Atiyah and `The End of Science'

[Stephen G Simpson]

John P. Burgess writes:
 > I didn't have the references at my fingertips, which is why I
 > didn't give them.  I'll have to thumb through the back issues of
 > the BAMS.  As I recall, though the article appeared there, the
 > discussion of it was mostly in several subsequent issues of the AMS
 > Notices.  The article by a Sci Amer staff writer named Horgan (or
 > something like that) gets cited in the discussion and may be easier
 > to find that way than by looking through Sci Amer itself.  Also,
 > Horgan has a book out entitled, I think, "The End of Science" which
 > will probably include a reference and/or a rewritten version.  I
 > will look around and see what references I can track down.  I
 > really have been meaning to prepare a regular bibliography on this
 > topic but haven't gotten around to it.

John, thanks very much for your comments and references.  In the
meantime Lou van den Dries pointed me to the `Theoretical Mathematics'
article by Jaffe and Quinn in BAMS (vol 29, 1993, pp. 1-13), and the
subsequent discussion in BAMS (vol 30, 1994, no. 2).  But I haven't
yet tracked down the followup discussion in the AMS Notices.  

I saw `The End of Science' in a bookstore.  I didn't buy it, because I
don't want to subsidize the authors and publishers of this kind of
trash.  I also vowed never again to subscribe to Scientific American.

If you get around to preparing a bibliography on this topic
(anti-foundationalism?), I'd very much appreciate it.  By the way, I
followed the Sokal hoax and read the Gross-Levitt book last year.  The
Gross-Levitt book is excellent; it documents the sheer quantity of
fashionable anti-scientific rubbish that is out there in our culture.

The BAMS articles consist of some not-very-meaty comments by a large
number of outstanding mathematicians about the role of conjecture,
speculation, and what we might call pre-rigorous mathematics as it
relates to mathematical discovery.  The focus is on recent
developments in quantum field theory (string theory, Witten, etc.).
Atiyah has two pages of comments in which he goes overboard in praise
of `sloppy reasoning,' a `buccaneering style,' and `happy inspiration
triumphing over a lack of rigour.'  But at the same time, he points
out that the goal of this speculative work is to obtain a fully
rigorous, definition-theorem-proof type of treatment of the subjects
in question.  To me as a mathematician, it's clear that Atiyah didn't
intend to deny or denigrate the essential role of rigorous proof in
mathematics, but I can also see how enemies of science such as Horgan
(if that is his name) are able to latch onto this stuff and use it for
their own ends.  I wish Atiyah had exercised a little more prudence.

-- Steve Simpson