FOM: Summer 2001 Seminar Opportunity

Colin McLarty cxm7 at
Fri Sep 1 21:26:03 EDT 2000

	David Corfield and I will be running a National Endowment for Humanities
seminar titled "Proofs and Refutations in Mathematics Today", at Case
Western Reserve University from 25 June to 3 August 2001. Participants will
get a stipend of $3,700. Unfortunately, as this US federal money,
participants must be US citizens or residents for more than 3 years.
Participants must be teachers at a college or university.

	In July 1993, Arthur Jaffe and Frank Quinn published an article in the
Bull. Amer. Math. Soc. titled '``Theoretical mathematics'': Toward a
cultural synthesis of mathematics and theoretical physics'. They claim
there are serious practical questions about the role of proof in
mathematical practice today. Their abstract reads:

	Is speculative mathematics dangerous? Recent interactions 
between physics and mathematics pose the question with some force: 
traditional mathematical norms discourage speculation, but it is 
the fabric of theoretical physics. In practice there can be benefits, 
but there can also be unpleasant and destructive consequences. Serious 
caution is required, and the issue should be considered before, rather 
than after, obvious damage occurs. With the hazards carefully in mind, 
we propose a framework that should allow a healthy and positive role 
for speculation.

	The whole article is available, in several formats, at

	The editors of the BAMS collected responses to the article by 18 prominent
mathematicians, including Sir Michael Atiyah, Gregory Chaitin, Jeremy Gray,
Saunders Mac Lane, Benoit Mandelbrot, Rene Thom, Ed Witten, and a terrific
piece by Thurston. These were published in April 1994 and are at

	It happens that much of the math they talk about is topology, closely
descended from the 19th century topology that Lakatos wrote about in his
book PROOFS AND REFUTATIONS, which is also on the relations of speculation
and proof. 

	The seminar will read the debate, and other things by some of the
mathematicians in it, along with Lakatos and other philosophers. 
	There is funding for 15 participants. Application procedures are being
revised but the application deadline is March 1 2001. You can e-mail me for
more information on the seminar, and on application procedures as NEH
establishes them.

Colin McLarty

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