From subhas@research.att.com Thu Jun 24 19:39:11 1993 To: adam@vlsi.cs.caltech.edu Subject: fermat.. one more Date: Thu, 24 Jun 1993 19:28:15 -0700 From: More Select News Mathematician Claims to Have Solved Fermat's Famous Theorem Jun 23 ----------------------------------------------------------------------------- New York, N.Y. -- A mathematician claims to have solved the most famous problem in mathematics with a dense, twisting, 200-page argument proving Fermat's last theorem, a colleague told the Associated Press Wednesday. "When we heard it, people started walking on air," said Simon Kochen, chairman of the Princeton University mathematics department. "It was an incredible feeling that this has been done after all this time." The proof was presented Wednesday at a conference of mathematicians at Cambridge University in England by Andrew Wiles, a Princeton mathematics professor. Now, for Wiles, the waiting begins. Experts will begin poring over his argument, trying to find flaws. "There have been proofs claimed in the past, and eventually somebody found an error. Until it's checked and actually published, it's hard to say," Tom Apostol, a mathematician at the California Institute of Technology in Pasadena, told AP. "A lot of us believe the theorem is true, and we think a proof is going to come up eventually, and maybe the time is right," said Apostol, who hadn't heard of the claim. "I hope it's correct. It will be a very exciting chapter in the history of mathematics." The theorem -- actually a conjecture -- was stated by the French mathematician Pierre de Fermat, who with Rene Descartes was considered one of the leading mathematicians of the 17th century. The problem is intriguingly simple: If "n" represents any whole number larger than two, there is no solution to the equation "x to the nth power plus y to the nth power equals z to the nth power." There are solutions if "n" equals two -- for example, three squared (9) plus four squared (16) equals five squared (25). But if "n" equals three or more, according to Fermat, there are no solutions. "This is something you could state to a high school boy, but it's so, so difficult to prove," Kochen told AP. Interest in the problem has been especially keen because of a mischievous note Fermat left in the margin of a book. He claimed he had found an "admirable proof of this theorem, but the margin is too narrow to contain it." "Most people don't anymore believe he had a proof for the general case," Kochen told AP. Fermat did prove the truth of the theorem in certain special cases, as have others. In 1988, a Japanese mathematician, Yoichi Miyaoka, stunned the mathematical world when he claimed an overall proof, only to find the claim wither under scrutiny. Wiles' proof relies on the work of scores of mathematicians over the centuries, but adds a conceptual breakthrough, Kochen told the Associated Press. From subhas@research.att.com Fri Jul 2 08:51:49 1993 To: adam@vlsi.cs.caltech.edu Subject: Re: Fermat > I still wish there were a simple, elegant proof. I guess > that will never happen though. 200 pages are necessary. Such a simple theorem needs such a complex (probably correct) proof! This may be because probably the background/foundation/theory necessary to build the proof was not developed and he had to start from the scratch. ---------- Sound medical advice: An orgasm a day keeps doctors away From pkstoc@cs.wm.edu Fri Jul 2 11:24:15 1993 To: adam@vlsi.cs.caltech.edu Subject: Re: Fermat's Last Theorem proved! Adam: Yes, I have heard the claim about Fermat's last problem. I am skepical, for the moment. Claims like this get made regularly. This one may well be valid, but we'll have to see. As I understand the situation, a written version of the proof doesn't exist yet -- just a set of conference talks. As for the length of any eventual proofs, that sort of depends on what machinery one uses. There may well be a 5-page proof written some day, making reference to lots of tools that will be proved between now and then. Personally, I hope the new proof is flawed. I like the idea that there might exist easily stated problems that might never be settled. I'm hoping that Fermat's conjecture is false, but that the smallest counterexample is too large to be comprehended, invisioned, or denoted in any way by human beings. Best regards, PKS From karro@MATH.ORST.EDU Fri Jul 2 13:13:12 1993 To: adam@vlsi.cs.caltech.edu (Adam Schwarzenegger) Subject: Re: Fermat solved!!! Yes, I've heard all about the Fermat's Last Thrm proof. And thats what I was going to do for the project, too!!! Damn. Well, that leaves me more time to work on a simple proof of the 4-color thrm. From pkstoc@cs.wm.edu Mon Jul 12 13:06:04 1993 To: adam@vlsi.cs.caltech.edu Subject: Re: Fermat's Last Theorem proved! Adam: After I last wrote to you I realized that what you were probably asking was, did I think that there would ever be an elementary proof found? I feel confident that the answer to that is "NO". Fermat was a first-rate mathematician (even though he made his living as a lawyer), and he most likely didn't have a proof. And many of the top mathematicians since then have tried without success. If there were an elementary proof, I am sure it would have been found by now. (A side note: I just finished reading a book called "mathematical cranks', about people who are convinced that they have trisected an arbitrary angle, or proved that pi is really the square root of 10, or that they have proved Fermat's last problem. Most of these people become convinced that they are the victims of a huge conspiracy to keep them quite and prevent them from upsetting the foundations of mathematics). Actually, I believe that there never will be a proof discovered that I will be capable of following. About the CACM note: The editor sent Park a copy of the Sullivan letter back in February, and invited him to respond. At first neither he nor Miller believed the results, but they repeated the experiment and found out that he was right. Keith showed it to me, and I was able to get some feel for what was going on, so they invited me to help with their response. Now we (mostly me) are writing a full paper on why Sullivan got the results he did, how to avoid it, and how to generate parallel streams of random numbers correctly. The trick is to pick the set of original seeds well (NOT 1, 2, 3, ... as Sullivan did. That guarentees non-independence of the streams). Stay tuned. I am now working hard teaching in the Governor's School in math/cs for gifted high school students. They are here at W&M for four weeks. Some of them are quite bright. Best regards, Paul