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

From: Vaughan Pratt <[email-masked]>
Date: Tue, 18 Apr 2006 10:12:59 -0700

Dear Marta,

I couldn't agree more.  Usually I find myself disagreeing with some
picky point or other but somehow your message managed to completely
avoid my (too many) hot buttons!

Your two points (broad publicity for the general benefits of the subject
but only taking the best students to actually work in it) are of course
applicable to any subject.   Executing well on both brings a new subject
up to the stature of the established subjects.  CT has done very well on
the latter but might be judged as having fallen short on the former so
far, though perhaps not for want of trying but rather the manner of
presentation.  When in Rome speak Italian (and don't mention home
delivery pizza).

On the concern you raised a while back about perceptions of crankiness,
physics runs the gamut from well-publicized spectacular advances to more
cranks than just about any other scientific discipline; in that respect
it nicely brackets both CT and chemistry on both sides.  Whether CT has
accumulated more cranks than chemists is an interesting question, which
brings to mind the category theory professors from the Mahareshi Yogi's
TM university in Fairfield buttonholing Bill Lawvere at an AMAST meeting
in Iowa a while back.  Wish I could have video'd that.

Best,
Vaughan

Marta Bunge wrote:
> 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 whlo 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 mysef 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 "matrhematica;l experience",
> not before.
>
> I can take the time some time this summer to make a list of such
> atractive results in the fields I know within category theory. I am too
> busy now.
>
> Best wishes,
> Marta
>
>