FOM: Atiyah's Bakerian lecture
Stephen G Simpson
simpson at math.psu.edu
Wed Oct 15 19:02:11 EDT 1997
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
\\ || //
==| 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?
> [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.
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