FOM: Atiyah's Bakerian lecture

[Stephen G Simpson]

Lou van den Dries writes:
 > PS Leading mathematicians of our time also write about broad issues
 > concerning math and its relations to science and society. A good way
 > to find out is to take a look at Collected Works, things like that.
 > As I mentioned before (since Atiyah's name came up), volume 1 of
 > his Collected Works contains several quite thoughtful essays of
 > this kind.  (I liked his Bakerian lecture where he sketches for a
 > general educated audience the preeminent role of geometric thinking
 > ...

Lou, I just took a look at this essay.  I found it to be remarkably
lame.  Among Atiyah's so-called `thoughtful comments concerning math
and its relations to science and society' I found:

   Mathematics can I think be viewed as the *science of analogy* and
   the widespread applicability of mathematics in the natural
   sciences, which has intrigued all mathematicians of a philosophical
   bent, arises from the fundamental r^ole which comparisons play in
   the mental process we refer to as `understanding'.

and the following gem:

   Consider mathematics as some kind of giant computer with a large
   number of terminals on its periphery, representing fields of
   application.
                       \\   ||    //
                       ------------
                      /             \
                   ==|  mathematics  |==
                      \             /
                       ------------
                       //   ||    \\

   A practicing scientist is like the terminal user.... It is the
   increasing sophistication of mathematics which has led to the large
   gap between `users' and `designers'.

This arrogant drivel is inferior to just about anything Hilbert wrote
on foundations of mathematics.  Not to mention Dedekind, von Neumann,
Poincare, Brouwer, Weyl, and G"odel.

Again I ask, what is the cause of this historic intellectual decline?

Lou continues:
 > [Atiyah] alludes indirectly to cohomology when talking about the
 > various kinds of holes in mathematical spaces; he even manages to
 > give a very rough idea of the Weil conjectures in this
 > connection. Maybe Steve would like this, as he seems very eager to
 > find out what all this is about.)

This suggestion from Lou is why I bothered to go to the library to get
Atiyah's essay in the first place.  Unfortunately, my high hopes were
disappointed.  The essay didn't tell me anything I didn't know before.
Yes, it adroitly hints at the familiar technical analogy between
p-adic manifolds and complex manifolds, leading to the Weil
conjectures.  But so what?  It's not foundational, and it's of no
interest whatsoever to anyone outside pure mathematics.  I pity the
poor chemists and physicists who had to sit through Atiyah's lecture,
on which this essay was based.

Sincerely,
-- Steve