Delivery-Date: 
Date: Wed, 21 Apr 93 16:04:58 EDT
From: mumford@math.harvard.edu (david mumford)
Message-Id: <9304212004.AA05327@math.harvard.edu>
To: qed@mcs.anl.gov, beeson@cats.UCSC.EDU
Subject: Re: Why should a mathematician be interested in QED?
Sender: qed-owner@mcs.anl.gov
Precedence: bulk


Maybe I can pipe up once in this blizzard of comments: the great
attraction of Bourbaki for mathematicians was the promise that the
project would clarify the basic structures and theories used in
algebra, geometry and analysis. The hope was that a fairly small
simple set of basic structures were the basis of most research.

I think it is also true that for a while, this was generally believed.
But for the last 20 years, it has been increasingly doubted: first
because Bourbaki began to drown in its own need to be general enough,
and they never could be sure when to stop (e.g. before doing the
reals, they need a general theory of topological fields). Secondly,
because math began to be driven by complex theories rather than simple
ones: e.g. the Langlands conjecture at the abstract end, control theory
and probability at the applied end. These theories don't benefit much
from the Bourbaki program.

D.Mumford