Elegant 17th-Century Proof of Fermat's Last Theorem
David Fabian
any ideas about how I should capitalize on it?
(On another note, I wonder about the validity of Wiles' proof. As
complex as it is, it does not seen so safe to assume that there *are*
no more holes in it, just because the few mathematicians who under-
stand it *cannot find* any more holes in it.)
Dave
The text enclosed below is from:
http://www.nsf.gov/discoveries/disc_summ.jsp?cntn_id=100029&org=DMS
=============================================
The most famous note ever scribbled in a book may very well be,
"I have a truly marvelous demonstration of this proposition that this
margin is too narrow to contain."
In the 1630s, French mathematician Pierre de Fermat jotted that
unassuming statement and set a thorny challenge for three centuries'
of mathematicians. He was referring to the claim that there are no
positive integers for which x^n + y^n = z^n when n is greater than 2.
Fermat never got around to writing down his "marvelous" proof,
and the margin note wasn't discovered until after his death.
For 350 years, Fermat's statement was known in mathematical cir-
cles as Fermat's Last Theorem, despite remaining stubbornly un-
proved.
[Snipped story about Taniyama-Shimura conjecture & Wiles' proof,
using 20th-century math.]
And what of Fermat? Because of the complexity the final proof --
certainly too large to fit in a book margin -- and because many
techniques Wiles used had not been invented in Fermat's day, it's
been suggested that Fermat didn't really have a proof after all.
Even so, idealists, diehards and enthusiasts continue the quest for
the more elegant and "truly marvelous demonstration" that they
believe Fermat had in mind.
-- David Hart
=============================================
Gareth Erskine-Jones
<david.m...@sbcglobal.net> wrote:
>Assuming I have found Fermat's elegant proof, does anyone have
>any ideas about how I should capitalize on it?
Publish it?
GEJ
A N Niel
<david.m...@sbcglobal.net> wrote:
> Assuming I have found Fermat's elegant proof, does anyone have
> any ideas about how I should capitalize on it?
There is no money in it. If you are a mathematician, it would
add a certain amount to your reputation. That's it.
However, it is extremely likely that the proof is flawed. In which
case, there is still no money in it, but if you are a mathematician
it would decrease your reputation.
If you want advice of what to do ... Put the proof on the web, send
a link here. On occasion readers of sci.math have offered sensible
criticism for such posts.
Don Del Grande
>Assuming I have found Fermat's elegant proof, does anyone have
>any ideas about how I should capitalize on it?
Somebody claimed a few years ago that they had figured out what
"Fermat's marvelous proof" was, and offered the solution on eBay for
$1,000,000. (Presumably, there were no takers.)
-- Don
W. Dale Hall
> Assuming I have found Fermat's elegant proof, does anyone have any ideas
> about how I should capitalize on it?
>
... stuff deleted ...
>
> -- David Hart
> =============================================
>
>
>
I'd take the letter at the beginning of each sentence, including
those direct quotes that include the beginnings of sentences,
and the first letter of each proper name, and place it in upper
case. If you refer to days of the week, months of the year, and
any deity, I'd place the initial letter of each of these into
upper case as well. For all other letters, I'd use lower case.
howzat?
Dave Parker
David Fabian
And how does that make money?
David Fabian
Thank you for the advice; but I am interested in making money, not
improving my reputation.
David Fabian
That is right... so I pulled the offer. (However, I said that the proof
would take only one page, but it will actually take about ten pages.)
Information can be sold to multiple buyers via eBay (as soon as eBay
enhances their software). (A few years ago, I emailed a person at
eBay, whose job title was "Innovative Disruptor" [one who disrupts
the normal flow of business, in order to make an improvement], but
he never wrote back.)
For example, I would have paid at least one penny to find out how
the pyramids were built (i.e. they rolled the blocks of stone, by
strapping on curved pieces of wood, which effectively turned the
blocks into cylinders); so the person who actually found one of the
pieces of wood could have made a fortune.
An information auction would work like this: The seller states that
he will release his information for a certain amount of money. Each
buyer would state that he will buy the information for whatever it is
worth to him. Optionally, a buyer can stipulate that his offer is good
only if (1) each other buyer pays at least a certain amount, or (2)
there is a specific limited number of buyers. (Of course, the money
would stay in escrow until the information was delivered.)
Dave
Carl G.
"David Fabian" <david.m...@sbcglobal.net> wrote in message
news:JPC7l.12709$YU2....@nlpi066.nbdc.sbc.com...
> Assuming I have found Fermat's elegant proof, does anyone have any ideas
> about how I should capitalize on it?
>
been verified as authentic, it could likely be sold at auction for nice sum.
It would not have to be a valid proof. Indeed, many present-day
mathematicians would be relieved if Fermat made an error in his marginal
claim.
If there is no physical document, then the proof by itself may or may not be
profitable. For example, if the proof led to better cryptographic
algorithms, it might be profitable. It's unlikely that the proof would be
profitable to you, unless you developed the profitable algorithms.
Below is one way to capitalize on the theorem itself:
IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
If an integer n is greater than 2,
then the equation a^n + b^n = c^n
has no solutions in non-zero
integers a, b, and c
Carl G.
David R Tribble
>> Assuming I have found Fermat's elegant proof, does anyone have
>> any ideas about how I should capitalize on it?
>
Gareth Erskine-Jones wrote:
>> Publish it?
>
David Fabian wrote:
> And how does that make money?
By cashing the royalty checks from the publisher, the same way
everyone else makes money by publishing books?
Eric Sosman
Keep control of the movie rights.
--
Eric Sosman
eso...@ieee-dot-org.invalid
Gareth Erskine-Jones
<david.m...@sbcglobal.net> wrote:
>"Gareth Erskine-Jones" <g...@uberdog.net> wrote in message news:piiul49qa27ms1ec5...@4ax.com...
>> On Fri, 2 Jan 2009 23:36:37 -0600, "David Fabian"
>> <david.m...@sbcglobal.net> wrote:
>>
>>>Assuming I have found Fermat's elegant proof, does anyone have
>>>any ideas about how I should capitalize on it?
>>
>> Publish it?
>>
>> GEJ
>
>And how does that make money?
If it was a much simpler proof than that of Wiles, you'd achieve
recognition (obviously amongst mathematicians, but also to a lesser
extent amongst the general public). I'd imagine it wouldn't do any
harm for your career as a professional mathematician, and you'd
probably get on a chat show or two.
Other than that, I don't see any way to profit from it...
GEJ
David Fabian
>
> By cashing the royalty checks from the publisher, the same way
> everyone else makes money by publishing books?
The proof will be only about ten pages, so it would have to be
published in a journal (unless someone has the time to expand it
into a book, by adding lots of fluff), which would require that I
(1) give up all copyrights, and (2) take what little money the
publisher decides to toss me.
Gareth Erskine-Jones
Then I suspect you're barking up the wrong tree. Proving a theorem
that has already been proved ... I don't see how you can make money
from that.
Of course, if you could figure a way of making a fortune from proving
theorems which had already been proved - you could possibly patent
that technique, and then make money from that...
Here's a more interesting question (IMHO) - you discover an algorithm
to factor large numbers very rapidly. How do you capitalize on that?
How would you even survive that? You publish on the net, and most of
the world's cryto systems are useless. You go to your government, and
... well, you don't come back.
GEJ
Kevin Stone
> about how I should capitalize on it?
By your subject are we to assume that you've unearthed an existing 350 year
old document with the proof?
A pretty valuable piece of parchment methinks.
--
Kev
David R Tribble
>> By cashing the royalty checks from the publisher, the same way
>> everyone else makes money by publishing books?
>
David Fabian wrote:
> The proof will be only about ten pages, so it would have to be
> published in a journal (unless someone has the time to expand it
> into a book, by adding lots of fluff), which would require that I
> (1) give up all copyrights, and (2) take what little money the
> publisher decides to toss me.
They can copyright the text of your proof article, but they
can't copyright the proof itself. You knew that, right?
So then you're free to write another whole book about your
discovery, how you came up with the idea, the history of
the problem, etc. Just like most pop-math authors do.
Marilyn vos Savant wrote a book about Wile's proof just
a few months after he published it, and she seems to be
doing okay.
spudnik
per gross; he didn't make a single mistake,
that has come down to us!
so, does it use "congruence surds?"
> It would not have to be a valid proof. Indeed, many present-day
thus:
isn't that an award for journalism,
not the "actual hyper-hype physics?"
Dick Hoagland is dumber than a pile of rocks,
just by comparison with the Face and Genitals
on Mars.
> Entity will say: the Angstrom Institude got it right, the Angstrom
> Hoagland got it right, too: won a prize for hyperdimensional
thus:
I will guess that Wookiepoopya has no rational explanation
for cropcircles, other than "Doug and Dave with 2by9s,"
the obviously fake Druids.
David Fabian
> On Sat, 3 Jan 2009 14:28:40 -0600, "David Fabian"
> <david.m...@sbcglobal.net> wrote:
> >
>>Thank you for the advice; but I am interested in making money, not
>>improving my reputation.
>
> Then I suspect you're barking up the wrong tree. Proving a theorem
> that has already been proved ... I don't see how you can make money
> from that.
There are many mathematicians who would like to see a proof (especially
one that Fermat himself probably had in mild) that is much simpler than
Wiles' proof... so I should be able to capitalize in some way.
> Of course, if you could figure a way of making a fortune from proving
> theorems which had already been proved - you could possibly patent
> that technique, and then make money from that...
You are being facetious and|or sarcastic.
> Here's a more interesting question (IMHO) - you discover an algorithm
> to factor large numbers very rapidly. How do you capitalize on that?
> How would you even survive that? You publish on the net, and most of
> the world's cryto systems are useless. You go to your government, and
> ... well, you don't come back.
You are right. There is not much point in pursuing a goal, when success
costs you your life.
Dave
> GEJ
David Fabian
>> Assuming I have found Fermat's elegant proof, does anyone have any ideas
>> about how I should capitalize on it?
>
> By your subject are we to assume that you've unearthed an existing 350 year
> old document with the proof?
No. I devised the proof using the math tools that were available to Fermat
in the 17th-century.
Dave
Matt
wrote:
> "Kevin Stone" <newsacco...@hotpop.com> wrote in messagenews:6sa9iiF...@mid.individual.net...
> >> Assuming I have found Fermat's elegant proof, does anyone have any ideas
> >> about how I should capitalize on it?
>
> > By your subject are we to assume that you've unearthed an existing 350 year
> > old document with the proof?
>
> No. I devised the proof using the math tools that were available to Fermat
> in the 17th-century.
Has it been checked by anyone else? The default position, until there
is evidence otherwise, has to be that your proof is wrong. I hope for
your sake it's correct, but realistically the chances are slim.
CBFalconer
>
... snip ...
>
> If the proof was written in Fermat's own hand, then once the
> document has been verified as authentic, it could likely be sold
> at auction for nice sum. It would not have to be a valid proof.
> Indeed, many present-day mathematicians would be relieved if
> Fermat made an error in his marginal claim.
Why not face it? It is IMPOSSIBLE to prove Fermat made a mistake.
It IS possible to prove he was correct. It hasn't been done.
--
[mail]: Chuck F (cbfalconer at maineline dot net)
[page]: <http://cbfalconer.home.att.net>
Try the download section.
Don Del Grande
> Don Del Grande wrote:
>
>> David Fabian wrote:
>>
>>>Assuming I have found Fermat's elegant proof, does anyone have
>>>any ideas about how I should capitalize on it?
>>
>> Somebody claimed a few years ago that they had figured out what
>> "Fermat's marvelous proof" was, and offered the solution on eBay for
>> $1,000,000. (Presumably, there were no takers.)
>
>That is right... so I pulled the offer. (However, I said that the proof
>would take only one page, but it will actually take about ten pages.)
Pardon me for asking, but (a) just how much money are you looking to
make from this proof, and (b) what guarantee does anybody have that,
if the proof is incorrect, they won't have to pay anything?
-- Don
David Fabian
> David Fabian wrote:
>
>> Don Del Grande wrote:
>>
>>> David Fabian wrote:
>>>
>>>>Assuming I have found Fermat's elegant proof, does anyone have
>>>>any ideas about how I should capitalize on it?
>>>
>>> Somebody claimed a few years ago that they had figured out what
>>> "Fermat's marvelous proof" was, and offered the solution on eBay for
>>> $1,000,000. (Presumably, there were no takers.)
>>
>>That is right... so I pulled the offer. (However, I said that the proof
>>would take only one page, but it will actually take about ten pages.)
>
> Pardon me for asking, but (a) just how much money are you looking to
> make from this proof, and
I don't know. If eBay enhances their software to sell information
(see other thread for details), I would probably come up with an
asking price. Every year or so, I would, of course, have to lower
my price. On the other hand, some auctions do not even require
the seller to commit to an asking price -- if no one bids what the
seller wants by a certain time, the auction is off until a later date.
But that strategy seems kind of cheesy to me.
> (b) what guarantee does anybody have that,
> if the proof is incorrect, they won't have to pay anything?
Please read the final sentence of my previous post.
Dave
> -- Don
Mensanator
You forgot to add "...despite being as stupid as JSH."
Mensanator
wrote:
> "A N Niel" <ann...@nym.alias.net.invalid> wrote in messagenews:030120090857076134%ann...@nym.alias.net.invalid...
>
>
>
>
>
> > <david.m.fab...@sbcglobal.net> wrote:
>
> >> Assuming I have found Fermat's elegant proof, does anyone have
> >> any ideas about how I should capitalize on it?
>
> > There is no money in it. �If you are a mathematician, it would
> > add a certain amount to your reputation. �That's it.
>
> > However, it is extremely likely that the proof is flawed. �In which
> > case, there is still no money in it, but if you are a mathematician
> > it would decrease your reputation.
>
> > If you want advice of what to do ... Put the proof on the web, send
> > a link here. �On occasion readers of sci.math have offered sensible
> > criticism for such posts.
>
> Thank you for the advice; but I am interested in making money, not
> improving my reputation.
Ask JSH, he knows all about such matters. He claimed to
have proved it also, demonstarted that Wiles did not prove it,
and his only motive was money and chicks. I'm sure he can
give you all kinds of good advice.
David Fabian
>
> Has it been checked by anyone else?
No one but myself.
> The default position, until there is evidence otherwise,
> has to be that your proof is wrong.
The fact that I have solved many difficult logic problems
(e.g. http://www.eskimo.com/~miyaguch/powerresults.html)
indicates that there is at least a better-than-average chance
that I have solved *this* problem (although it does not logic-
ally prove it [argumentum ad verecundiam]).
> I hope for your sake it's correct, but realistically the
> chances are slim.
The chances are slim from your point of view, because you
have not yet seen my work.
Dave
David Fabian
>
> They can copyright the text of your proof article, but they
> can't copyright the proof itself. You knew that, right?
No, I didn't. But the text is what sells...
> So then you're free to write another whole book about your
> discovery, how you came up with the idea, the history of
> the problem, etc. Just like most pop-math authors do.
> Marilyn vos Savant wrote a book about Wile's proof just
> a few months after he published it, and she seems to be
> doing okay.
She is married to a famous heart surgeon... of course she
is doing well!
(Just teasing, Marilyn!)
Let me rephrase that... "Marilyn Savant is brilliant... of
course she is doing well."
Dave
Christopher Henrich
<16cc27b7-3c57-4139...@40g2000prx.googlegroups.com>,
Matt <matt271...@yahoo.co.uk> wrote:
Getting it checked is possible, but would be expensive. Mr. Fabian could
get a professional mathematician to check his work, for a fee, with a
non-disclosure agreement. I think it would take a lawyer to draft the
non-disclosure agreement. There's another fee, up front. Mr. F. is
going to have to spend a few thousand dollars, at least, to put himself
in position to even hope for earning anything directly from his proof.
So how does anybody ever get any benefit from doing pure mathematics?
Indirectly. One must "publish." If someone publishes good stuff, he
gains a reputation among the people whom he hopes to call his peers;
then he may get research grants or salaried positions.
--
Christopher J. Henrich
chen...@monmouth.com
http://www.mathinteract.com
Carl G.
"CBFalconer" <cbfal...@yahoo.com> wrote in message
news:49601D75...@yahoo.com...
> "Carl G." wrote:
>>
> ... snip ...
>>
>> If the proof was written in Fermat's own hand, then once the
>> document has been verified as authentic, it could likely be sold
>> at auction for nice sum. It would not have to be a valid proof.
>> Indeed, many present-day mathematicians would be relieved if
>> Fermat made an error in his marginal claim.
>
> Why not face it? It is IMPOSSIBLE to prove Fermat made a mistake.
> It IS possible to prove he was correct. It hasn't been done.
Why would a document, containing an invalid proof written by Fermat himself,
not be considered a reasonable proof that he made a mistake? Is it
impossible that such a document can exist? Is there a complete list of all
documents created by Fermat?
I agree with the following anagram (found by another):
FERMAT'S LAST THEOREM = REALM OF THE SMARTEST.
There _is_ a simple proof of the theorem that is based on the same
techniques used to prove Goldbach's conjecture, but I don't have enough ink
remaining to print it here. ;-)
Carl G.
David Fabian
>
> Getting it checked is possible, but would be expensive. Mr. Fabian
> could get a professional mathematician to check his work, for a fee,
> with a non-disclosure agreement.
I already have a friend who agreed to check my proof for free. He has
a PhD in computer science, has almost enough credit for a PhD in math,
and he graduated from Harvard in three years. You appear to live in
the same region:
http://www.monmouth.com/~colonel/
> I think it would take a lawyer to draft the non-disclosure agreement.
> There's another fee, up front. Mr. F. is going to have to spend a few
> thousand dollars, at least, to put himself in position to even hope for
> earning anything directly from his proof.
Non-disclosure agreements are standard forms. They do not really
require a lawyer.
> So how does anybody ever get any benefit from doing pure mathematics?
> Indirectly. One must "publish." If someone publishes good stuff, he
> gains a reputation among the people whom he hopes to call his peers;
> then he may get research grants or salaried positions.
Pure mathematics is just a hobby for me (so I do not need to publish,
gain recognition, and obtain research grants or a job). But I am still
not convinced that it is impossible for a hobbyist to make money.
I have already gained a reputation in my profession (software develop-
ment) and already have a good-paying job. However, research grants
are totally out of the question, because I am self-taught and do not have
the time or inclination to obtain the required college degree (i.e. research
grants are awarded by and for academia).
By the way, here are two papers that *others* have published about
my work:
http://front.math.ucdavis.edu/0803.1245
http://adsabs.harvard.edu/abs/1987SPIE..755..114C
Dave
David Fabian
>
> You forgot to add "...despite being as stupid as JSH."
I do not know much about JSH's knowledge or abilities,
but you should not attack him, because he is at least trying.
Dave
mike3
Movie?
mike3
> "David Fabian" <david.m.fab...@sbcglobal.net> wrote in message
>
> news:JPC7l.12709$YU2....@nlpi066.nbdc.sbc.com...> Assuming I have found Fermat's elegant proof, does anyone have any ideas
> > about how I should capitalize on it?
>
> If the proof was written in Fermat's own hand, then once the document has
> been verified as authentic, it could likely be sold at auction for nice sum.
> It would not have to be a valid proof. Indeed, many present-day
> mathematicians would be relieved if Fermat made an error in his marginal
> claim.
>
This I am curious about. How would the proof being valid be so bad for
mathematics,
anyway?
Mike Williams
It wouldn't be possible to get it published in a professional journal,
because they receive so many erroneous proofs that they no longer
consider such submissions. It can take a lot of effort to spot a subtle
error in 10 pages of equations, and the likelihood of an unknown
mathematician coming up with a valid proof isn't worth the effort.
--
Mike Williams
Gentleman of Leisure
N. Silver
> Pure mathematics is just a hobby for me (so I do not need to publish, gain
> recognition, and obtain research grants or a job). But I am still not
> convinced that it is impossible for a hobbyist to make money.
It's close to impossible.
> I have already gained a reputation in my profession (software develop-
> ment) and already have a good-paying job. However, research grants are
> totally out of the question, because I am self-taught and do not have the
> time or inclination to obtain the required college degree (i.e. research
> grants are awarded by and for academia).
>
> By the way, here are two papers that *others* have published about my
> work:
> http://front.math.ucdavis.edu/0803.1245
> http://adsabs.harvard.edu/abs/1987SPIE..755..114C
The papers are irrelevant to your claim. Moreover, one of the papers you
cite
is close to 30 years old. It all adds up to you being a crank and getting
crankier.
Richard Heathfield
> On Jan 3, 1:56 pm, "Carl G." <cgin...@socal.rr.com> wrote:
<snip>
>> Indeed, many present-day mathematicians would be relieved if
>> Fermat made an error in his marginal claim.
>>
>
> This I am curious about. How would the proof being valid be so bad
> for mathematics,
> anyway?
It would actually be very /good/ for mathematics, if it contained
some "OH! OF COURSE!" insight that everyone's just failed to spot
in the last 350 years. It might, however, be considered bad for
matheticians! At least, bad for those who had tried to prove FLT.
As Euler famously pointed out, V + F = E + 2 - where V is the
mathematician, F is the number of faces he has, and E is the egg.
--
Richard Heathfield <http://www.cpax.org.uk>
Email: -http://www. +rjh@
Google users: <http://www.cpax.org.uk/prg/writings/googly.php>
"Usenet is a strange place" - dmr 29 July 1999
Angus Rodgers
<mike...@yahoo.com> wrote:
>On Jan 3, 1:56 pm, "Carl G." <cgin...@socal.rr.com> wrote:
>> "David Fabian" <david.m.fab...@sbcglobal.net> wrote in message
>> news:JPC7l.12709$YU2....@nlpi066.nbdc.sbc.com...
>>
>> > Assuming I have
>> > found Fermat's elegant proof, does anyone have any ideas
>> > about how I should capitalize on it?
>>
>> If the proof was written in Fermat's own hand, then once the document has
>> been verified as authentic, it could likely be sold at auction for nice sum.
>> It would not have to be a valid proof. Indeed, many present-day
>> mathematicians would be relieved if Fermat made an error in his marginal
>> claim.
>
>This I am curious about. How would the proof being valid be so bad for
>mathematics, anyway?
It seemed a curious judgement to me, too. Of course, I'm no
professional mathematician, but, for what it's worth, I would
be delighted if Fabian's (or anyone else's) claimed elementary
proof of FLT were valid; and my feeling is that most professional
mathematicians would be even more delighted than me. (OK, perhaps
Andrew Wiles wouldn't, but that would be perfectly understandable!)
--
Angus Rodgers
Angus Rodgers
Very. :-)
--
Angus Rodgers
Marc 'BlackJack' Rintsch
Yep. And merchandising of course!
Ciao,
Marc 'BlackJack' Rintsch
Kevin Stone
> about how I should capitalize on it?
How about a wager with someone?
You each stake a million dollars and if your 'proof' is flawed, then you
lose your million.
Sound like an idea?
Actually, surely someone clever enough to find a proof doesn't need our
help? The interviews, on radio and TV, along with the books will make you a
wealthy man.
--
Kev
Mike Williams
>> Assuming I have found Fermat's elegant proof, does anyone have any ideas
>> about how I should capitalize on it?
>
>How about a wager with someone?
>
>You each stake a million dollars and if your 'proof' is flawed, then you
>lose your million.
>
>Sound like an idea?
It sounds like an idea to me. I don't have a million to bet against you,
but I'd be in for ten thousand. All you need now is to find another 99
people like me, and an a procedure for deciding whether the proof is
flawed that we can all agree on.
Nick
If I had any confidence he could find the million he'd need I'd be in
for it - put me down for 10000 quid (which I don't have, but which I
could find if I absolutely had to).
--
Online waterways route planner: http://canalplan.org.uk
development version: http://canalplan.eu
--CELKO--
These days, you put the ten pages into a theorem proving software
package and push a button. If you solved Fermat with just algebra and
a little calculus, this will be fairly quick work.
David Bernier
The December 2008 issue of the Notices of the AMS is about formal proofs and proof assistants,
which assist in developing formal proofs. There's an article by Thomas Hales,
who submitted a proof to Annals of Math. on the Kepler Conjecture.
After a year, the referees couldn't certify the proof, but had checked
sub-claims. Later, Hale started project Flyspeck (k is for Kepler),
whose aim is to arrive at a formal proof of the Kepler Conjecture.
So based on what's already been formalized, 10 pages at the undergraduate
level seems formalizable by "experts" in a reasonable amount of time.
AMS Notices, 12/2008:
http://www.ams.org/notices/200811/index.html
David Bernier
hagman
> On Sat, 3 Jan 2009 14:28:40 -0600, "David Fabian"
>
>
>
> <david.m.fab...@sbcglobal.net> wrote:
> >"A N Niel" <ann...@nym.alias.net.invalid> wrote in messagenews:030120090857076134%ann...@nym.alias.net.invalid...
> >> In article <JPC7l.12709$YU2.9...@nlpi066.nbdc.sbc.com>, David Fabian
>
> >>> Assuming I have found Fermat's elegant proof, does anyone have
> >>> any ideas about how I should capitalize on it?
>
> >> add a certain amount to your reputation. That's it.
>
> >> However, it is extremely likely that the proof is flawed. In which
> >> case, there is still no money in it, but if you are a mathematician
> >> it would decrease your reputation.
>
> >> If you want advice of what to do ... Put the proof on the web, send
> >> a link here. On occasion readers of sci.math have offered sensible
> >> criticism for such posts.
>
> >Thank you for the advice; but I am interested in making money, not
> >improving my reputation.
>
> that has already been proved ... I don't see how you can make money
> from that.
>
> Of course, if you could figure a way of making a fortune from proving
> theorems which had already been proved - you could possibly patent
> that technique, and then make money from that...
>
> Here's a more interesting question (IMHO) - you discover an algorithm
> to factor large numbers very rapidly. How do you capitalize on that?
> How would you even survive that? You publish on the net, and most of
> the world's cryto systems are useless. You go to your government, and
> ... well, you don't come back.
>
> GEJ
Some of such factoring experts just keep coming back *sigh*
quasi
<david.m...@sbcglobal.net> wrote:
Trying to deceive.
quasi
hagman
> "Don Del Grande" <del_grande_n...@earthlink.net> wrote in messagenews:1b70m4lddfa8aojo7...@4ax.com...
The final sentence of your previous post says
>(Of course, the money
> would stay in escrow until the information was delivered.)
You do not mention it, but should that mean that the information
(here: your proof) has to be *correct*? In what sense?
hagman
> Mike Williams <nos...@econym.demon.co.uk> writes:
> > Wasn't it Kevin Stone who wrote:
> >>> Assuming I have found Fermat's elegant proof, does anyone have any ideas
> >>> about how I should capitalize on it?
>
> >>How about a wager with someone?
>
> >>You each stake a million dollars and if your 'proof' is flawed, then you
> >>lose your million.
>
> >>Sound like an idea?
>
> > It sounds like an idea to me. I don't have a million to bet against
> > you, but I'd be in for ten thousand. All you need now is to find
> > another 99 people like me, and an a procedure for deciding whether the
> > proof is flawed that we can all agree on.
>
> If I had any confidence he could find the million he'd need I'd be in
> for it - put me down for 10000 quid (which I don't have, but which I
> could find if I absolutely had to).
Yep, if necessary you could get your 10000$ share from selling flying
pigs :)
Mensanator
wrote:
> "Mensanator" <mensana...@aol.com> wrote in messagenews:8c05e202-b3c8-4fe0...@w1g2000prm.googlegroups.com...
>
> > You forgot to add "...despite being as stupid as JSH."
>
> I do not know much about JSH's knowledge or abilities,
> but you should not attack him, because he is at least trying.
Ignorance is only skin deep,
but stupid goes to the bone.
>
> Dave
mike3
> David Fabian wrote:
> > Pure mathematics is just a hobby for me (so I do not need to publish, gain
> > recognition, and obtain research grants or a job). But I am still not
> > convinced that it is impossible for a hobbyist to make money.
>
> It's close to impossible.
>
Does this mean they could not attempt to publish the proof, at all?
mike3
wrote:
> "Kevin Stone" <newsacco...@hotpop.com> wrote in messagenews:6sa9iiF...@mid.individual.net...
> >> about how I should capitalize on it?
>
> > old document with the proof?
>
> No. I devised the proof using the math tools that were available to Fermat
> in the 17th-century.
>
So then even if your proof is right, you cannot assume it must be the
one that Fermat
had. The only way to know what Fermat had would be to unearth a 350
year old document
that could be verified to have been penned by Fermat's own hand.
Please, you should post the proof. You would not be able to make much
money on it if it
was right (you are probably making more in your current profession
right now than you could
off this proof), and if it was wrong, you could save yourself a lot of
grief that could come about
by betting lots of money on it being right. So I would not see how
posting it would be a big loss
for you.
Bill Dubuque
>
>> The default position, until there is evidence otherwise,
>> has to be that your proof is wrong.
>
> (e.g. http://www.eskimo.com/~miyaguch/powerresults.html) indicates
> that there is at least a better-than-average chance that I have solved
> *this* problem (although it does not logic-
> ally prove it [argumentum ad verecundiam]).
Certainly not. Your performance on some random "IQ test" says
absolutely nothing at all about your higher mathematical skills.
Marilyn vos Savant is a prime example. The woman who supposedly
has the "world's highest IQ" published a Parade magazine column and
a book about Wiles proof of FLT. Her nonsensical arguments proved
beyond a doubt that she (and her advisors) has no clue about higher
mathematics and, worse, doesn't have the intelligence to realize
that she's completely clueless on such matters (even after many
experts pointed out gaping flaws in her extremely naive arguments).
Even more mathematical tests (IMO, Putnam, etc) are not necessarily
good measures of ability to solve longstanding problems such as
FLT since such tests merely measure the ability to _quickly_ solve
problems that are _explicitly constructed_ for such purposes.
>> I hope for your sake it's correct, but realistically the chances are slim.
>
> The chances are slim from your point of view, because you have not yet
> seen my work.
There is no chance involved. Your proof is surely wrong.
I'm so sure of this I'll bet you 10-1 odds. I'll pay you
$1000 if your proof is correct, you pay me $100 if it is
wrong (or incomprehensible). So here's your sought chance
to "capitalize on the proof". Most likely other sci.math
folks would happily join in at those odds. Even more likely
is that you will never reveal any such elementary FLT proof.
If you don't accept it'll be clear you're just blowing smoke.
Robert Israel
Probably, but I think it would be a lot harder than just "pushing a button".
Translating a human-written proof into something like HOL Light is not a
trivial task. It requires careful attention to each step. I suspect it
would be easier to spot the error "by hand".
--
Robert Israel isr...@math.MyUniversitysInitials.ca
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
Gareth Erskine-Jones
wrote:
Yeah, but no-one's ever succeeded yet.... but if someone did, what
could they do? If they reveal to the whole world at once, then they'd
cause chaos, but might escape with their lives. If they revealed it to
their own nation's security services - well, would the NSA or GCHQ
hesitate to grab the solution for themselves and to eliminate any
potential leaks?
GEJ
Richard Heathfield
> On Sun, 4 Jan 2009 08:30:31 -0800 (PST), hagman
> <goo...@von-eitzen.de> wrote:
>
>>On 3 Jan., 23:27, Gareth Erskine-Jones <g...@uberdog.net> wrote:
>
>>> Here's a more interesting question (IMHO) - you discover an
>>> algorithm to factor large numbers very rapidly. How do you
>>> capitalize on that? How would you even survive that? You publish
>>> on the net, and most of the world's cryto systems are useless.
>>> You go to your government, and ... well, you don't come back.
>>>
>>> GEJ
>>
>>Some of such factoring experts just keep coming back *sigh*
>
> Yeah, but no-one's ever succeeded yet....
How do you know?
> but if someone did, what
> could they do? If they reveal to the whole world at once, then
> they'd cause chaos, but might escape with their lives. If they
> revealed it to their own nation's security services - well, would
> the NSA or GCHQ hesitate to grab the solution for themselves and
> to eliminate any potential leaks?
What makes you believe this hasn't already happened?
No, I don't have inside information. Contrary to unpopular belief, I
really don't work for the British intelligence services. (But I
would say that, wouldn't I?)
CBFalconer
>
... snip ...
>
> Here's a more interesting question (IMHO) - you discover an
> algorithm to factor large numbers very rapidly. How do you
> capitalize on that? How would you even survive that? You publish
> on the net, and most of the world's cryto systems are useless.
> You go to your government, and ... well, you don't come back.
No, you keep it to yourself and set yourself up as a master invader
of secrecy systems. I am sure you will find something that you can
blow up into a lot of money.
That way you get rich, not famous. You also eventually get
forgotten.
--
[mail]: Chuck F (cbfalconer at maineline dot net)
[page]: <http://cbfalconer.home.att.net>
Try the download section.
Nick Wedd
<david.m...@sbcglobal.net> writes
>Assuming I have found Fermat's elegant proof, does anyone have any
>ideas about how I should capitalize on it?
In case you have not already learned the answer from other replies -
You publicise the fact that you have a proof. You also publicise the
fact that you are willing to accept bets against the validity of your
proof. There are enough cynical people in the world that you should be
able to get very good odds. Once you have accepted bets against all the
capital you can raise, you publish your proof and collect your winnings.
Nick
--
Nick Wedd ni...@maproom.co.uk
tc...@lsa.umich.edu
Robert Israel <isr...@math.MyUniversitysInitials.ca> wrote:
>Probably, but I think it would be a lot harder than just "pushing a button".
>Translating a human-written proof into something like HOL Light is not a
>trivial task. It requires careful attention to each step. I suspect it
>would be easier to spot the error "by hand".
Yes, of course, but I think the point was that *if* the proof is correct,
then an unknown author has a chance of getting people to take him or her
seriously by producing a machine-checked version. In principle, this is
one nice thing about machine-checkable proofs.
In practice, unfortunately, the most likely outcome is that even if a crank
succeeds in learning some HOL Light (say), the crank will produce a proof
of something that isn't actually Fermat's Last Theorem, and it may be
even harder to decipher what HOL Light theorem the crank has proved than
to decipher a conventional handwritten proof. And then, of course, one
will get into interminable arguments with the crank of the form "What
you've proved isn't Fermat's Last Theorem...Yes it is!...No it isn't!"
--
Tim Chow tchow-at-alum-dot-mit-dot-edu
The range of our projectiles---even ... the artillery---however great, will
never exceed four of those miles of which as many thousand separate us from
the center of the earth. ---Galileo, Dialogues Concerning Two New Sciences
junoexpress
wrote:
> "Matt" <matt271829-n...@yahoo.co.uk> wrote in messagenews:16cc27b7-3c57-4139...@40g2000prx.googlegroups.com...
>
>
> > The default position, until there is evidence otherwise,
> > has to be that your proof is wrong.
>
> The fact that I have solved many difficult logic problems
> indicates that there is at least a better-than-average chance
> that I have solved *this* problem
>
Well, I wouldn't rate your ability at probability too highly. There
have been a large number of mathematicians unable to solve FLT who
were bone fide geniuses and had the knowledge and experience which you
admittedly lack. In light of that fact, for you to say that you have
"at least a better-than average chance" of solving FLT (on the basis
of a high score on a problem in an IQ test and two papers published),
seems to me, to be on the contrary unlikely.
M
Matthew Russotto
Gareth Erskine-Jones <g...@uberdog.net> wrote:
>
>Here's a more interesting question (IMHO) - you discover an algorithm
>to factor large numbers very rapidly. How do you capitalize on that?
I think there's a few factoring contests still out there. Aside from
that, there's crime.
--
It's times like these which make me glad my bank is Dial-a-Mattress
G. A. Edgar
<a6c39bc9-d872-4e77...@r15g2000prh.googlegroups.com>,
mike3 <mike...@yahoo.com> wrote:
Mathematics research journals do not pay their authors, so that would
not be a way to make money.
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/
David Bernier
> In article <rbisrael.20090104203548$5c...@news.acm.uiuc.edu>,
> Robert Israel <isr...@math.MyUniversitysInitials.ca> wrote:
>> Probably, but I think it would be a lot harder than just "pushing a button".
>> Translating a human-written proof into something like HOL Light is not a
>> trivial task. It requires careful attention to each step. I suspect it
>> would be easier to spot the error "by hand".
>
> Yes, of course, but I think the point was that *if* the proof is correct,
> then an unknown author has a chance of getting people to take him or her
> seriously by producing a machine-checked version. In principle, this is
> one nice thing about machine-checkable proofs.
>
> In practice, unfortunately, the most likely outcome is that even if a crank
> succeeds in learning some HOL Light (say), the crank will produce a proof
> of something that isn't actually Fermat's Last Theorem, and it may be
> even harder to decipher what HOL Light theorem the crank has proved than
> to decipher a conventional handwritten proof. And then, of course, one
> will get into interminable arguments with the crank of the form "What
> you've proved isn't Fermat's Last Theorem...Yes it is!...No it isn't!"
Of course, it's best to have the supposed proof hand-checked first.
I was thinking of HOL Light as a Gold Standard (if it passes
hand-checking and formalization, it's very likely right).
I was imagining the proof proposer protesting that "HOL is wrong!"
if it didn't accept the proposed proof.
David Bernier
David Fabian
news:d953c849-937f-4e67...@v39g2000pro.googlegroups.com...
>
> The final sentence of your previous post says
> >(Of course, the money
> > would stay in escrow until the information was delivered.)
> You do not mention it, but should that mean that the information
> (here: your proof) has to be *correct*? In what sense?
Of course it would have to be correct. Otherwise, it would not
be the information that the seller claimed he would produce. It
would legally fall under "implied warranty".
David Fabian
news:wdSjqnZJ...@maproom.demon.co.uk...
| In message <JPC7l.12709$YU2....@nlpi066.nbdc.sbc.com>, David Fabian
| <david.m...@sbcglobal.net> writes
| >Assuming I have found Fermat's elegant proof, does anyone have
| >any ideas about how I should capitalize on it?
|
| In case you have not already learned the answer from other replies -
|
| You publicise the fact that you have a proof. You also publicise
| the fact that you are willing to accept bets against the validity of
| your proof. There are enough cynical people in the world that
| cepted bets against all the capital you can raise, you publish your
| proof and collect your winnings.
Here is one strategy that might work (after I have verified the
legality of making Internet bets [which, if illegal {e.g. it might
be illegal to accept a bet from a person under 18 in Morocco},
might mean that our whole discussion here constitutes "con-
spiracy to commit a crime"]):
(1) I put $10,000 in escrow (since I do not have $1,000,000).
(2) I accept bets for any amount, with the stipulation that, if I
lose, my opponents divvy up my $10,000 in proportion to
the amounts they each bet, and if I win, I receive everything
my opponents bet. (However, I would require that the bet-
ting period ends when both (a) six months have transpired
since the opening bet, and (b) my opponents' bets total to
at least $1,000,000.)
(I am pretty sure I can find enough skeptics who will settle for
100:1 odds.)
Dave
David Fabian
news:6sbgh5F...@mid.individual.net...
|> Assuming I have found Fermat's elegant proof, does anyone
| > have any ideas about how I should capitalize on it?
|
| How about a wager with someone?
|
| You each stake a million dollars and if your 'proof' is flawed,
| then you lose your million.
|
| Sound like an idea?
First, I do not have a million dollars. Second, I do not think
any single person would risk one million dollars.
| Actually, surely someone clever enough to find a proof
| doesn't need our help?
No, I do not think that I am God, just because I believe I
solved a difficult problem. Posters have already given me
much help.
| The interviews, on radio and TV, along with the books
| will make you a wealthy man.
What makes you so sure? I don't think anyone would pay
me for an interview or for book rights. (CNN once asked
to interview me, but they did not mention any money, so I
immediately declined.)
Dave
| --
| Kev
anonymous....@yahoo.com
wrote:
> "Nick Wedd" <n...@maproom.co.uk> wrote in message
>
> news:wdSjqnZJ...@maproom.demon.co.uk...
> | In message <JPC7l.12709$YU2.9...@nlpi066.nbdc.sbc.com>, David Fabian
> | <david.m.fab...@sbcglobal.net> writes
100:1 odds might be too extreme--I don't have more than a few thousand
dollars I could put into something like this, and at 100:1 odds, the
$20 or $30 I would make from winning wouldn't be worth the few hours
it would take to verify that you had some kind of legitimate setup and
jump through the logistics hoops to actually put down the money. The
problem of finding an escrow service that is so obviously reliable
that your audience won't think they're being scammed, and which would
streamline the betting process enough that it wouldn't be too big a
hassle to even get involved--that is a significant problem.
Have you looked into the 19th century attacks on FLT? Are you sure
that your putative proof isn't one of the (failed, but for subtle
reasons) 19th century ones? The reason that Kummer's proof of FLT for
regular prime exponents isn't a proof for ALL exponents are subtle,
and many people stumble there, thinking they have a proof because they
have assumed a certain class group is trivial (or something equivalent
to this), when it is not.
David Fabian
news:7c86d71f-7368-42c8...@m22g2000vbp.googlegroups.com...
>
>100:1 odds might be too extreme--I don't have more than a few thousand
>dollars I could put into something like this, and at 100:1 odds, the
>$20 or $30 I would make from winning wouldn't be worth the few hours
>it would take to verify that you had some kind of legitimate setup and
>jump through the logistics hoops to actually put down the money. The
>problem of finding an escrow service that is so obviously reliable
>that your audience won't think they're being scammed, and which would
>streamline the betting process enough that it wouldn't be too big a
>hassle to even get involved--that is a significant problem.
Good points. I will have to sleep on this...
>Have you looked into the 19th century attacks on FLT? Are you sure
>that your putative proof isn't one of the (failed, but for subtle reasons)
>19th century ones? The reason that Kummer's proof of FLT for
>regular prime exponents isn't a proof for ALL exponents are subtle,
>and many people stumble there, thinking they have a proof because they
>have assumed a certain class group is trivial (or something equivalent
>to this), when it is not.
No, I have not seen any of those flawed proofs.
quasi
It's a very naive plan.
(1) Not many people, if any, would be willing place a large amount of
money in escrow, then have to wait possibly as much as 6 months in
order to complete the transaction.
(2) Not many people, if any will offer 100-1 odds. It's not that the
odds are unfair -- in fact, the true odds, given your background, are
probably at least 10,000-1. Still, the reason people will not offer
100-1 is because the potential profit is simply not worth the trouble.
Would I bet $10,000 against your $100? Why should I bother? I would
have to wait possibly 6 months, all the time worrying about possible
fraud. Is the escrow service legitimate? Is the referee secretly in
collusion with you? Etc.
(3) You haven't specified how the referees would be selected. I
suspect that most bettors would insist on more than one referee, and
that the referees be world class mathematicians, widely regarded as
Number Theory gurus. What makes you think any such mathematicians
would agree to be a referee for your scheme? It seems pretty unlikely.
In my opinion, your betting idea is just a foolish fantasy -- it will
never get off the ground. Forget it.
However, it is true that if you publish your proof (on the web, for
example), and if it magically survives public criticism, you _will_
become famous, and at that point, you would be widely sought after for
interviews, tv appearances, guest talks at colleges, etc. Appearance
fees would definitely be offered.
And has been suggested, you could write a book describing the problem,
some of its history, your quest for the proof, the actual proof
together with expanded explanations of the key ideas, your struggle to
convince the skeptics, your attempts to capitalize on your discovery,
and finally, the eventual worldwide recognition.
Fees and royalties -- it's a more standard approach, and while not
guaranteed to make you millions, it might reach $100,000 over time.
In any case, regardless of how you proceed, you are not going to make
a million dollars. Unless ... Unless you can also prove that Wiles'
proof is invalid. In that case, your fame escalates, and so does the
money.
But my gut sense is that it's all just an ego trip on your part. The
more you talk about selling your proof on eBay, or your ultra-naive
100-1 escrow-based betting scheme, the more I'm convinced that in
essence, you're just another JSH-like troll, and that your true goal
is just to be a center of attention for awhile.
quasi
Phil Carmody
By offering such odds, he's saying that he believes that there's
a 99% chance of him being wrong.
I think we can at that point, to 1 significant figure, simply
agree with him.
Phil
--
I tried the Vista speech recognition by running the tutorial. I was
amazed, it was awesome, recognised every word I said. Then I said the
wrong word ... and it typed the right one. It was actually just
detecting a sound and printing the expected word! -- pbhj on /.
Gareth Erskine-Jones
<r...@see.sig.invalid> wrote:
>Gareth Erskine-Jones said:
>
>> On Sun, 4 Jan 2009 08:30:31 -0800 (PST), hagman
>> <goo...@von-eitzen.de> wrote:
>>
>>>On 3 Jan., 23:27, Gareth Erskine-Jones <g...@uberdog.net> wrote:
>>
>>>> Here's a more interesting question (IMHO) - you discover an
>>>> algorithm to factor large numbers very rapidly. How do you
>>>> capitalize on that? How would you even survive that? You publish
>>>> on the net, and most of the world's cryto systems are useless.
>>>> You go to your government, and ... well, you don't come back.
>>>>
>>>> GEJ
>>>
>>>Some of such factoring experts just keep coming back *sigh*
>>
>> Yeah, but no-one's ever succeeded yet....
>
>How do you know?
True - I don't know.
>> but if someone did, what
>> could they do? If they reveal to the whole world at once, then
>> they'd cause chaos, but might escape with their lives. If they
>> revealed it to their own nation's security services - well, would
>> the NSA or GCHQ hesitate to grab the solution for themselves and
>> to eliminate any potential leaks?
>
>What makes you believe this hasn't already happened?
>
>No, I don't have inside information. Contrary to unpopular belief, I
>really don't work for the British intelligence services. (But I
>would say that, wouldn't I?)
I don't either. See you in the office tomorrow btw. :-)
GEJ
Gareth Erskine-Jones
(Matthew Russotto) wrote:
>In article <c7pvl41i4mjfdjvq2...@4ax.com>,
>Gareth Erskine-Jones <g...@uberdog.net> wrote:
>>
>>Here's a more interesting question (IMHO) - you discover an algorithm
>>to factor large numbers very rapidly. How do you capitalize on that?
>
>I think there's a few factoring contests still out there.
Sure, but if you've really got an efficient algorithm, your problem
remains - you reveal it (even in the context of a contest) and you
could cause chaos around the world as trusted cryptographic systems
become useless.
> Aside from
>that, there's crime.
That's the only thing I can think of to capitalize on a discovery like
that. Not quite so nice as being known as the one who solved a very
difficult and important problem though.
GEJ
Jasen Betts
> "Gareth Erskine-Jones" <g...@uberdog.net> wrote in message news:c7pvl41i4mjfdjvq2...@4ax.com...
>> On Sat, 3 Jan 2009 14:28:40 -0600, "David Fabian"
>> <david.m...@sbcglobal.net> wrote:
>> >
>>>Thank you for the advice; but I am interested in making money, not
>>>improving my reputation.
>>
>> Then I suspect you're barking up the wrong tree. Proving a theorem
>> that has already been proved ... I don't see how you can make money
>> from that.
>
> There are many mathematicians who would like to see a proof (especially
> one that Fermat himself probably had in mild) that is much simpler than
> Wiles' proof... so I should be able to capitalize in some way.
>
write an E-book sell it through clickbank (or similar)
put signed copies on e-bay ?
try and sell it to a math journal? or Nature?
sell movie rights?
Han de Bruijn
Sure. Why not do it the typical American way ? Sell before you have !
Han de Bruijn
Tim Smith
Gareth Erskine-Jones <g...@uberdog.net> wrote:
> >>Here's a more interesting question (IMHO) - you discover an algorithm
> >>to factor large numbers very rapidly. How do you capitalize on that?
> >
> >I think there's a few factoring contests still out there.
>
> Sure, but if you've really got an efficient algorithm, your problem
> remains - you reveal it (even in the context of a contest) and you
> could cause chaos around the world as trusted cryptographic systems
> become useless.
The factoring contests don't require you to reveal your methods, I
believe. What you could do is skip some of the challenge numbers, and
hint that you skipped them because you do NOT have a factoring
breakthrough--you found a flaw in how they generated the challenge
numbers and were able to exploit it for some of them.
>
> > Aside from
> >that, there's crime.
>
> That's the only thing I can think of to capitalize on a discovery
> like that. Not quite so nice as being known as the one who solved a
> very difficult and important problem though.
Anti-crime would also be a possibility. Start a data recovery service,
specializing in recovering incriminating evidence for police from
alleged criminal's computers.
--
--Tim Smith
Tim Smith
quasi <qu...@null.set> wrote:
> (2) Not many people, if any will offer 100-1 odds. It's not that the
> odds are unfair -- in fact, the true odds, given your background, are
> probably at least 10,000-1. Still, the reason people will not offer
> 100-1 is because the potential profit is simply not worth the trouble.
> Would I bet $10,000 against your $100? Why should I bother? I would
> have to wait possibly 6 months, all the time worrying about possible
> fraud. Is the escrow service legitimate? Is the referee secretly in
> collusion with you? Etc.
If the escrow is with someone trustworthy, I don't think there would be
that much problem finding people willing to bet. Looking at how my
investments have performed over the last year, putting money up on a bet
against a 17th-century technology proof of FLT looks like a better
investment than what I've got now. :-(
--
--Tim Smith
Tim Smith
Gareth Erskine-Jones <g...@uberdog.net> wrote:
[How to proceed if you have a factoring breakthrough?]
> Yeah, but no-one's ever succeeded yet.... but if someone did, what
> could they do? If they reveal to the whole world at once, then they'd
> cause chaos, but might escape with their lives. If they revealed it to
> their own nation's security services - well, would the NSA or GCHQ
> hesitate to grab the solution for themselves and to eliminate any
> potential leaks?
That's overly dramatic. The NSA supposedly is the world's largest
employer of mathematicians. You go to them and show them a significant
factoring breakthrough, then they will indeed take steps to eliminate
leaks--by showing you to your new office, and putting you on the payroll
with a good salary and benefits.
--
--Tim Smith
G. A. Edgar
Tim Smith <reply_i...@mouse-potato.com> wrote:
> The NSA supposedly is the world's largest
> employer of mathematicians.
The version I heard said "largest non-academic employer of
mathematicians"
quasi
But note the bars on the windows, and the lack of a handle on the
inside of the door.
Still, it sounds like an offer that you just can't refuse.
quasi
Angus Rodgers
"And now it's time to meet your line manager, Mr. Harris."
--
Angus Rodgers
junoexpress
> It's a very naive plan.
>
>
> never get off the ground. Forget it.
>
> However, it is true that if you publish your proof (on the web, for
> example), and if it magically survives public criticism, you _will_
> become famous, and at that point, you would be widely sought after for
> interviews, tv appearances, guest talks at colleges, etc. Appearance
> fees would definitely be offered.
>
>
Quasi is right: the betting is pie-in-the-sky stuff. IF you publish
and IF you are correct, you'll get your 15 minutes of fame. Milk it
for all it's worth (ain't that the American way?) It might help if you
had some sort of human interest angle that the general public would
eat up. Maybe you had a battle with the bottle or an abusive family,
or a drug dependency, and yet you overcame it to come back and solve
the world's hardest problem. That sort of thing always seems to keep
people glued to their TV sets, fat and happy. But I'm no expert in
such matters, so besides an attorney, you might want to hire a PR firm
too.
However, you might be a bit short-sighted on this one David. You want
one big payout, but if you did publish wouldn't your reputation among
your peers now go from impressively smart guy who scores high on those
IQ tests, to super-genius? Maybe the publicity would get you a better
paying job, lucrative jobs as a consultant to solve difficult
problems, which in the *long-term* might be worth more than the short-
term pay-off (not to mention the enhanced, long-term prestige and
security vs the 15 minute "flash-in the pan" routine).
HTH,
M
Dave L. Renfro
http://groups.google.com/group/sci.math/msg/0d4d7d1571209bc4
>> Thank you for the advice; but I am interested in making money,
>> not improving my reputation.
quasi wrote (in part):
http://groups.google.com/group/sci.math/msg/1ed5d11ad39f5eaa
> However, it is true that if you publish your proof (on the web,
> for example), and if it magically survives public criticism,
> you _will_ become famous, and at that point, you would be
> widely sought after for interviews, tv appearances, guest
> talks at colleges, etc. Appearance fees would definitely
> be offered.
>
> And has been suggested, you could write a book describing
> the problem, some of its history, your quest for the proof,
> the actual proof together with expanded explanations of the
> key ideas, your struggle to convince the skeptics, your
> attempts to capitalize on your discovery, and finally,
> the eventual worldwide recognition.
>
> Fees and royalties -- it's a more standard approach, and
> while not guaranteed to make you millions, it might reach
> $100,000 over time.
I was going to write something similar to what quasi wrote
in response to David Fabian's comment above, but decided to
first scan through the posts in this thread to see if anyone
commented on the obvious, which quasi did.
David Fabian -- If you truly want to make money off this,
then you need to realize that what will be valuable is _you_,
not the proof. Most of the public probably won't even be
interested in trying to read the proof and most mathematicians
won't be interested in buying the proof (not when, after it's
available, they can just look at it). What people will be
interested in is _you_ and thus it's _you_ that will be
marketable, not the proof. And I disagree with quasi about
"might reach $100,000 over time", because I have little doubt
that you could easily get several million in marketing yourself
after you become world famous.
Again, there is little chance of making money directly from
the proof itself. The money will come from the fame and human
interest that the proof will generate for _you_.
Dave L. Renfro
junoexpress
>
> Most of the public probably won't even be
> interested in trying to read the proof and most mathematicians
> won't be interested in buying the proof (not when, after it's
> available, they can just look at it).
> Dave L. Renfro
Because by definition the proof involves elementary methods,
mathematicians might not have much interest in it. A good deal of the
interest in FLT was not from the solution itself (which from past work
and simulations people pretty much a good idea which way things would
go), but rather from the *new* math it generated. Math people might
regard your clever soln more as you being more of a "one-trick" pony.
To reiterate what I said in my previous post, use your publicity to
enhance your career. If you're as smart as you think you are, you have
more than the soln of just one tough problem in you. People pay very
good $$ for such people. (Of course, the obvious rebuttal is "Well, I
want to get rich quick and retire to the Bahamas with a boatful of
babes". Well, we all do, but it ain't happening, so get real and think
of a practical soln.)
HTH,
M
tc...@lsa.umich.edu
junoexpress <MTBre...@gmail.com> wrote:
>Because by definition the proof involves elementary methods,
>mathematicians might not have much interest in it. A good deal of the
>interest in FLT was not from the solution itself (which from past work
>and simulations people pretty much a good idea which way things would
>go), but rather from the *new* math it generated. Math people might
>regard your clever soln more as you being more of a "one-trick" pony.
I don't believe this for a second. A (correct) elementary proof of FLT
would be enormously interesting to mathematicians. They would certainly
study it very carefully, and *if* they were certain it was correct,
some would even pay to see it. The reason is that there has been a lot
of effort expended trying to prove the theorem by elementary means, and
so any correct elementary proof must involve some highly original ideas.
Furthermore, mathematicians are human beings. Because of the history and
human interest angle, FLT fascinates mathematicians. They may *say* that
what's "really" interesting about the papers by Wiles and Taylor-Wiles is
that they established the semistable case of the Shimura-Taniyama-Weil
conjecture. But don't believe them. Yes, STW is more important
*theoretically* than FLT. But if there were no known connection between
STW and FLT, then for the most part, only number theorists would care
about the semistable case of STW. Even Wiles would probably not have
thrown himself so thoroughly into STW if FLT weren't part of the picture.
Compare, for example, Apery's elementary proof of the irrationality of
zeta(3). This did not generalize to zeta(2n+1), and while it has inspired
some further research, it has not been as theoretically fruitful as the
work of Wiles. Nevertheless, Apery's proof is very interesting to
mathematicians and has a permanent place in the history of mathematics,
because the problem was so famous.
spudnik
it is probably quantifiable in the zillions/ths,
mod a certifiable Don or two at Harry Potter PS#2..
If monsieur Munk is alive, he is over a hundred;
<br/>this book was published, as I recall, in '76, although
<br/>I came across it in the late '90s. Now, he is perfectly
qualified
<br/>to be an amateur a la Fermat, having been an engineer
<br/>at NACA, the predecessor to NASA, where he worked
<br/>on aerodynamics. His main claim to fame is an early analysis
<br/>of (2d) sections of airfoils.
<br/>
<br/>He wrote the first introduction for laymen on aerodynamics; since
<br/>it was published in the Great Depression, he used a "vanity
press,"
<br/>Vantage Books, which he also used for his alleged proof
<br/>of Fermat's "last" theorem.
<br/>
<br/>The insight that I got into Fermat is not acutally stated in the
book
<br/>-- it goes with monsieur Munk's *vitae* --
<br/>suffice to say that the undisclosed theorem was probably amongst
<br/>his first insights into Diophantine eequations. You could guess
that
<br/>it was a key to his Method.
<br/>
<br/>The book is quite elementary and enjoyably written,
<br/>occaisionally funny and quite a tour de force. Now, although
<br/>Fermat made no known errors -- unless possibly,
<br/>you question the veracity of Wiles' proof of FLT, tee-hee --
<br/>that is not to say that monsieur Munk made no mistakes.
<br/>
<br/>Underwood Dudley includes Munk in his chapter, in _Mathematical
Cranks_
<br/>(from MAA.org [*:]),
<br/>of "fermatistes," which you will have seen if you have ever used
any
<br/>of the sci.math newsgroups. As he admitted, when I wrote to him,
<br/>it was obvious that he did not read the whole, slim book, but
<br/>jumped to the pen-intimate section from the table of content,
<br/>where the nib of the matter would be written.
<br/>
<br/>There *is* a problem, there, but it may just be a peculiarity
<br/>of "English as a second language," because everything else is
beautiful,
<br/>including the remaining chapters that explain the workings of
congruence surds,
<br/>which is Munk's coinage. "They are not p-adic numbers."
<br/>
<br/>Numbertheory is part of the *quadrivium*, which is Latin for
*mathematica*,
<br/>which is the four subjects of classical Greek science; as an
example
<br/>of this "modular arithmetic," what is the meaning
<br/>of Platform Nine & Three-quarters?
<br/>
<br/>Get this book back into print!
<br/>
<br/>* The MAA's *Mathematics Magazine* is fantastic, and accessible
at any level.
junoexpress
> In article <c64b7160-48b1-4724-aa77-72169f171...@d36g2000prf.googlegroups.com>,
>
> junoexpress <MTBrenne...@gmail.com> wrote:
> >Because by definition the proof involves elementary methods,
> >regard your clever soln more as you being more of a "one-trick" pony.
>
> I don't believe this for a second. A (correct) elementary proof of FLT
> would be enormously interesting to mathematicians. They would certainly
> study it very carefully, and *if* they were certain it was correct,
> some would even pay to see it. The reason is that there has been a lot
> of effort expended trying to prove the theorem by elementary means, and
> so any correct elementary proof must involve some highly original ideas.
>
>
> Tim Chow tchow-at-alum-dot-mit-dot-edu
Hence, the quantifier "might", since it really depends on whether
there is something mathematically substantial underlying this
approach. But even if your last statement was correct, would many
people pay to see something "elementary"? Isn't it likely that if just
one person who had seen it communicated the gist of the proof
throughout the math community, such an *elementary* proof would be
replicated by others independently?
M
galathaea
> In article <c64b7160-48b1-4724-aa77-72169f171...@d36g2000prf.googlegroups.com>,
>
> >Because by definition the proof involves elementary methods,
> >mathematicians might not have much interest in it. A good deal of the
> >interest in FLT was not from the solution itself (which from past work
> >and simulations people pretty much a good idea which way things would
> >go), but rather from the *new* math it generated. Math people might
> >regard your clever soln more as you being more of a "one-trick" pony.
>
> I don't believe this for a second. A (correct) elementary proof of FLT
> would be enormously interesting to mathematicians. They would certainly
> study it very carefully, and *if* they were certain it was correct,
> some would even pay to see it. The reason is that there has been a lot
> of effort expended trying to prove the theorem by elementary means, and
> so any correct elementary proof must involve some highly original ideas.
>
> Furthermore, mathematicians are human beings. Because of the history and
> human interest angle, FLT fascinates mathematicians. They may *say* that
> what's "really" interesting about the papers by Wiles and Taylor-Wiles is
> that they established the semistable case of the Shimura-Taniyama-Weil
> conjecture. But don't believe them. Yes, STW is more important
> *theoretically* than FLT. But if there were no known connection between
> STW and FLT, then for the most part, only number theorists would care
> about the semistable case of STW. Even Wiles would probably not have
> thrown himself so thoroughly into STW if FLT weren't part of the picture.
speaking of the human angle
i am still surprised at the continued association
of weil's name in relation to the conjecture
http://www.ams.org/notices/199511/forum.pdf
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar
Gareth Erskine-Jones
<reply_i...@mouse-potato.com> wrote:
>In article <e4e2m4hoerr02ec4s...@4ax.com>,
> Gareth Erskine-Jones <g...@uberdog.net> wrote:
>
>[How to proceed if you have a factoring breakthrough?]
>
>> Yeah, but no-one's ever succeeded yet.... but if someone did, what
>> could they do? If they reveal to the whole world at once, then they'd
>> cause chaos, but might escape with their lives. If they revealed it to
>> their own nation's security services - well, would the NSA or GCHQ
>> hesitate to grab the solution for themselves and to eliminate any
>> potential leaks?
>
>That's overly dramatic.
I'm not sure about that...
>The NSA supposedly is the world's largest
>employer of mathematicians. You go to them and show them a significant
>factoring breakthrough, then they will indeed take steps to eliminate
>leaks--by showing you to your new office, and putting you on the payroll
>with a good salary and benefits.
Sure, but perhaps this is just me, but I wouldn't work for the NSA. As
as an IT contractor, I routinely turn down roles with government
departments as a matter of principle (for various reasons - I don't
like governments, especially big, powerful and invasive ones, and I
certainly don't like the idea of handing that sort of power to one
government).
I think the only ethical thing to do would be to give the information
to everyone. I suppose one way would be to demonstrate that the
algorithm existed (e.g. factor a large product of two primes, and
publish the result anonymously (and there's the tricky bit)), and then
say that the actual algorithm will be published in a couple of years'
time (giving everyone a chance to do something about those
cryptographic algorithms which would be broken). The demonstration and
final publication of the algorithm could be signed with the same
private key so the author could be credited for the work.... it would
be the last private key that actually worked :-).
GEJ
tc...@lsa.umich.edu
galathaea <gala...@gmail.com> wrote:
>speaking of the human angle
>i am still surprised at the continued association
> of weil's name in relation to the conjecture
Many people drop it now, but I personally feel that Weil's role in
popularizing the conjecture and arguing for it, despite his initial
skepticism, was significant enough that I don't drop it.
For comparison, consider the Pell equation. There's even less reason to
keep Pell's name, but I still do so, and in this case so does everyone
else. It's mainly because Lang got enraged and turned the issue into
one of his legendary crusades that people stopped using Weil's name.
I don't really want to encourage people to emulate Lang's tactics.
Tim Smith
"G. A. Edgar" <ed...@math.ohio-state.edu.invalid> wrote:
> In article <reply_in_group-D8E...@news.supernews.com>,
> Tim Smith <reply_i...@mouse-potato.com> wrote:
>
> > The NSA supposedly is the world's largest
> > employer of mathematicians.
>
> The version I heard said "largest non-academic employer of
> mathematicians"
Are there any academic large employers of mathematicians?
--
--Tim Smith
tc...@lsa.umich.edu
junoexpress <MTBre...@gmail.com> wrote:
>On Jan 5, 1:37 pm, tc...@lsa.umich.edu wrote:
>> The reason is that there has been a lot
>> of effort expended trying to prove the theorem by elementary means, and
>> so any correct elementary proof must involve some highly original ideas.
>
>there is something mathematically substantial underlying this
>approach. But even if your last statement was correct, would many
>people pay to see something "elementary"?
Yes, I think so. While I'm glad that it's not common practice to have to
pay to see theorems, I believe that people would have paid to see the
Erdos-Selberg elementary proof of the prime number theorem, or Apery's
proof of the irrationality of zeta(3), if they were sure it was correct.
>Isn't it likely that if just
>one person who had seen it communicated the gist of the proof
>throughout the math community, such an *elementary* proof would be
>replicated by others independently?
There are so many errors here that I don't even know where to begin.
1. One person versus many people. This seems to me to be a quibble.
Forgetting about the "gist" business for a second, is your point that
if one person pays for the proof and tells everyone else about it for
free, then others wouldn't pay for it? Well, of course. But that's
a quibble about logistics and law and so forth. I'm just saying that
it would be worth enough to the mathematical community that it would
likely produce money somehow, if forced to. You're taking my use of
the plural too literally.
2. Gist versus full details. Of course it's possible to reconstruct
something from the gist. This is true regardless of whether the proof
is elementary. Perelman's preprints communicated the gist of his proof
of the Poincare conjecture, and the mathematical community completed
the reconstruction some years later. Perelman still gets the lion's
share of the credit for solving the problem. The gist, almost by
definition, is incalculably more than nothing, and close to the full
details. But in my scenario, how are you going to get the gist, except
by paying for it? Again, gist versus full details is a red herring.
3. Your real question, stripped of the two red herrings above, seems to
be whether an elementary proof can have enough intellectual content to
be worth paying for. Wouldn't people find it independently anyway,
for free? Well, no. There is no such guarantee. I think it was van
der Poorten who dubbed Apery's proof "the proof that Euler missed."
It was elementary; Euler could have found it, as well as any number
of people since Euler. But they didn't. "Elementary" does not mean
"easy to find." Look at the work of mathematicians like Bert Kostant
or Manjul Bhargava, and you will marvel at the beauty and simplicity
of their arguments, that are often totally elementary. Not just anyone
could come up with those ideas, and not just anyone did.
It's not *likely* that there is an elementary proof of FLT. But I
don't think many mathematicians would bet their house that there
definitely isn't one that someone, someday, will find.
Steve Fry
"Dave Parker" wrote:
> Faster-than-light USB toaster.
>
Great -- using FTL to solve FLT.
Simon Tatham
> Yes, I think so. While I'm glad that it's not common practice to have to
> pay to see theorems, I believe that people would have paid to see the
> Erdos-Selberg elementary proof of the prime number theorem, or Apery's
> proof of the irrationality of zeta(3), if they were sure it was correct.
But this is a virtually impossible premise. How would someone become
sure that a proof was correct, if not by seeing it? So they won't
pay until they're sure (otherwise, cranks charging money in advance
for bogus proofs would be two a penny), but they can't be sure until
they've paid.
--
Simon Tatham "_shin_, n. An ingenious device for
<ana...@pobox.com> finding tables and chairs in the dark."
tc...@lsa.umich.edu
Simon Tatham <ana...@pobox.com> wrote:
><tc...@lsa.umich.edu> wrote:
>> Yes, I think so. While I'm glad that it's not common practice to have to
>> pay to see theorems, I believe that people would have paid to see the
>> Erdos-Selberg elementary proof of the prime number theorem, or Apery's
>> proof of the irrationality of zeta(3), if they were sure it was correct.
>
>But this is a virtually impossible premise. How would someone become
>sure that a proof was correct, if not by seeing it? So they won't
>pay until they're sure (otherwise, cranks charging money in advance
>for bogus proofs would be two a penny), but they can't be sure until
>they've paid.
It's basically impossible in the case of a crank, but in the (distasteful,
to be sure) world where charging for theorems is standard, you would
soon be able to sort out who the cranks were. Unknown people would be
forced to charge low amounts of money. After you got a reputation for
solving hard problems correctly, people would be confident enough in
your abilities that you could charge more money. There would still be
the risk of an honest mistake, of course, but people would be tolerant
of that, I think. And most people who had painstakingly built a reputation
for delivering the goods would be afraid of losing their income stream by
committing deliberate fraud.
CBFalconer
> Jasen Betts wrote:
>
... snip ...
>
>> write an E-book sell it through clickbank (or similar)
>> put signed copies on e-bay ?
>>
>> try and sell it to a math journal? or Nature?
>>
>> sell movie rights?
>
> Sure. Why not do it the typical American way? Sell before you have!
You haven't got the idea yet. Sell securities with rights to the
profits. Then create a further line that deals in those
securities. By this time it doesn't take much to make the final
object increase in value by a large factor. Take the income from
that and disappear.
--
[mail]: Chuck F (cbfalconer at maineline dot net)
[page]: <http://cbfalconer.home.att.net>
Try the download section.
Tim Smith
tc...@lsa.umich.edu wrote:
>
> Furthermore, mathematicians are human beings. Because of the history and
> human interest angle, FLT fascinates mathematicians. They may *say* that
> what's "really" interesting about the papers by Wiles and Taylor-Wiles is
> that they established the semistable case of the Shimura-Taniyama-Weil
> conjecture. But don't believe them. Yes, STW is more important
> *theoretically* than FLT. But if there were no known connection between
> STW and FLT, then for the most part, only number theorists would care
> about the semistable case of STW. Even Wiles would probably not have
> thrown himself so thoroughly into STW if FLT weren't part of the picture.
I think that "probably" can be replaced with "certainly". I believe
he's stated in interviews that FLT was always, from early childhood,
what he was interested in working on--it was only that it wasn't really
respectable from a career point of view to work full time on FLT that
held him back. When the connection between STW and FLT was found, so
that proving STW would settle FLT, his reaction was something like
"Alright! There's a way I can work on FLT now that is respectable!".
--
--Tim Smith
Mensanator
> <tc...@lsa.umich.edu> wrote:
> > Yes, I think so. While I'm glad that it's not common practice to have to
> > pay to see theorems, I believe that people would have paid to see the
> > Erdos-Selberg elementary proof of the prime number theorem, or Apery's
> > proof of the irrationality of zeta(3), if they were sure it was correct.
>
> But this is a virtually impossible premise. How would someone become
> sure that a proof was correct, if not by seeing it? So they won't
> pay until they're sure (otherwise, cranks charging money in advance
> for bogus proofs would be two a penny
Perhaps not that many, but they're certainly trying.
There's Danny Fleming's "How to Prove The Collatz Conjecture"
available on Amazon, which certainly looks crackpot from
the excerpts. And certainly not worth $28.52 for the joke
as I would wager I already know what the fallacy is.
Then there's JSH trying to sell his blog entries (and sold
nearly one).
Both published by the appropriately named Lulu.
So the book route is certainly worth exploring.
David Bernier
Wasn't there Serre's epsilon-conjecture, that a Frey elliptic
curve would not be modular? And that that was eventually proved by
Ribet? NOVA (PBS network, US) had an episode "The Proof".
David Bernier
spudnik
Wiles was working on it in his basement office
for seven years, I think, sheletering himself
from imminent exposure to respectability.
> Wasn't there Serre's epsilon-conjecture, that a Frey elliptic
> curve would not be modular? And that that was eventually proved by
> Ribet? NOVA (PBS network, US) had an episode "The Proof".
thus:
I don't recall if Deffeyes is Dutch, but
he did work with Hubbert at Shell, which is half British;
between the "free market" in the City of London, and
the massive ports of Rotterdam, the cartel is anglo-dutch. well,
that's probably not quite what he says, and
he seems to believe in the mainstream paradigm as
to the ultimate source of oil, based on that funny word, and
that funny dinosaur in the Mobil commercial,
which he dysavows.
just wish I'd read his first book, when it came out, and
it might have had most of what is in this one.
the most important thing, so far, is that, although
heat engines are restrained absolutely by the Carnot cycle,
fuel cells & such are not. still,
they ain't the panacea, either ...
that is probably your God-am what's-her-name,
that you started this funky item with.
thus:
although they have no other simple valuation,
any congruence surd that repeats across the decimal point,
is equal to zero, such as ...9999.9999...; so,
the whole import of Hensel,
was to show that integers have the same properties
as decimals, properly oriented -- except that
he didn't use the commonsense ordering of the digits!
thus:
now, isn't that what the key method
of "remote viewers?" well, it depends....
anyway, that's the impression I got from Ghost
to Ghost BC radio; there's a reason, they're called, Spooks!
thus:
no, no, no;
Fermat's unstated proof was not qualified
as to whether or not it applied to n=4, or
he thought at first that it did; clearly,
he wouldn't have needed to prove that case
with his infinite descent contradiction, if
he had already "had" the unstated proof. but,
isn't it clear that n=4 is very special,
after a while of consideration?
thus:
shouldn't it be clear that photons are an artifact of the idea
of point-particles?... of course, iff
they exist, then they would have to be *the* particles
that actually were zero-dimensional points, but,
since they are waves, as shown by Young, Huyghens et al,
there is really no need for them,
except in the Pauli matrix formalism of statistical bosons; eh?
Schroedinger's cat is dead -- long-live Schoredinger's cat!
--only 24 hours to impeach Trickier Dick from the N.Admin,
metaphorically typing, or Cheeny & Zbiggy, fo'mo' years;
Good Morning, Afghanistan!
... Good Afternoon, Sudan!
http://tarpley.net/bush12.htm
http://wlym.com/campaigner/8011.pdf -- Brits hate Shakes, Why?
http://www.wlym.com/~seattle/dynamis/
http://www.21stcenturysciencetech.com/current.html
http://www.rwgrayprojects.com/synergetics/plates/plates.html
http://mathdl.maa.org/mathDL/46/?pa=content&sa=viewDocument&nodeId=3163
http://wlym.com/campaigner/8011.pdf -- English, not! (see Psalms 46)
Tim Smith
> <tc...@lsa.umich.edu> wrote:
> > Yes, I think so. While I'm glad that it's not common practice to have to
> > pay to see theorems, I believe that people would have paid to see the
> > Erdos-Selberg elementary proof of the prime number theorem, or Apery's
> > proof of the irrationality of zeta(3), if they were sure it was correct.
>
> But this is a virtually impossible premise. How would someone become
> sure that a proof was correct, if not by seeing it? So they won't
> pay until they're sure (otherwise, cranks charging money in advance
> for bogus proofs would be two a penny), but they can't be sure until
> they've paid.
You'd use a zero-knowledge proof. There was a cool article about this a
very long time ago in MAA FOCUS. The idea goes something like this. It
is possible to map a purported theorem to a graph (a graph theory kind
of graph, not a pretty picture kind of graph), such that proving the
theorem is equivalent to finding a Hamiltonian circuit on the graph. I
don't recall if the article talked about *how* this is done or not--if
it did, I don't remember the details.
Thus, you can reduce the problem of convincing mathematicians that you
have a correct proof, without showing them the proof, to the problem of
showing that you know a Hamiltonian circuit on a particular graph,
without showing them the actual circuit.
This latter problem has been solved (if we assume P != NP). The basic
idea is that you've got your graph, G, for which you know a Hamiltonian
circuit, H (or so you claim). Repeat the following procedure until
everyone is convinced you do indeed have a correct circuit:
1. Generate a graph, G', that is isomorphic to G, and let H' be the
Hamiltonian circuit on G' corresponding to H on G.
2. Reveal G'.
3. The people you are trying to convince get to ask you exactly one of
the following two questions:
A. Show us the isomorphism from G to G'.
B. Show us H' on G'.
4. You answer their question, and they verify the answer (which they can
easily do). This is safe from your point of view, because you only are
answering one of these questions. If they ask and you answer A, you
given them no information about the circuit. If they ask and you answer
B, it is still useless to them, because they don't know how to map H' on
G' back to H on G. To do that, they need to solve the graph isomorphism
problem--which is NP-complete.
5. Go back to step #1, unless they concede that you do have a proof.
If you are on the level, and really have a correct proof, you'll be able
to satisfy them, regardless of which question they pick. If, on the
other hand, you are faking it, best you can do is try to guess which
question they are going to ask. If you think they will ask A, you
generate G' isomorphic to G. But then if they ask B, you are screwed,
because you won't know a circuit on G'. If you think they will ask B,
you can generate a G' for which you know an H', but if they ask A, you
are screwed, because your G' won't be isomorphic to G. Putting that all
together, if you are faking, there is a 50% chance you will get caught
each time they ask you a question.
So, in principle, you could in fact convince mathematicians that you
have a correct proof of a theorem, without giving them any information
about the proof.
--
--Tim Smith