MATC Mathematics Club
Lecture #112

Madison Area Technical College
Madison, Wisconsin


Spring 2012 Presentation #112 (March 2, 2012)

Prof. Nigel Boston, UW-Madison

"Congruent Numbers"

Previous Lectures: (Invariant-Based Face Recognition)

Abstract: The area of a 3,4,5 triangle is 6. There exists a right-angled triangle with rational sides and area 5. Does there exist a right-angled triangle with rational sides and area 1? The integers that arise in this way are called congruent and we still do not know which integers are and which aren't. I shall describe how a $1 million problem, the Birch Swinnerton-Dyer conjecture, leads to a conjectural answer to the question of which integers are congruent.


Nigel Boston grew up in England and attended Cambridge and Harvard. His postdoctoral work in Paris and Berkeley was followed by 12 years at the University of Illinois, except for six months as Rosenbaum Fellow at the Newton Institute in Cambridge, UK, when he witnessed Wiles's announcement of a proof of Fermat's Last Theorem. Nigel subsequently produced a survey article and a book on the proof. In recent years he moved towards engineering, becoming founding director of the Illinois Center for Cryptography and Information Protection. In 2002, he was hired by the University of Wisconsin - Madison as part of the computational sciences cluster, with joint appointments in Mathematics and Electrical and Computer Engineering. He spent 2006-7 as Hedberg Chair at the University of South Carolina and 2008-9 as Stokes Professor of Pure and Applied Algebra at University College Dublin, Ireland.


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