[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?
It has occurred to me that Wilder was an example of something I have quite
frequently observed over the years.
Quite a few mathematicians, when they are young, and into their middle
years, work in quite specialized areas. The degree of specialization
varies, of course. One might say that the source of R L Moore's
displeasure with Wilder was that Moore wanted a greater degree of
specialization than Wilder was willing to accept. Still, topology of
general manifolds is specialized within mathematics as a whole.
Then, as many mathematicians age further, they begin to want to place their
work in a larger context. They want to speculate on mathematics as a whole
so far as they can, and beyond that on the place of mathematics in some
cultural whole (synchronically), and/or on the overall history of
mathematics (diachronically). Some people, like van der Waerden and a
number of others, have gone quite deeply into history of mathematics after
having been accomplish specialized mathematicians earlier. As I recall
Wilder's later books that you've mentioned, he was more concerned with a
contemporary place of mathematics in the world than with its place or
places in the history of the world.
Gordon Fisher gfisher@shentel.net