Newsgroups: sci.math From: palais@binah.cc.brandeis.edu Subject: FLT Date: Tue Oct 25 14:25:38 CDT 1994 Organization: Brandeis University Lines: 8 Well, the news has not got around as fast this time I guess. I was surprised to scan sci.math and not see any mention of the fact that two manuscripts were released this morning---one by R. Taylor & A. Wiles, the other (using the first) by A. Wiles. The two together claim to be a complete proof of Fermat's Last Theorem. R. Palais &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& From: lamaster@viking.arc.nasa.gov (Hugh LaMaster -- RCS) Newsgroups: sci.math Subject: Re: FLT Date: Wed Oct 26 11:08:08 CDT 1994 Organization: NASA Ames Research Center Lines: 19 Distribution: world In article <38jm3i$mht@news.cs.brandeis.edu>, palais@binah.cc.brandeis.edu writes: |> Well, the news has not got around as fast this time I guess. |> I was surprised to scan sci.math and not see any mention of the |> fact that two manuscripts were released this morning---one by |> R. Taylor & A. Wiles, the other (using the first) by A. Wiles. |> The two together claim to be a complete proof of Fermat's Last |> Theorem. |> |> R. Palais Are (electronic) preprints of the manuscripts available on the Internet somewhere? -- Hugh LaMaster, M/S 233-9, UUCP: ames!lamaster NASA Ames Research Center Internet: lamaster@ames.arc.nasa.gov Moffett Field, CA 94035-1000 Or: lamaster@george.arc.nasa.gov Phone: 415/604-1056 #include &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Newsgroups: sci.math From: mckay@alcor.concordia.ca (John McKay) Subject: News of FLT Date: Tue Oct 25 14:57:25 CDT 1994 According to a note of Karl Rubin currently circulating there are preprints - one by Wiles and one joint with Richard Taylor - which may provide a proof of FLT avoid- ing the notorious gap that was found earlier. -- Deep ideas are simple. Odd groups are even. Even simples are not. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Newsgroups: sci.math,sci.math.research From: bs@linus.mitre.org (Robert D. Silverman) Subject: Wiles/Richard Taylor Close the Gap Date: Wed Oct 26 07:30:51 CDT 1994 I pass the following along without comment: ----------------------------------------------------------------------- Newsgroups: bit.listserv.nmbrthry Date: Tue, 25 Oct 1994 17:55:55 EDT From: Victor Miller Subject: Wiles and Fermat To: Multiple recipients of list NMBRTHRY I just heard the following from Al Hales: Wiles has announced that he has fixed his proof (with assistance of Richard Taylor). He has proved the "gap" by using Hecke Algebras instead of Euler systems. Does anyone know anything else about this? Victor -- Bob Silverman These are my opinions and not MITRE's. Mitre Corporation, Bedford, MA 01730 "You can lead a horse's ass to knowledge, but you can't make him think" &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Newsgroups: sci.math From: jacobson@oucsace.cs.ohiou.edu (8-{P) Subject: Fermat's Last Theorem -- Round 2 Date: Wed Oct 26 09:51:00 CDT 1994 Lines: 67 I received this a few minutes ago: ------------------------------------------------------------------ Reply-To: fermat@e-math.ams.org Originator: fermat@e-math.ams.com Sender: fermat@e-math.ams.org Precedence: bulk From: ion@VAX02.AMS.ORG (Patrick D. F. Ion) To: Multiple recipients of list Subject: [FERMAT:190] Re: Wiles and Fermat (fwd) X-Listprocessor-Version: 6.0b -- ListProcessor by Anastasios Kotsikonas X-Comment: From the Fermat's Last Theorem bulletin board I think the latest information goes back to the message following: Path: math.ohio-state.edu!gateway From: rubin@math.harvard.edu (Karl Rubin) Newsgroups: math.announce Subject: update on Fermat's Last Theorem Date: 25 Oct 1994 10:29:18 -0400 Organization: The Ohio State University, Department of Mathematics Lines: 34 Sender: daemon@math.ohio-state.edu Message-ID: <9410251424.AA03857@math.harvard.edu> NNTP-Posting-Host: mathserv.mps.ohio-state.edu As of this morning, two manuscripts have been released Modular elliptic curves and Fermat's Last Theorem, by Andrew Wiles Ring theoretic properties of certain Hecke algebras, by Richard Taylor and Andrew Wiles. The first one (long) announces a proof of, among other things, Fermat's Last Theorem, relying on the second one (short) for one crucial step. As most of you know, the argument described by Wiles in his Cambridge lectures turned out to have a serious gap, namely the construction of an Euler system. After trying unsuccessfully to repair that construction, Wiles went back to a different approach, which he had tried earlier but abandoned in favor of the Euler system idea. He was able to complete his proof, under the hypothesis that certain Hecke algebras are local complete intersections. This and the rest of the ideas described in Wiles' Cambridge lectures are written up in the first manuscript. Jointly, Taylor and Wiles establish the necessary property of the Hecke algebras in the second paper. The overall outline of the argument is similar to the one Wiles described in Cambridge. The new approach turns out to be significantly simpler and shorter than the original one, because of the removal of the Euler system. (In fact, after seeing these manuscripts Faltings has apparently come up with a further significant simplification of that part of the argument.) Versions of these manuscripts have been in the hands of a small number of people for (in some cases) a few weeks. While it is wise to be cautious for a little while longer, there is certainly reason for optimism. Karl Rubin -- Somewhere in Rural Southeast Ohio ... E-mail: jacobson@oucsace.cs.ohiou.edu WWW: http://oucsace.cs.ohiou.edu/personal/jacobson.html &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&