Re: [HM] History in Mathematics

Gordon Fisher (gfisher@shentel.net)
Sat, 07 Aug 1999 12:06:04

[Gordon Fisher]
> I remember when R L Wilder (a student of Moore) was, so to speak,
> drummed out of the Moore coterie by R L Moore for descending to
> the study of general manifolds, using (ugh) algebraic techniques
> and other alien devices.

[Duncan Melville]
> Of course, in R.L. Wilder's case, the use of algebraic techniques was
> the beginning of a slippery slope leading to his work in history and
> sociology of science culminating in the books 'Evolution of mathematical
> concepts' and 'Mathematics as a cultural system' and papers such as
> 'Hereditary stress as a cultural force in mathematics' (Hist. Math. 1
> (1974) 29-46). Was his topological work as creative?

In my judgment, Wilder was also a notably creative mathematician. I
suppose his most distinguished work appears in his book *Topology of
Manifolds*, published in the American Mathematical Society Colloquium
series. At any rate, I learned a lot from the book that I don't remember
seeing elsewhere, and in addition was a good expositor of stuff I did see
elsewhere, such as the Hahn-Mazurkiewicz and similar theorems of the Polish
school of topology (of course, Hahn was German). On the other hand,
Kuratowski was a good expositor of such matters, too, and I may at this
late date have these two, and some others, run together.

Gordon Fisher gfisher@shentel.net