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From: hbs%BUGS%Nosc@sri-unix.UUCP
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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
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From:  Harlan Sexton 

  It 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