Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxl!eagle!harpo!seismo!hao!hplabs!sri-unix!MJackson.Wbst@PARC-MAXC.ARPA From: MJackson.Wbst@PARC-MAXC.ARPA Newsgroups: net.ai Subject: Re: Fermat's Last Theorem & Undecidable Propositions Message-ID: <17227@sri-arpa.UUCP> Date: Thu, 1-Mar-84 08:34:00 EST Article-I.D.: sri-arpa.17227 Posted: Thu Mar 1 08:34:00 1984 Date-Received: Fri, 9-Mar-84 01:20:10 EST Lines: 30 Fermat's Last Theorem: is the assertion that A^N + B^N = C^N has no solution in integers for N > 2. (For N = 2, of course, all the well-known right triangles like [3,4,5] are solutions.) The Four-Color Theorem: states that any planar map can be colored so that no two adjacent regions are the same color using no more than four different colors. (Regions must be connected; "adjacent" means having a common boundary of finite length, i.e. not just touching at a point. The latter was shown to be true by two mathematicians at the University of Illinois, using a combination of traditional mathematical reasoning and computer-assisted analysis of a large set of graphs. An article describing the proof can be found in a back issue of /Scientific American/. The former appears in a manuscript by Fermat, with a marginal notation to the effect that he had found a slick proof, but didn't have enough space to write it down. This was discovered after his death, of course. Most mathematicians believe the theorem to be true, and most do not think Fermat is likely to have found a valid proof, but neither proposition has been proved beyond question. Mark