proof of fermat's last theorem disproved
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Date: May 11th, 2005 9:41 PM Author: APPLE SAUCE
UP Math prof proves Princeton man wrong
By Rony V. Diaz
Edgar Escultura, a professor of mathematics at the University of the Philippines, proved that Andrew Wiles’ proof of Fermat’s last theorem is false.
In 1993 Andrew Wiles of Princeton University announced at a lecture in London that he had proved Fermat’s last theorem (FLT). This is a conjecture by the French mathematician Pierre de Fermat in 1637 that for any integer n greater than 2, Fermat’s equation that claimed xn + yn = zn has no solution in integers x, y z except 0 which satisfies the equation.
Integers are whole numbers like 8, 73, 1,257, etc. Since that time mathematicians and amateurs had been trying to find a proof but failed.
When Wiles made the announcement it was celebrated around the world. In Chicago, for instance, mathematicians marched on the streets in euphoric celebration.
Escultura, who had been working on the problem since 1992, disputed Wiles’ claim and inserted his refutation in the appendix to his book, Diophantus: Introduction to Mathematical Philosophy. He went on to present his results at the Second International Conference on Dynamic Systems and Applications in Atlanta in 1995.
In 1998 he published his formal refutation in “Exact solutions of Fermat’s equations (A definitive resolution of Fermat’s last theorem)” in the Journal of Nonlinear Studies, Vol. 5, No. 2, pp. 227–254. Since then Escultura has published over two dozen papers on the subject, and its applications to physics, in international scientific journals.
Escultura’s refutation sparked much discussion on the Internet that has spilled over to other fields such as physics, astronomy, cosmology, intelligence, learning, chaos, turbulence, gravity and nonlinear analysis.
He took the position that the failure to resolve the problem for over 360 years reveals the inadequacy and defects of foundations, number theory and the real number system. He undertook a thorough critiquerectification of these fields and found, among others, that the real number system in basic algebra, the foundation of mathematics, is defective. Specifically, two of its axioms (the trichotomy and completeness axioms, for those who took basic algebra in high school and college) are false.
Escultura went on to overhaul the real number system and reconstructed it without these false axioms using only three simple axioms instead of 12. The result is a new real number system that is free from defects and contradictions, finite and enriched with new numbers that have important applications for physics.
Using the new real number system Escultura constructed many counterexamples to FLT showing that it is false.
On April 26, Andrew Wiles conceded an error in his proof. His letter and Escultura’s reply are below.
Tuesday 04/26/2005 6:57:33am
Dear Sir,
Your work is incredible, I read all of it just yesterday and let me tell you I respect you. I am going to review all my ‘proof’ which I am sure is wrong (thanks to you!).
Would you like to collaborate with me in this work? I have noticed some imperfections in your perfect proof (that sounds like you), and I’d like to create a perfect proof with you, great professor.
Also I’d like to have the address of the guy who let you get a PhD 30 years ago. I’d like to discuss few things with him. . .
Very respectfully,
A. Wiles
Dear Prof. Wiles,
I welcome and appreciate your comments and I hope we can have a continuing dialogue. Regarding your invitation to collaborate with you, I would be glad to. But here is the situation:
My critique of mathematics is focused not on your work but mainly on the underlying fields of FLT which are foundations, number theory and the real number system. Here is what I found:
1) Two of the axioms of the real number system are false, namely, the trichotomy and completeness axioms (the latter is a variant of the axiom of choice), counterexamples to them were constructed by Brouwer and BanachTarski, respectively.
2) I also noted a flaw in the use of the universal or existential quantifiers on infinite set.
3) To avoid contradictions, it is necessary to well define a mathematical space and its concepts by a consistent set of axioms. A concept is well defined if its existence, properties and relationship with other concepts are specified by the axioms. Most of the concepts of mathematics today are illdefined.
Based on these findings I constructed the new real number system on three simple axioms. Its most updated version appears in the Journal of Nonlinear Analysis and Phenomena. An extended abstract of it appears in my updated website in June.
Yes, indeed, there are imperfections in my work but not on principles. And if there are major ones, I would like to know.
Regarding my academic advisor, he was the late L. C. Young, distinguished research professor and professor emeritus at the University of Wisconsin.
Again, thank you for your interest in my work and for inviting me to collaborate with you.
With my very best wishes.
E. E. Escultura
Escultura was a former math and science editor and columnist of The Manila Times. He also taught math at The Manila Times School of Journalism.
He is currently working with Bernard Ziegler of the University of Texas at Houston on the new calculus based on Escultura’s real number system.
Ziegler and Escultura will also collaborate on a new nonstandard analysis, a subject on which Escultura has published many papers in peerreviewed international journals.
http://www.manilatimes.net/national/2005/may/05/yehey/top_stories/20050505top4.html
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2759164) 

Date: May 11th, 2005 10:22 PM Author: egress
That was a poorly written article. It sucks.
And Wile's response was stinging. Ouch.
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2759534) 
Date: May 11th, 2005 9:54 PM Author: EpsiHpsi
hahahahaha. Andrew Wiles = pwned
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2759286) 
Date: May 12th, 2005 12:57 PM Author: LillOfTheFarm Subject: Look at Escultura's other commentary:
http://www.manilatimes.net/national/2004/dec/18/yehey/opinion/20041218opi4.html
Among other things, he says that "the complex number i is nonsense", and "The irrationals pi and the nth root of a prime, n = 2, 3, …, are welldefined because their digits are computable." He also claims "qualitative mathematics extends the breadth and reach of computation ".
Draw your own conclusions.
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2764225) 

Date: May 12th, 2005 5:43 PM Author: Faen
From that link it is clear that this guy is a moron. I'm actually embarrassed on his behalf when I read that crap.
And I can't believe he calls "1 = 0.99…" the "UllrichIsrael equation"
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2766542) 
Date: May 12th, 2005 3:44 PM Author: Concerned.Mom
Wiles' proof was shown faulty some time in the 90's (someone pointed out that all evens and all odds hadn't been proven as making up the entire number set)
Wiles found a recent proof that this was so and revised his own proof.
As far as I know it still holds
That email was very odd. "Who let you have a PhD" sounds like it's very pointed, but the rest of the letter gives no indication of insult.
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2765524) 

Date: May 12th, 2005 5:28 PM Author: egress
You have shitty reading comprehension if you couldn't pick up the overflowing sarcasm.
I'll break it down for you:
"Your work is incredible, I read all of it just yesterday and let me tell you I respect you."
No good mathematician has produced work that could be reviewed in one day. Wile is implying that E's work is so simple, he could "read all of it just yesterday". Notice the untempered praise; this, juxtaposed with the insult, makes it clear that it's facetious.
"I am going to review all my ‘proof’ which I am sure is wrong (thanks to you!)."
Again, obvious sarcasm. He pretends to concede that his life's work and claim to fame is all wrong, and he uses an exclamation mark to indicate earnestness.
"Would you like to collaborate with me in this work? I have noticed some imperfections in your perfect proof (that sounds like you), and I’d like to create a perfect proof with you, great professor."
Need I go on...?
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2766384) 
Date: May 12th, 2005 4:29 PM Author: not
Edgar Escultura does, indeed, have a PhD from the University of Wisconsin, 1970. The title of his thesis: "The Trajectories, Reachable Set, Minimal Level and Chain of Trajectories in a Control System". He did indeed have Laurence Chisholm Young as his advisor. (Source: http://www.genealogy.ams.org/html/id.phtml?id=9115 )
It seems that Dr. Wiles is being stingingly ironic in his letter, not making a concession.
As for the history of FLT, there were flaws in Wiles's first proof of it, which were later corrected.
Having read some of Dr. Escultura's writings (or writings attributed to him; he could be the victim of some kind of hatchet job on the Usenet) I conclude that he is probably very intelligent, but this doesn't, however, make him necessarily mathematically right. A lot of his ideas about mathematics are clearly wrong.
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2765907) 

Date: May 12th, 2005 4:33 PM Author: arnold schwarzenigga
here's a discussion on Andrew Wiles being possibly a douchebag http://www.livejournal.com/community/ucberkeley/230272.html
"Andrew Wiles is a douchebag. You know, the guy who proved Fermat's last theorem. Well, not without Ribet's help. Ribet proved that A implies B, and Wiles proved A, or something. And Wiles gets all the credit. No Ribet isn't bitter, he is brilliant, he deserves more credit. I told him that I think he is cool, and that Wiles was a loser because he spent 7 years in his attic trying to prove the theorem. Ribet smiled, and said that Wiles was "uptight". In adult speak, this means he is a douchebag. Wiles is a professor at Princeton, and Ribet tried to get him to come to Berkeley. But when Wiles came, he would only go around in a car, and freaked out when he saw two people kissing in public. Hmmm makes me rethink wanting to go to Princeton (not that I could get in there anyway for grad school)."
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2765958) 

Date: May 17th, 2005 12:59 AM Author: [officially retired from this disgusting hellhole]
I think you would've fit right in....
What DID you end up majoring in?
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2803133) 

Date: May 12th, 2005 5:49 PM Author: Faen
> "I conclude that he is both very intelligent and a maverick. Neither of these things, however, makes him necessarily mathematically right. A lot of his ideas about mathematics seem bizarre and are at least very counterintuitive."
Are you serious? The guy has absolutely no fucking clue what he's talking about. Even I can see that
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2766595) 

Date: May 12th, 2005 5:54 PM Author: not
He's accomplished enough that I wouldn't discount him entirely. On the other hand, a lot of his ideas are so maverick that they seem, even to me (and I consider myself quite openminded; some would say gullible and naive) to be malarkey.
There are also lots of intelligent people who don't know what they're talking about. Watch one of those CNN "discussion panels" some time.
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2766637) 

Date: May 12th, 2005 6:39 PM Author: not
He may have become (and I would have no way of knowing, just a hunch) mentally ill some time after getting tenure. That would explain the contrast between his prior record of accomplishment and some of his more questionable (a polite term for "wrong") mathematical ideas.
He's not as idiotic as "Sollog", though; one has to give him that.
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2767084) 

Date: May 12th, 2005 6:49 PM Author: corlonedon (nitpick extraordinaire)
An example of what makes him so laughable:
I'll give him the benefit of the doubt that he doesn't know about April Fool's, so I won't blame him for taking the post seriously (though it's pretty clearly bullsht/a joke anyway). But consider his reply to the MathForge post:
"Andrew Wiles should be happy that Prof. Vincenza found only an error in his comptuation. Everyone commits such error. But, his error is quite profound: he constructed his proof in the real number system whose two axioms, namely, the trichotomy and completeness axioms, are false."
As if a computational error is somehow basic, but using the 'real numbers' is a truly special, deep error.
SOLLOG (about whom I know basically nothing) might be crazy, but whatever. It's much funner when someone tries to use standard methods of reasoning to explain ludicrous ideas.
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2767166) 

Date: May 17th, 2005 1:01 AM Author: [officially retired from this disgusting hellhole]
completeness axiom is false?
There goes calculus!
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2803138) 

Date: May 12th, 2005 6:02 PM Author: Joe (Caltech '04) (jjewell@prepme.com) Subject: RE: "very intelligent and a maverick"
On another thread, pensive also claims that it's always the "usually very interesting people" at his school that end up developing reputations for creepiness.
Also, he's defending this Phillipines guy because he went to Wisconsin, no other reason. He likes Wiles enough to refer to Fermat's Last Theorem as "Wiles' Theorem" (and please, spare me the lecture on how theorems get namedeveryone still calls it Fermat's), which makes this even more interesting.
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2766702) 

Date: May 12th, 2005 6:51 PM Author: corlonedon (nitpick extraordinaire)
The snobby sic's are the best part.
Well, that or the way they wrote a story in the style of a 'discovery' piece about some interesting guy the came upon...when he works there.
Man, I should get a job at the NYT and get a story written about 'Man has world's largest cock', I guess.
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2767183) 
Date: May 12th, 2005 6:44 PM Author: not
For what it's worth, I've done some more websearch and Escultura (or someone using his identity) seems to have claimed, on the Usenet, to have specific counterexamples to FLT. If this were true, they would be easily verifiable and it would have made detectable waves in the mathematical community (of course, it has not). Therefore, Dr. Escultura's supposed "refutation" is probably a crock.
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2767123) 

Date: May 12th, 2005 6:58 PM Author: not
Ouch. So he's basically defining an entirely new (and possibly not consistent) number system and disproving FLT over that... but FLT is a statement over the integers, not some weird number system (in fact, it's trivially false over the reals) so his "counterexample" is irrelevant.
His claim of the real numbers going "down the drain" is also bogus. A high schooler could break that argument. He claims that i is "nonsense" because sqrt(1) = i; but in the same regard, sqrt(25) = 5, 5 = 5. Of course, this is an entirely fallacious argument.
He seems to reject the concept that geometric series converge as we're used to. This is why, to him, 0.99999... != 1. However, I don't see anything useful that emerges when you reject that concept, and you basically flush a lot of good analysis down the toilet.
I think the man is probably, unfortunately, suffering from mental illness.
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2767249) 

Date: May 12th, 2005 7:08 PM Author: Faen
> "I think the man is probably, unfortunately, suffering from mental illness."
That, or he's just stupid. Who knows..
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2767307) 
Date: May 12th, 2005 9:32 PM Author: worf Subject: The basis for Wiles' proof
rests on two pillars: (1) the TaniyamaShimura (TS) conjecture (every elliptic equation is associated with a modular form), and (2) Gerhard Frey's1984 assertion that proving TS automatically proves FLT, and demonstrating that if FLT were false (i.e. there exist A, B, and C such that
A^N + B^N = C^N for N>2), then Fermat's equation can be rearranged as:
y^2 = x^3 + (A^NB^N)x^2  (A^N)(B^N) which is an elliptic equation. Hence, IF there existed a solution to Fermat's equation, the rearranged equation must also exist. However, when Frey looked at the Eseries associated with the equation, it was clear that it was impossible for it to be related to a modular form, which would contradict TS.
So, Frey's argument went as follows:
1. If TS is true, every elliptic equation is modular
2. If every elliptic equation is modular, they Frey's equation cannot exist.
3. If Frey's equation cannot exist, there can be no solutions to FLT
4. Therefore, FLT is true.
This is the basis of all of Wiles' work on FLT.
(http://www.autoadmit.com/thread.php?thread_id=180172&forum_id=1#2768490) 

