Subject: categories: Re: [Fwd: du Sautoy]

From: "Marta Bunge" <[email-masked]>
Date: Tue, 18 Apr 2006 09:59:56 -0400

Dear Vaughan,

I meant to write a more substantial reply to your question, but I was
interrupted by an important  telephone call and accidentally I sent a
partial reply.

I meant to say that there are many attractive results in classical
mathematics than can be shown to advantage using category theory, and that
I found that emphasizing those in my courses (which of course I have given
also repeatedly here at McGill, not just in Spain, Mexico and Egypt) is
the key to interest students who do not even intend to work in categories.
After all, we want to educate future analysts, topologists, algebraists,
computer scientists, logicians to feel that knowing a bit of categories
can help in their fields. To me, this is the goal in teaching categories.
I only take (or have taken so far) students with a broad mathematical
culture and who can get motivated to do categories with a view to better
understand and relate different mathematical fields. This is how
Gorthendieck pursued mathematics and of course, as it must happen, often
going off tangent to develop a theory suggested by obstructions in
ordinary work. I feel happier when that happens and do not necessarily
think that one ought to aim at forming (often poor) students in category
theory. Only the very best, if they can be lured to do so, should work in
category theory. Of course, I would myself have been eliminated at the
onset had my "rules" been applied in those days. But in the 60's it was
different and I now see that catgegory theory must come after the
"mathematical experience", not before.

I can take the time some time this summer to make a list of such
attractive results in the fields I know within category theory. I am too
busy now.

Best wishes,
Marta