Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!watmath!clyde!burl!mgnetp!ihnp4!mhuxl!ulysses!unc!mcnc!decvax!ittvax!dcdwest!sdcsvax!sdcrdcf!hplabs!sri-unix!hbs%BUGS@Nosc From: hbs%BUGS%Nosc@sri-unix.UUCP Newsgroups: net.ai Subject: Mathematical Methods Message-ID: <952@sri-arpa.UUCP> Date: Fri, 15-Jun-84 14:36:00 EDT Article-I.D.: sri-arpa.952 Posted: Fri Jun 15 14:36:00 1984 Date-Received: Fri, 22-Jun-84 09:19:19 EDT Lines: 44 From: Harlan SextonIt is true that most mathematics papers contain little of the sort of informal, sloppy, and confused thinking that always accompanies any of the mathematical discovery that I have been a party to, but these papers are written for and by professional mathematicians in journals that are quite backlogged. Also, although I have always been intrigued by the differences beween modes of discovery among various mathematicians of my acquaintance, I never found knowing how others thought about problems of much use to me, and I think that most practicing mathematicians are even less inclined to wonder about such things than I was when I was a "real" mathematician. However, in response to the comment by David ???, I can only say that I, and most of my fellow graduate students to whom I talked about such things, had no trouble recalling the processes whereby we arrived at the ideas behind proofs (and the process of proving something given an "idea" was just tedious provided the idea was solid). The process used to arrive at the idea, however, was as idiosyncratic as the process one uses to choose a spouse, and it was generally as portable. I found it very useful to know WHAT people thought about various things, and I learned a great deal from my advisor about valuable attitudes toward PDE's, for example (sort of expert knowledge about what to expect from a PDE), but HOW he thought about them was not useful. (With the exception of the infamous Paul J. Cohen, I felt that I appreciated HOW these other people thought; it was just that it felt like wearing someone else's shoes to think that way. In Cohen's case we just figured that Paul was so smart that he didn't have to think, at least like normal people.) In the last year or so of my graduate career, someone came to the mathematics department and interviewed a number of graduate students, including me, about something which had to do with how we thought about mathematical constructs (of very simple types which they specified). Presumably this information, and related things, would be of some interest to Bundy. I'm sorry that I can't be more specific, but if he would contact the School of Education at Stanford (or maybe the Psychology Dept., but I think this had to do with some project on mathematics education), they might be able to help him. There is also a short book by J. Hadamard, published by Dover, and some writings by H. Poincare', but as I recall these weren't very detailed (and he probably knows of them already anyway). Finally, I know that for a while Paul Cohen was interested in mathematical theorem proving, and so he might have some useful information and ideas, as well. (I believe that he is still in the Math. Dept. at Stanford. The AMS MAA SIAM Combined Membership List should have his address.) --Harlan Sexton