Fall 2007 meeting of the Indiana section of the Mathematical Association of America

Saturday, October 27, 2007

Manchester College

Invited Speaker: John Swallow

Invited Talks :

An elementary history of Fermat's Last Theorem

Fermat's Last "Theorem" occupies a singular place in the history of mathematics, having informed and inspired mathematicians over three centuries.  Surprisingly diverse branches of mathematics have sprung from the search for a proof of its simple conjecture:

For n>2, x^n + y^n = z^n has no solutions in positive integers.

This talk chronicles the history of the theorem, stopping short of Wiles' proof and placing emphasis on the significant ideas and methods of proof which the problem engendered.  The talk should be accessible to everyone who is familiar with the unique factorization of integers into primes and who would enjoy charting the history of arithmetic amidst innovations in algebra, geometry, and computers.

Circular irrationalities: From Galois to Kummer and back again

The truth value of the statement "Harry and Isabel are siblings, and Joe and Karl are siblings" is very probably not invariant under every permutation of the names. Surprisingly, the study of roots such as 2^(1/2) and 3^(1/5) proceeds similarly: in place of sentences, consider equations relating the roots and ask which of them hold true under certain permutations of the roots. We introduce this study of nth roots and then tell the story of how some basic questions, solved with real contributions by undergraduates, pointed the way to some significant new results in field theory. This work is joint with Davidson undergraduates Frank Chemotti '05 and Andy Schultz '02, as well as D. Benson, N. Lemire, and J. Minác.

Cost:

(Late registration deadline to be determined).

Biography: John Swallow was tripped up by Galois theory as a graduate student. He's loved doing it, teaching it, and writing about it ever since, and he is particularly grateful to have been awarded an NSF-RUI grant to support all three. The author of Exploratory Galois Theory (Cambridge, 2004), he has enjoyed writing research articles as well as pieces for the Bulletin, the Monthly, the Notices, and the American Scholar. John teaches at Davidson College as Kimbrough Professor of Mathematics and Humanities.

Contributed Talks: Talks can be submitted here.