Re: [HM] History in Mathematics

Robert Tragesser (RTragesser@compuserve.com)
Mon, 2 Aug 1999 07:58:08 -0400

Ralph A. Raimi: [["I wonder why Grattan-Guinness made such a statement.
Perhaps he really meant something else, something associated with the
idea that mathematics stands on its own philosophical foundations and in
principle does not use experience (i.e. history) for its validation."]]

First, while I don't have an idea of how extensive it was
(diachronically or synchronically), in the 60's and 70's in the U.S.
there was something of a "fad" among mathematicians supervising graduate
students to discourage their students from looking into the history
(which is to say recent history) of their problems. For example, I saw
a not exactly gracious letter from a prominent mathematician to his --
now prominent -- student upon completion of his degree informing the
student that now that he had completed his work, he could be informed
of previous work anticipating the ideas in his dissertation (which it
had been the graduate advisor's pedagogical duty to suppress -- whether
this was misguided or not, I don't know).
Second, there is a more general phenomenon well described by
John Stillwell in the preface of his MATHEMATICS AND ITS HISTORY:

[[Stillwell: One of the disappointments experienced by most
mathematics students is that they never get a course in mathematics.]]

On this view mathematics, which is to say mathematical
thinking, in its creative rather than crank-turning mode, _develops_
ideas and is therefore intrinsically historical. But I dare say there
are/have been an uncountable number of mathematics courses/textbooks
that do not convey any of this to the students. The uncountable number
of mathematicians teaching such courses and writing such texts might not
ever have expressed contempt for history, but they certainly have
damned it by faint attention.

Robert Tragesser
424 Old Clinton Road
West(running)brook, Ct. 06498
USA