chongo@nsc.uucp (Curt Noll) (09/09/83)
i have been told that someone just showed that the number of solutions to: n n n a + b = c (a,b,c integers > 0, n integer >2) were finite. this someone, in Germany, also was reported to have generalized this finite solution set to include a,b,c being rational. sorry if a may have mistated the theorem. (*send flames to /dev/null*) any info out there? chongo /\../\
sher@rochester.UUCP (David Sher) (02/09/84)
The interesting part of the proof of the 4 color theorem was the proof that
you need only check it for a finite set of special cases. This was proved
some time ago. (I think, I'm not a graph theorist so am not authoritative)
If you believe this then the 4 color theorem is definitely decidable. You
may dispute the efficacy of this particular proof technique.
-David Sher (ofttimes AI project) {he's back}
sher@rochester
seismo!rochester!shervasudev@druxt.UUCP (BhandarkarVK) (07/10/84)
A few months ago, National Public Radio reported that a British mathematician had claimed to have solved Fermat's last Theorem. (Statement: x^n = y^n + z^n has no solutions for n >= 3, and x, y, z, n integers) They interviewed two professors from Cambridge who said that they had seen this mathematician's work and the proof seemed to be correct. Considering that this theorem had been unsolved since Fermat's death about two centuries ago (Fermat himself only stated the theorem and wrote in his diary margin that the proof was simple), I expected that there would be several followup news items on this historic discovery. However, no followup seems to be forthcoming. The theorem has profound implications in computing, particularly in the field of cryptography. But no computer magazine that I have seen seems to think that this item is newsworthy. Did anyone else on the net hear about this news item? Maybe our net-friends across the Atlantic can shed some light on this? -vasudev -ihnp4!drux2!druxt!vasudev
darrelj@sdcrdcf.UUCP (Darrel VanBuer) (12/24/84)
References:
A few days ago, Ken Law's AI List digest contained an inquiry about:
AMS abstract 816-11-188 by Chen Wengen
"The missing proof of Fermat's last theorem has been rediscovered. The
proof is elementary, zigzag, and truly wonderful as claimed by Fermat nearly
three and a half centuries ago. ..."
Has the proof been found? If not, who's smoking what? Anybody close enough
to a math library to find the abstract and it's source document?
--
Darrel J. Van Buer, PhD
System Development Corp.
2500 Colorado Ave
Santa Monica, CA 90406
(213)820-4111 x5449
...{allegra,burdvax,cbosgd,hplabs,ihnp4,orstcs,sdcsvax,ucla-cs,akgua}
!sdcrdcf!darrelj
VANBUER@USC-ECL.ARPAparker@psuvax1.UUCP (Bruce Parker) (01/04/85)
The abstract reads in full:
816-11-188 CHIEN WENJEN, 4297 Candleberry Avenue, Seal Beach, CA 90740.
"Fermat's Last Theorem". Preliminary Report
The missing proof of Fermat's Last Theorem has been rediscovered.
The proof is elementary, zigzag, and truly wonderful as claimed by Fermat
nearly three and a half centuries ago. The relation
p p p
x + y = z for any prime p > 2 is called Case I if none of the solution
integers x, y, z is divisible by p and Case II if one of the integers is
divisible by p. In this article, unlike the classical work, we show
first the nonexistence of Case II and the the impossibility of Case I.
[Harold M. Edwards, "Fermat's Last Theorem - A Genetic Introduction to
Algebraic Number Theory," or L. J. Mordell, "Three Lectures on
Fermat's Last Theorem," and "13 Lectures on Fermat's Last Theorem" by
Paulo Ribenboim.]
It's to be presented as part of the AMS annual meeting 9-13 Jan 85.
--
Bruce Parker
Computer Science Department (814) 863-1545
334 Whitmore Lab {allegra|ihnp4}!psuvax1!parker
The Pennsylvania State University parker@penn-state (csnet)
University Park, Pennsylvania 16802 parker@psuvax1 (bitnet)gjk@talcott.UUCP (Greg Kuperberg) (01/05/85)
> The abstract reads in full: > > 816-11-188 CHIEN WENJEN, 4297 Candleberry Avenue, Seal Beach, CA 90740. > "Fermat's Last Theorem". Preliminary Report > > The missing proof of Fermat's Last Theorem has been rediscovered. ... > It's to be presented as part of the AMS annual meeting 9-13 Jan 85. > -- > Bruce Parker And the National Enquirer is hot on the trail! --- Greg Kuperberg harvard!talcott!gjk
chuck@dartvax.UUCP (Chuck Simmons) (01/07/85)
> The missing proof of Fermat's Last Theorem has been rediscovered. >The proof is elementary, zigzag, and truly wonderful as claimed by Fermat >nearly three and a half centuries ago. The relation > p p p >x + y = z for any prime p > 2 is called Case I if none of the solution >integers x, y, z is divisible by p and Case II if one of the integers is >divisible by p. In this article, unlike the classical work, we show >first the nonexistence of Case II and the the impossibility of Case I. This subject interests me greatly. Does a valid simple proof along these lines really exist? Or are you just pulling my gullible leg? I would appreciate hearing about any followups and would love to see the proof (or at least a more complete outline) if it does exist. Thanks, dartvax!chuck
pmontgom@sdcrdcf.UUCP (Peter Montgomery) (01/15/85)
> The abstract reads in full: > > 816-11-188 CHIEN WENJEN, 4297 Candleberry Avenue, Seal Beach, CA 90740. > "Fermat's Last Theorem". Preliminary Report > > The missing proof of Fermat's Last Theorem has been rediscovered. > The proof is elementary, zigzag, and truly wonderful as claimed by Fermat > nearly three and a half centuries ago. The relation > p p p > x + y = z for any prime p > 2 is called Case I if none of the solution > integers x, y, z is divisible by p and Case II if one of the integers is > divisible by p. In this article, unlike the classical work, we show > first the nonexistence of Case II and then the impossibility of Case I. > [Harold M. Edwards, "Fermat's Last Theorem - A Genetic Introduction to > Algebraic Number Theory," or L. J. Mordell, "Three Lectures on > Fermat's Last Theorem," and "13 Lectures on Fermat's Last Theorem" by > Paulo Ribenboim.] On January 9, at the AMS meeting in Anaheim, CA, Chien Wenjen's wife announced that her husband had Parkinson's disease. She gave the presentation while he sat in the rear of the overcrowded room in his wheelchair. She said he is now retired and has had time to study the problem, and thanked a D. H. Young for bring it to her husband's attention. Then she read the abstract as printed in the AMS and said he would publish in the near future. No technical details were presented and there were no viewgraphs. p p p Also, the printed abstract used the equation x + y = x rather than p p p x + y = z . Of course it is elementary if we use that equation. -- Peter Montgomery {aero,allegra,bmcg,burdvax,hplabs, ihnp4,psivax,randvax,sdcsvax,trwrb}!sdcrdcf!pmontgom Don't blame me for the crowded freeways - I don't drive.
fgmoller@water.UUCP (Faron Moller) (01/22/85)
To respond to a number of letter's dealing with this January's presentation of a paper by Chien Wenjen which claimed to have discovered a proof to Fermat's last theorem, I'd like to provide the following information. A recent writer provided references to three papers in Portugaliae Mathematica which also claimed to prove Fermat's last theorem. It is interesting that the University of Waterloo library, well-known for math resources, only has sporadic copies of this journal, the latest issue being dated 1974. Over a four-year-period three papers were published by Q A M M Yahya, each of which claimed the proof of Fermat's theorem. Obviously, they weren't taken seriously if the proof is still being sought after. It is also interesting that three papers by the same author, claiming to prove one of math's greatest unsolved riddles, went unnoticed - surely as much fervour should have bbeen generated over his proofs as over the current proof. On the other hand, the journal is not completely without credibility: in looking through past issues, I noted that contributors included: Alonzo Church, (Church-Turing), John von Neumann, i.n. herstein, Heinz Hopf, as well as several people at the University of Waterloo. What I really found fascinating was the appearance of the name of Chien Wenjen, in an edition immediately preceding another paper by Yahya, in the list of contributors. It is also interesting that Wenjen's wife thanked D.H. Young on behalf of her husband, for introducing him to the problem, when this problem is well-known to every high-school math student. Furthermore, it would be hard to believe that he wouldn't have seen Yahya's solution. .