH claimed to have resolved it?
**** Perhaps, but I think they both are way beyond down-to-Earth
> >On Sunday, January 22, 2012 6:00:22 AM UTC-5, Tonico wrote:
> >> This is one of the main reasons why there are so many cranks and
> >> trolls stinking around the web about Cantor's Theorem, FLT or Goldbach
> >> Conj., but you can hardly find any of these beasts dealing with R.H.,
> >> Poincare's Conjecture (already a Theorem)
>
> >So there's a niche waiting to be filled: We need a Riemann Hypothesis
> >crank.
>
> Haven't both AP and JSH claimed to have resolved it?
cranks: I think they both, and perhaps AP even more, are (almost or
not) deranged individuals, edging on schizophrenia and suffering from
an almost complete loss of touch with anything ressembling reality,
whatever that might be for most of us.
But for some newbies and some rather earnest hunters, almost nobody
else dealt with AP a few years ago, and if I'm a regular sample of the
forum, I think the huge majority of us don't even open anything signed
by AP already a good ammount of time.
JSH, OTOH, as been away for quite a while now.
Tonio
1treePetrifiedForestLane
Jan 24, 2012, 11:01:55 PM1/24/12
to
possibly, because RH involves complex numbers.
can the angle be trisected by origami?
thus:
Peak Oil is the oilcos' own statistical paradigm --
see Deffreyes' two books on this, excellent
for comprehending the oilcos' paradigm.... and,
cap & trade is just "free-er trade," undoubtedly gamed
as much as by any as the oilcos, for hedging purposes ... but,
however, the Koch brothers refer to it as a "tax,"
which it certainly is not.
just ask my Congressman Waxman about his original ('91) cap
and trade bill, passed unanimously by both houses --
it was mandatory; his new bill would
mandatorize the huge "voluntary" cap & trade regime,
behind the market-maker of the EU's mandatory scheme;
the British are really big on this, as you can see
in the article on CCX and ICE on http://larouchepub.com .-)
> it cannot be possible that Big Oil and Coal are using money
do you know,
the angle of total reflection of calm, open arctic water?...
do you know,
Morner's re-reanalysis of satellite telemetry on sea level?
can the angle be trisected by origami?
thus:
Peak Oil is the oilcos' own statistical paradigm --
see Deffreyes' two books on this, excellent
for comprehending the oilcos' paradigm.... and,
cap & trade is just "free-er trade," undoubtedly gamed
as much as by any as the oilcos, for hedging purposes ... but,
however, the Koch brothers refer to it as a "tax,"
which it certainly is not.
just ask my Congressman Waxman about his original ('91) cap
and trade bill, passed unanimously by both houses --
it was mandatory; his new bill would
mandatorize the huge "voluntary" cap & trade regime,
behind the market-maker of the EU's mandatory scheme;
the British are really big on this, as you can see
in the article on CCX and ICE on http://larouchepub.com .-)
> it cannot be possible that Big Oil and Coal are using money
do you know,
the angle of total reflection of calm, open arctic water?...
do you know,
Morner's re-reanalysis of satellite telemetry on sea level?
Paul
Jan 25, 2012, 8:16:47 AM1/25/12
to
On Jan 23, 10:56 pm, quasi <qu...@null.set> wrote:
...
It depends what you mean by "should" and it depends what the
individual hopes or expects to achieve.
Your first quoted para though is a reasonable summary of my views
(accepting your questions as rhetorical.)
I would modify it somewhat and wouldn't be critical if a number
theorist tried to use their expert knowledge to form an elementary
proof. Amateur attempst at elementary proofs are not a good idea, in
my opinion.
The reason I think they're a bad idea is that it's a far better
approach in every way, to spend a few years learning number theory,
and then think about the problem.
It has happened that untrained mathematicians in their 30s or 40s have
acquired expert knowledge themselves and gone on to become good
research mathematicians. This is a much more sensible thing for an
amateur to attempt, and is much more likely to succeed. Even if the
amateur's sole focus is to prove Goldbach, the important thing is to
_get the expert knowledge first_.
I would think that with determination and enough time to spare, expert
(Ph.D level) knowledge in number theory could well be achievable from
high-school knowledge in 6 to 10 years.
In reply to other criticisms of myself, no, I didn't open up a thread
to insult Hovdan. I asked some questions (which don't relate to
Hovdan) and am interested in the answers. For example, I was very
interested to read about the Dot conjecture.
I tried to explain that the Hovdan thread experience was perhaps part
of my _unconscious motivation_ for thinking about this issue of
elementary mathematics done by amateurs.
No, I wasn't insulting Hovdan. This is purely semantics.
I define a "mathematical crank" as being an amateur who tries to use
elementary means to solve great unsolved maths problems. Hovdan
behaved like a mathematical crank _according to the above definition_.
That's simply my definition of the term. I don't know if it's the
standard definition of the term. If the usual definition of the
phrase "mathematical crank" is different, then the more standard
definition should be used.
Dudley Underwood wrote a book about the issue so I would accept his
definition.
People might object to my definition with the challenge: "But what if
the amateur elementary proof is correct?"
My answer is that, if such a thing happens, the way in which we think
about amateur mathematics will be radically changed, and the way
notions of crankhood etc. are perceived will be radically changed.
Analogously, someone who regularly drives at 100 mph on the wrong side
of the road would be termed a "dangerous driver."
However, if it is demonstrated clearly that such a way to drive is in
fact safe, then our notions of what constitutes a "dangerous driver"
would be changed.
Paul Epstein
...
>
> So no one should even bother _trying_ to solve a famous
> unsolved problem using an elementary (sub-graduate level)
> approach? A total waste of time? No point? No chance of
> success?
>
> And if despite your pessimistic "don't bother" advice, they
> try anyway, they shouldn't dare to post a proposed argument to
> an informal discussion group such as sci.math, for fear of
> being called a crank?
>
> In my opinion, your point of view is oppressive and overly
> aristocratic.
With regard to "no one should even bother trying...?"
> So no one should even bother _trying_ to solve a famous
> unsolved problem using an elementary (sub-graduate level)
> approach? A total waste of time? No point? No chance of
> success?
>
> And if despite your pessimistic "don't bother" advice, they
> try anyway, they shouldn't dare to post a proposed argument to
> an informal discussion group such as sci.math, for fear of
> being called a crank?
>
> In my opinion, your point of view is oppressive and overly
> aristocratic.
It depends what you mean by "should" and it depends what the
individual hopes or expects to achieve.
Your first quoted para though is a reasonable summary of my views
(accepting your questions as rhetorical.)
I would modify it somewhat and wouldn't be critical if a number
theorist tried to use their expert knowledge to form an elementary
proof. Amateur attempst at elementary proofs are not a good idea, in
my opinion.
The reason I think they're a bad idea is that it's a far better
approach in every way, to spend a few years learning number theory,
and then think about the problem.
It has happened that untrained mathematicians in their 30s or 40s have
acquired expert knowledge themselves and gone on to become good
research mathematicians. This is a much more sensible thing for an
amateur to attempt, and is much more likely to succeed. Even if the
amateur's sole focus is to prove Goldbach, the important thing is to
_get the expert knowledge first_.
I would think that with determination and enough time to spare, expert
(Ph.D level) knowledge in number theory could well be achievable from
high-school knowledge in 6 to 10 years.
In reply to other criticisms of myself, no, I didn't open up a thread
to insult Hovdan. I asked some questions (which don't relate to
Hovdan) and am interested in the answers. For example, I was very
interested to read about the Dot conjecture.
I tried to explain that the Hovdan thread experience was perhaps part
of my _unconscious motivation_ for thinking about this issue of
elementary mathematics done by amateurs.
No, I wasn't insulting Hovdan. This is purely semantics.
I define a "mathematical crank" as being an amateur who tries to use
elementary means to solve great unsolved maths problems. Hovdan
behaved like a mathematical crank _according to the above definition_.
That's simply my definition of the term. I don't know if it's the
standard definition of the term. If the usual definition of the
phrase "mathematical crank" is different, then the more standard
definition should be used.
Dudley Underwood wrote a book about the issue so I would accept his
definition.
People might object to my definition with the challenge: "But what if
the amateur elementary proof is correct?"
My answer is that, if such a thing happens, the way in which we think
about amateur mathematics will be radically changed, and the way
notions of crankhood etc. are perceived will be radically changed.
Analogously, someone who regularly drives at 100 mph on the wrong side
of the road would be termed a "dangerous driver."
However, if it is demonstrated clearly that such a way to drive is in
fact safe, then our notions of what constitutes a "dangerous driver"
would be changed.
Paul Epstein
Pubkeybreaker
Jan 25, 2012, 9:57:00 AM1/25/12
to
On Jan 25, 8:16 am, Paul <pepste...@gmail.com> wrote:
> On Jan 23, 10:56 pm, quasi <qu...@null.set> wrote:
> ...
> On Jan 23, 10:56 pm, quasi <qu...@null.set> wrote:
> ...
> With regard to "no one should even bother trying...?"
>
>
> Amateur attempst at elementary proofs are not a good idea, in
> my opinion.
I agree.
> my opinion.
>
> The reason I think they're a bad idea is that it's a far better
> approach in every way, to spend a few years learning number theory,
> and then think about the problem.
> Even if the
> amateur's sole focus is to prove Goldbach, the important thing is to
> _get the expert knowledge first_.
>
> I would think that with determination and enough time to spare, expert
> (Ph.D level) knowledge in number theory could well be achievable from
> high-school knowledge in 6 to 10 years.
> I define a "mathematical crank" as being an amateur who tries to use
> elementary means to solve great unsolved maths problems.
apply it.
One thing that earns points is for someone to attempt a proof of a
problem without being aware of what attempts have been tried and
failed.....
>Hovdan
> behaved like a mathematical crank _according to the above definition_.
> Dudley Underwood wrote a book about the issue so I would accept his
> definition.
>
> People might object to my definition with the challenge: "But what if
> the amateur elementary proof is correct?"
Timothy Murphy
Jan 25, 2012, 11:43:20 AM1/25/12
to
Pubkeybreaker wrote:
>> People might object to my definition with the challenge: "But what if
>> the amateur elementary proof is correct?"
>
> Winning the lottery is more likely.
That seems to me a bad parallel, since _someone_ wins the lottery.
>> People might object to my definition with the challenge: "But what if
>> the amateur elementary proof is correct?"
>
> Winning the lottery is more likely.
Tonico
Jan 25, 2012, 1:51:15 PM1/25/12
to
that period of their life. I can't agree with that definition of crank
as it lacks what I consider two essential ingredients of it:
stubborness and an inner feeling of superiority over professionals.
For me, a crank is not merely someone being an amateur attempting to
tackle open, or whatever, mathematical problems, but mainly someone
doing so with a pigheadness that astonishes and with a haughtyness
that causes awe.
He will not only reject any attempt to make him understand his
mistkaes (many times pretty crass ones), but will also lecture YOU,
the mathematician, not only about how deeply and sadly mistaken you
are in saying he's wrong but even sometimes about how mathematicians
and mathematics as a whole is wrong and he has just discovered that.
As a particular I'd rather encourage mathematical greenhorns in trying
their strength at whatever they want, as long as they AT LEAST
understand the basic assumptions and rules of the game, although as a
professional academic I won't even dare to dream to read, leave alone
research and answer, what many enthusiastic but many times ignorant
amateurs have to say about squaring circles, solving the quintic or
Fermat's Last Theorem, as well intentioned, honest and open-minded as
they can be (well...perhaps if I were offered a rather hefty ammount
of money by some nutcase or something like that), and this is why I'd
advice any honest, intelligent and diligent amateur wishing to write
something to get some mathematician to read, check, correct and/or
eventually reject whatever they may be trying to do, and I think this
forum can do the job pretty well: some amateur comes in, presents his
efforts in whatever and waits, reads, answers backs and accepts
respectfully for some responses, reactions, advices, rejections, etc.
by mathematicians.
Because of the above I still don't consider Hovdan anything even close
to the usual annoying cranks we've all met in this forum, and I even
tend to appraise positively his efforts trying to tackle a hard
problem, as long as he LEARNS from his mistakes, continues to
study...and why not, tries once again later.
Tonio
Paul
Jan 25, 2012, 2:14:58 PM1/25/12
to
> > I define a "mathematical crank" as being an amateur who tries to use
> > elementary means to solve great unsolved maths problems. Hovdan
> > behaved like a mathematical crank _according to the above definition_.
>
> Well, yes...and so did Fermat, Euler and some others during this or
> that period of their life. I can't agree with that definition of crank
> as it lacks what I consider two essential ingredients of it:
> stubborness and an inner feeling of superiority over professionals.
>
...
> > elementary means to solve great unsolved maths problems. Hovdan
> > behaved like a mathematical crank _according to the above definition_.
>
> Well, yes...and so did Fermat, Euler and some others during this or
> that period of their life. I can't agree with that definition of crank
> as it lacks what I consider two essential ingredients of it:
> stubborness and an inner feeling of superiority over professionals.
>
But didn't Fermat and Euler know and use the most sophisticated
mathematics knowledge of their day? This is a genuine question -- I
don't know the answer.
I agree with a large part of your posting but I don't get the Fermat
and Euler reference.
Yes, Fermat, in particular, did try elementary attempts to prove his
(then) conjecture. But isn't that just because the more sophisticated
number theory hadn't been developed yet?
My definition of "mathematical crank" simply differs from yours.
In particular, I would indeed deem it maths-cranky behaviour to try
and prove Goldbach's conjecture without learning any machinery that
was developed after Euler.
The Fermat & Euler comparison only seems to hold water if you can
claim that they never learned or used what their predecessors had
achieved.
Paul Epstein
quasi
Jan 25, 2012, 3:24:41 PM1/25/12
to
On Wed, 25 Jan 2012 05:16:47 -0800 (PST), Paul <peps...@gmail.com>
wrote:
>On Jan 23, 10:56 pm, quasi <qu...@null.set> wrote:
>...
>>
>> So no one should even bother _trying_ to solve a famous
>> unsolved problem using an elementary (sub-graduate level)
>> approach? A total waste of time? No point? No chance of
>> success?
>>
>> And if despite your pessimistic "don't bother" advice, they
>> try anyway, they shouldn't dare to post a proposed argument
>> to an informal discussion group such as sci.math, for fear
>> of being called a crank?
>>
>> In my opinion, your point of view is oppressive and overly
>> aristocratic.
>
>With regard to "no one should even bother trying...?"
>
>It depends what you mean by "should" and it depends what the
>individual hopes or expects to achieve. Your first quoted para
>though is a reasonable summary of my views (accepting your
>questions as rhetorical.)
>
>I would modify it somewhat and wouldn't be critical if a
>number theorist tried to use their expert knowledge to form
>an elementary proof. Amateur attempst at elementary proofs
>are not a good idea, in my opinion.
>
>The reason I think they're a bad idea is that it's a far
>better approach in every way, to spend a few years learning
>number theory, and then think about the problem.
What makes you think Hovdan didn't spend a few years learning
Number Theory?
>It has happened that untrained mathematicians in their 30s
>or 40s have acquired expert knowledge themselves and gone on
>to become good research mathematicians. This is a much more
>sensible thing for an amateur to attempt, and is much more
>likely to succeed.
How does the above relate to your labeling of Hovdan?
>Even if the amateur's sole focus is to prove Goldbach, the
>important thing is to _get the expert knowledge first_.
>
>I would think that with determination and enough time to
>spare, expert (Ph.D level) knowledge in number theory could
>well be achievable from high-school knowledge in 6 to 10
>years.
>
>In reply to other criticisms of myself, no, I didn't open up
>a thread to insult Hovdan.
I didn't claim that. Guilty conscience, perhaps?
But no matter -- the fact is, you _did_ insult Hovdan.
>I asked some questions (which don't relate to Hovdan) and am
>interested in the answers. For example, I was very interested
>to read about the Dot conjecture.
>
>I tried to explain that the Hovdan thread experience was
>perhaps part of my _unconscious motivation_
Unconscious motivation -- yeah, right.
>for thinking about this issue of elementary mathematics done
>by amateurs.
>
>No, I wasn't insulting Hovdan. This is purely semantics.
You must be kidding.
>I define a "mathematical crank" as being an amateur who
>tries to use elementary means to solve great unsolved maths
>problems. Hovdan behaved like a mathematical crank
>_according to the above definition_.
>
>That's simply my definition of the term. I don't know if it's
>the standard definition of the term.
But actually, since you've been in this forum for a number of
years, you _do_ know. In fact, you know that your "definition"
is _not_ consistent with how the term is typically used in
sci.math.
>If the usual definition of the phrase "mathematical crank" is
>different, then the more standard definition should be used.
Then get with the program. Otherwise pretty soon, if you keep
on relaxing the qualifying criteria for crankhood, we'll all
be cranks.
>Dudley Underwood wrote a book about the issue so I would accept
>his definition.
Because he wrote a book makes his definition the "standard"?
I don't think so. We are talking about the word "crank" which
is used informally as an insult, not a mathematical phrase such
as "finite field" for which the meaning is essentially standard
and universal.
Informal language elements are implicitly defined within a
community based on common usage.
In _this_ community (specifically sci.math) the word crank is
a strong insult typically targeted at those (and there are
plenty of them) who (1) post obvious nonsense and (2) can't be
reasoned with.
By that criterion, short of more evidence, Hovdan doesn't
deserve to be labeled a crank.
>People might object to my definition with the challenge: "But
>what if the amateur elementary proof is correct?" My answer is
>that, if such a thing happens, the way in which we think about
>amateur mathematics will be radically changed, and the way
>notions of crankhood etc. are perceived will be radically
>changed.
>
>Analogously, someone who regularly drives at 100 mph on the
>wrong side of the road would be termed a "dangerous driver."
A straw-man argument, once again.
You called Hovdan a crank. I objected.
But in your analogy above, the driver is clearly a lunatic.
We've had some cranks in sci.math who were clearly lunatics.
But Hovdan appears quite sane.
>However, if it is demonstrated clearly that such a way to
>drive is in fact safe, then our notions of what constitutes
>a "dangerous driver" would be changed.
As I said, it's a straw-man argument.
Bottom line:
(1) You are using your own overly broad definition of crank
which does not match normal usage in sci.math.
(2) Hovdan doesn't qualify as a crank (at least not yet).
quasi
wrote:
>On Jan 23, 10:56 pm, quasi <qu...@null.set> wrote:
>...
>>
>> So no one should even bother _trying_ to solve a famous
>> unsolved problem using an elementary (sub-graduate level)
>> approach? A total waste of time? No point? No chance of
>> success?
>>
>> And if despite your pessimistic "don't bother" advice, they
>> try anyway, they shouldn't dare to post a proposed argument
>> to an informal discussion group such as sci.math, for fear
>> of being called a crank?
>>
>> In my opinion, your point of view is oppressive and overly
>> aristocratic.
>
>With regard to "no one should even bother trying...?"
>
>It depends what you mean by "should" and it depends what the
>individual hopes or expects to achieve. Your first quoted para
>though is a reasonable summary of my views (accepting your
>questions as rhetorical.)
>
>I would modify it somewhat and wouldn't be critical if a
>number theorist tried to use their expert knowledge to form
>an elementary proof. Amateur attempst at elementary proofs
>are not a good idea, in my opinion.
>
>The reason I think they're a bad idea is that it's a far
>better approach in every way, to spend a few years learning
>number theory, and then think about the problem.
Number Theory?
>It has happened that untrained mathematicians in their 30s
>or 40s have acquired expert knowledge themselves and gone on
>to become good research mathematicians. This is a much more
>sensible thing for an amateur to attempt, and is much more
>likely to succeed.
>Even if the amateur's sole focus is to prove Goldbach, the
>important thing is to _get the expert knowledge first_.
>
>I would think that with determination and enough time to
>spare, expert (Ph.D level) knowledge in number theory could
>well be achievable from high-school knowledge in 6 to 10
>years.
>
>In reply to other criticisms of myself, no, I didn't open up
>a thread to insult Hovdan.
But no matter -- the fact is, you _did_ insult Hovdan.
>I asked some questions (which don't relate to Hovdan) and am
>interested in the answers. For example, I was very interested
>to read about the Dot conjecture.
>
>I tried to explain that the Hovdan thread experience was
>perhaps part of my _unconscious motivation_
>for thinking about this issue of elementary mathematics done
>by amateurs.
>
>No, I wasn't insulting Hovdan. This is purely semantics.
>I define a "mathematical crank" as being an amateur who
>tries to use elementary means to solve great unsolved maths
>problems. Hovdan behaved like a mathematical crank
>_according to the above definition_.
>
>That's simply my definition of the term. I don't know if it's
>the standard definition of the term.
years, you _do_ know. In fact, you know that your "definition"
is _not_ consistent with how the term is typically used in
sci.math.
>If the usual definition of the phrase "mathematical crank" is
>different, then the more standard definition should be used.
on relaxing the qualifying criteria for crankhood, we'll all
be cranks.
>Dudley Underwood wrote a book about the issue so I would accept
>his definition.
I don't think so. We are talking about the word "crank" which
is used informally as an insult, not a mathematical phrase such
as "finite field" for which the meaning is essentially standard
and universal.
Informal language elements are implicitly defined within a
community based on common usage.
In _this_ community (specifically sci.math) the word crank is
a strong insult typically targeted at those (and there are
plenty of them) who (1) post obvious nonsense and (2) can't be
reasoned with.
By that criterion, short of more evidence, Hovdan doesn't
deserve to be labeled a crank.
>People might object to my definition with the challenge: "But
>what if the amateur elementary proof is correct?" My answer is
>that, if such a thing happens, the way in which we think about
>amateur mathematics will be radically changed, and the way
>notions of crankhood etc. are perceived will be radically
>changed.
>
>Analogously, someone who regularly drives at 100 mph on the
>wrong side of the road would be termed a "dangerous driver."
You called Hovdan a crank. I objected.
But in your analogy above, the driver is clearly a lunatic.
We've had some cranks in sci.math who were clearly lunatics.
But Hovdan appears quite sane.
>However, if it is demonstrated clearly that such a way to
>drive is in fact safe, then our notions of what constitutes
>a "dangerous driver" would be changed.
Bottom line:
(1) You are using your own overly broad definition of crank
which does not match normal usage in sci.math.
(2) Hovdan doesn't qualify as a crank (at least not yet).
quasi
Paul
Jan 25, 2012, 3:36:40 PM1/25/12
to
On Jan 25, 8:24 pm, quasi <qu...@null.set> wrote:
...
...
> >In reply to other criticisms of myself, no, I didn't open up
> >a thread to insult Hovdan.
>
> I didn't claim that. Guilty conscience, perhaps?
No, no guilty conscience. Someone else on this thread (other than
> >a thread to insult Hovdan.
>
> I didn't claim that. Guilty conscience, perhaps?
you) did claim that.
> But actually, since you've been in this forum for a number of
> years, you _do_ know. In fact, you know that your "definition"
> is _not_ consistent with how the term is typically used in
> sci.math.
...
> In _this_ community (specifically sci.math) the word crank is
> a strong insult typically targeted at those (and there are
> plenty of them) who (1) post obvious nonsense and (2) can't be
> reasoned with.
>
> By that criterion, short of more evidence, Hovdan doesn't
> deserve to be labeled a crank.
...
> a strong insult typically targeted at those (and there are
> plenty of them) who (1) post obvious nonsense and (2) can't be
> reasoned with.
>
> By that criterion, short of more evidence, Hovdan doesn't
> deserve to be labeled a crank.
This is a very convincing argument that Hovdan should not be labelled
a crank on sci.math
However, the argument is based on information that I didn't know (see
above).
>
> Bottom line:
>
> (1) You are using your own overly broad definition of crank
> which does not match normal usage in sci.math.
>
> (2) Hovdan doesn't qualify as a crank (at least not yet).
>
Hovdan doesn't qualify as a crank by the sci-math definition.
Statements to the contrary by myself are hereby retracted/apologised
for etc. etc.
Paul Epstein
Tonico
Jan 26, 2012, 8:48:36 AM1/26/12
to
actually FORMALLY mathematics (this "formally" thing can be tricky,
but I guess we can content ourselves by agreeing it means "without
formal academic studies".
Euler studies philosophy in University, and tried his way (dad's
wishes...) inm Latin, Hebrew and some other stuff to become a pastor.
But he was AN AMATEUR studying some math here and there with
Bernoulli, one of Eulers' family's friends, and at this point he
already achieved some rather startling results.
It is also pretty well-known Euler's passion for using, working and
deducing stuff with infinite series that diverge (!) , and some of the
most amazing, prettiest formulae he ever discovered were obtained by
astonishing leaps of rigour and even logic (like the one for the
infinite product for the sine formula, which imho is one of the
finest, neatest formulae in the whole of mathematics).
Euler's work in the abovesense would get him kicked off in the buttox
now in any elementary analysis course, yet we all have so much learnt
from that...
So I won't ever, never hit amateurs trying their strength under the
assumptions I made clear in my past message, but I won't be shy of
showing my contempt on ignoramuses with an attitude with no respect
for anything.
Tonio
David Bernier
Jan 26, 2012, 9:45:26 AM1/26/12
to
very first person (pro. or amateur mathematecian)
to use in Diophantine equations what is
known in French as "methode de la descente de
Fermat" and in English as "Fermat method of
descent". Fermat applied it to showing that
x^4 + y^4 = z^4 implies xyz = 0,
under the assumption that x, y, z are in N.
(if memory serves me well).
I've been thinking that beyond formal definitions,
there are "embryonic ideas" that at some points
in time crystallize into at first somewhat vague
or mysterious technoques that "just work",
like the Heaviside methods that led to
"theorie des distributions" by L. Schwartz.
Another case might be Euler's generalization
of the little Fermat theorem:
g^k == 1 (mod m), where k = EulerTotient(m).
This can be understood as an exercise
in finite abelian group theory (admittedly
not finite group theory: I'm not sure
Euler perceived/channeled non-abelian
group theory methods ...)
Another case is Gauss, who seemed to be doing
basic commutative ring theory when he gave his
proofs for modular arithmetic basic theorems
in Disquisitiones Arithmeticae.
As for his discovery that the regular 17-gon
is constructible by ruler and compass,
I think it must be a stroke of genius, because
as far as I know, he was the first human to
know that ...
Dave
Paul
Jan 26, 2012, 10:00:59 AM1/26/12
to
domains in which they're operating.
For example, an amateur approach would be to try and prove Goldbach's
theorem without the knowledge obtainable from a standard undergraduate
number theory course. [No one's being accused of this, since, as has
been pointed out, it's hard to tell what someone does or doesn't
know.]
Even today, I think it's absolutely plausible that someone could
produce Fields-Medal work without going near a university. The
research is open to the public after all.
It's also completely plausible for an unemployed person to produce
historically important mathematics in this way.
But it seems implausible for someone to prove a great theorem without
acquiring Ph.D level expertise (as I said before). (But you don't
need to actually write a Ph.D of course. There are at least two great
active mathematicians who don't have one.)
Paul Epstein
1treePetrifiedForestLane
Jan 26, 2012, 8:20:48 PM1/26/12
to
incidentally, akin to the Fermat primes,
the origami-constructible polygons are those
with (non-second-power) factors,
being Pierpont primes, which I think includes all
of the Fermat ones.
thus:
Peak Oil is the oilcos' own statistical paradigm --
see Deffreyes' two books on this, excellent
for comprehending the oilcos' paradigm.... and,
cap & trade is just "free-er trade," undoubtedly gamed
as much as by any as the oilcos, for hedging purposes ... but,
however, the Koch brothers refer to it as a "tax,"
which it certainly is not.
thus:
the origami-constructible polygons are those
with (non-second-power) factors,
being Pierpont primes, which I think includes all
of the Fermat ones.
thus:
Peak Oil is the oilcos' own statistical paradigm --
see Deffreyes' two books on this, excellent
for comprehending the oilcos' paradigm.... and,
cap & trade is just "free-er trade," undoubtedly gamed
as much as by any as the oilcos, for hedging purposes ... but,
however, the Koch brothers refer to it as a "tax,"
which it certainly is not.
do you know,
the angle of total reflection of calm, open arctic water?...
do you know,
Morner's re-reanalysis of satellite telemetry on sea level?
> it cannot be possible that Big Oil and Coal are using money
the angle of total reflection of calm, open arctic water?...
do you know,
Morner's re-reanalysis of satellite telemetry on sea level?
> it cannot be possible that Big Oil and Coal are using money
amzoti
Jan 27, 2012, 12:02:11 PM1/27/12
to
Were you trying to get them to do what Wheatstone did (or something similar)?
http://en.wikipedia.org/wiki/Squared_triangular_number
http://en.wikipedia.org/wiki/Squared_triangular_number
Michael Press
Feb 1, 2012, 5:35:58 AM2/1/12
to
In article
<fb5f5c4f-a81f-4974...@o14g2000vbo.googlegroups.com>,
Paul <peps...@gmail.com> wrote:
> Does anyone know any examples of any significant theorems whose first
> proofs were elementary? By "elementary", I mean that they could be
> read by a non-exceptional first-year undergraduate.
An elementary proof often conveys very little
of what is going on. Still they are necessary first steps.
Take quadratic reciprocity. It has easily accessible
elementary proofs that came first.
The later proofs that rely on more advanced topics
are more illuminating.
The Chinese remainder theorem is first year
accessible. It is more explicable when expressed
in the realm of commutative rings.
The fundamental theorem of algebra is proved
straightforwardly with complex analysis
(not a first year topic); yet the proof using
differential topology is almost obvious, once
it is presented.
--
Michael Press
<fb5f5c4f-a81f-4974...@o14g2000vbo.googlegroups.com>,
Paul <peps...@gmail.com> wrote:
> Does anyone know any examples of any significant theorems whose first
> proofs were elementary? By "elementary", I mean that they could be
> read by a non-exceptional first-year undergraduate.
An elementary proof often conveys very little
of what is going on. Still they are necessary first steps.
Take quadratic reciprocity. It has easily accessible
elementary proofs that came first.
The later proofs that rely on more advanced topics
are more illuminating.
The Chinese remainder theorem is first year
accessible. It is more explicable when expressed
in the realm of commutative rings.
The fundamental theorem of algebra is proved
straightforwardly with complex analysis
(not a first year topic); yet the proof using
differential topology is almost obvious, once
it is presented.
--
Michael Press
taffer
Feb 1, 2012, 1:14:20 PM2/1/12
to
On Jan 23, 9:39 am, Paul <pepste...@gmail.com> wrote:
> I think that part of the (somewhat unconscious) motivation for my
> initial posting was to make a case against crankdom.
> However, I wouldn't say "No significant deep theorem has been proved
> by an amateur mathematician using elementary means" because I don't
> know if that's true. Perhaps the dot conjecture is a counter-example
> to the quoted statement above. By the way, after some casual
> googling, I couldn't find a clear (to me) statement of the dot
> conjecture, let alone a proof.
First of all, if theorem that has a statement that a total amateur
could understand, but only advanced algebraic number theory and
cohomology and whanot could prove, that's kind of an unarguable thing.
For example FLT (probably). These statements exist and are undeniably
interesting.
But if both the statement and the proof could be readily apprehended
by a total amateur, then what delineates it from any other theorem of
that sort? Luck, coincidence, the measure of desperation with which
mathematicians searched for a proof. I personally see no reason to
believe what Simon Singh says on that count.
After all in his book he also characterized the law of trichotomy "a<b
or a=b or a>b for any numbers a and b" as having gone hundreds of
years without proof before being proved in 1878 or something like
that. But this is misleading, because he means "cardinal numbers",
which had only recently being introduced.
> I think that part of the (somewhat unconscious) motivation for my
> initial posting was to make a case against crankdom.
> However, I wouldn't say "No significant deep theorem has been proved
> by an amateur mathematician using elementary means" because I don't
> know if that's true. Perhaps the dot conjecture is a counter-example
> to the quoted statement above. By the way, after some casual
> googling, I couldn't find a clear (to me) statement of the dot
> conjecture, let alone a proof.
First of all, if theorem that has a statement that a total amateur
could understand, but only advanced algebraic number theory and
cohomology and whanot could prove, that's kind of an unarguable thing.
For example FLT (probably). These statements exist and are undeniably
interesting.
But if both the statement and the proof could be readily apprehended
by a total amateur, then what delineates it from any other theorem of
that sort? Luck, coincidence, the measure of desperation with which
mathematicians searched for a proof. I personally see no reason to
believe what Simon Singh says on that count.
After all in his book he also characterized the law of trichotomy "a<b
or a=b or a>b for any numbers a and b" as having gone hundreds of
years without proof before being proved in 1878 or something like
that. But this is misleading, because he means "cardinal numbers",
which had only recently being introduced.
taffer
Feb 1, 2012, 1:49:04 PM2/1/12
to
about. It has a nice simple proof by sliding a point along a line and
looking at the height of the resulting triangle.
I suppose you could distinguish elementary and easy proofs.
Theoretically easy, and easy, respectively. Analytic number theory
sometimes looks much like much applied mathematics. Lots of estimates
and calculus and no abstraction or sets. Assuming the Riemann
Hypothesis is "as deep" as FLT, and thinking how it's an improvement
on the prime number theorem, you would obtain the interesting
situation where you have a theorem that has two versions, "standard"
and "deluxe". Obtaining the "standard" prime number theorem could
basically be done after leaving high school. Obtaining the "deluxe"
prime number theorem would require a degree, a phd, and several more
years of study in the most abstract and abstruse mathematics.
I think a theorem accessible by elementary means had better be either
a statement in Euclidean plane or cubic geometry, or be largely
quantitative. The word "elementary" really reflects how people learn
about mathematics.
I was reading about the teaching of graph theory and enumerative
combinatorics to advanced 16-18 year olds in Singapore, and it seems
like that abstraction required in graph theory was seen as
substantial, and enumerative combinatorics was quite a bit easier
because of this. Menger's theorem, for example, was perceived as very
very abstract. I got the impression that straying too far away from
the world of numbers, or from Euclidean geometry, was quite a big
deal.
Michael Press
Feb 1, 2012, 3:18:08 PM2/1/12
to
In article
<b907d043-b9ac-4a04...@4g2000pbz.googlegroups.com>,
that today's cranks cannot meet---namely a
working knowledge of plane geometry and an
ability to construct proofs.
--
Michael Press
<b907d043-b9ac-4a04...@4g2000pbz.googlegroups.com>,
Bill Taylor <wfc.t...@gmail.com> wrote:
> Finally, where have all the angle trisectors gone?
> They used to be so common in the old days!
There are prerequisites for angle trisectors
> Finally, where have all the angle trisectors gone?
> They used to be so common in the old days!
that today's cranks cannot meet---namely a
working knowledge of plane geometry and an
ability to construct proofs.
--
Michael Press
0 new messages