[FOM] Corfield-book-reply

W.Taylor@math.canterbury.ac.nz W.Taylor at math.canterbury.ac.nz
Sun Oct 5 06:25:28 EDT 2003

I made a private reply to Stephen G Simpson on one of his FOM posts,
and he has keenly urged me to send it on to the list, though this is
no longer my practice.  So, against my better judgement, I do so here.

Date: Thu, 2 Oct 2003 19:00:04 +1200 (NZST)
From: W.Taylor at math.canterbury.ac.nz
To: simpson at math.psu.edu
Subject: John Baez on David Corfield's book

You wrote:

> we are still waiting for someone to present an example of a piece of
> non-foundational mathematics that is of philosophical interest.

There is one that leaps to my mind.  It is something that I always thought
math philosophy should consider, but it doesn't seem to.

It is: complex variables, why is it so incredibly, *unexpectedly* tidy?

There are so many incredibly good things that occur in complex calculus,
things that you *want* to be true in real analysis but never are, fully.
But in complex analysis they almost always turn out to be true, with
*no exceptions*.  Everything is beautifully compact and tidy, and free
of loose ends.   Or so it seemed to me, when I first learned it, and still.

But why?  The originators and early explorers could have had no idea it
would work out so well.  They must have been overwhelmed at how well
everything from real analysis transferred - transferred better than
it was before, better than they, we, had any right to have hoped for.

Is this not a fit question for math philosophy?

There are other similar things in math, but none so stark as complex analysis.


This is a private reply.
I no longer post to the list due to disagreements with moderator policy.

Bill Taylor

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