Mathematics

2012 Lonseth Lecture Date: Tuesday, May 15, 2012 [awards ceremony 3:30 pm, lecture 4:00 pm, reception following]

Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture

Abstract: What is the role of proof in mathematics? Most of the time, the search for proof is less about establishing truth than it is about exploring unknown territory. In finding a route from what is known to the result one believes is out there, the mathematician often encounters unexpected insights into seemingly unrelated problems. I will illustrate this point with an example of recent research into a generalization of the permutation matrix known as the "alternating sign matrix." This is a story that began with Charles Dodgson (aka Lewis Carroll), matured at the Institute for Defense Analysis, drew in researchers from combinatorics, analysis, and algebra, and ultimately was solved with insights from statistical mechanics.