Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!burl!ulysses!unc!mcnc!decvax!ittvax!dcdwest!sdcsvax!sdcrdcf!hplabs!sri-unix!steve@Brl-Bmd.ARPA From: steve@Brl-Bmd.ARPA Newsgroups: net.ai Subject: Mathematical Methods Message-ID: <730@sri-arpa.UUCP> Date: Sun, 10-Jun-84 06:47:53 EDT Article-I.D.: sri-arpa.730 Posted: Sun Jun 10 06:47:53 1984 Date-Received: Tue, 12-Jun-84 00:37:53 EDT Lines: 72 From: Stephen WolffNot at all deep; maybe others will find our gropings briefly amusing ..... Date: Fri, 8 Jun 84 11:19:30 EDT From: Brint "The usual attitude of mathematicians is reflected in their published research papers and in mathematics textbooks. Proofs are revamped and polished until all trace of how they were discovered is completely hidden. The reader is left to assume that the proof came to the originator in a blinding flash, since it contains steps which no one could possibly have guessed would succeed. The painstaking process of trial and error, revision and adjustment are all invisible." Alan Bundy From: Stephen Wolff I have the greatest respect for Alan Bundy, and I agree with his words. I shall however adamantly disagree with his (or anyone's) implication that "The painstaking process of trial and error, revision and adjustment....." should NOT be invisible -- in a MATHEMATICS paper. The purpose of such a paper MUST be FIRST to advance knowledge; proofs MUST be as spare, concise and lucid as it is within the author's talent to make them -- for sloppy or wordy proofs are just that much harder to verify. And, indeed, the paper is diminished to PRECISELY the extent that the author's trials and fumbles are displayed -- for they may prejudice the world-view of a reader and lead him to the same (POSSIBLY erroneous) result. If you say that there are too few (maybe no) places to publish mathematicians' thought processes, methods of hypothesis, &c., then I shall agree. And, further, state my belief that UNTIL we are able to read how both successful and unsuccessful mathematicians derive the objects of their study, then all successful efforts at automated reasoning will be just blind beginners' luck. From: Paul Broome Bundy was not implying that the dead end paths in the search for a proof should be in the paper that publishes the proof. Just before the portion that Brint quoted, he discussed Polya's books, "How to Solve It" and "Mathematical Discovery" and introduced the paragraph containing the aforementioned quote with, "Polya's attitude in trying to understand the 'mysterious' aspects of problem solving is all too rare." His next paragraph begins with "The only attempt, of which I am aware, to explain the process by which a proof was constructed, is B.L. van der Waerden's paper, 'How the proof of Baudet's conjecture was found', .." He's giving motivation for a book on the modeling of mathematical reasoning. From: Brint Perhaps, as in so many endeavors, several bright people actually agree: 1. Mathematics papers are not the place for discussing trial_and_error, inspirational flashes, false starts, and other means for "discovering" truth and error. 2. Forums are needed for the discussion of such ideas in order to advance our understanding of the process at least toward the end of improving mathematical reasoning by computer. 3. In some limited way, such forums exist. We need to encourage and motivate our mathematicians to contribute to them. Brint