Department of Mathematics

Address: Mathematics 253-37 | Caltech | Pasadena, CA 91125
Telephone: (626) 395-4335 | Fax: (626) 585-1728

The 13th Annual Charles R. DePrima Memorial
Undergraduate Mathematics Lecture

Tuesday, January 11, 2005
4:15 p.m.  151 Sloan


Assistant Professor of Mathematics
Princeton University / University of Wisconsin



Diophantus, Fermat and Beyond

Abstract:  The problem at the heart of number theory — one which mathematicians have been wrestling with since the days of Pythagoras — is the challenge of finding solutions to equations. For instance, Fermat asked whether the equation

An + Bn = Cn

had any solutions in integers when n ≥3; Wiles famously proved in 1995 that the answer is no.

In this talk, I'll outline what mathematicians today know about this primal problem; I'll explain how digital security relies on the difficulty of finding solutions to equations; and I'll explain the hidden geometry in these problems, which seem on their face to be purely algebraic.


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Jordan Ellenberg was born in 1971 and grew up in Potomac, Maryland. While in high school, he won two gold medals in the International Math Olympiad. He received undergraduate and Ph.D. degrees in mathematics from Harvard, and is now Assistant Professor of Mathematics at Princeton University; his research interests are number theory and arithmetic algebraic geometry. He is the author of a column, Do the Math, in Slate Magazine, and a novel, The Grasshopper King.


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The Charles R. DePrima Memorial Undergraduate Mathematics Lecture was established by a gift from Charles R. DePrima and Margaret Thurmond DePrima. The Institute is privileged to honor the memory of Professor DePrima and his distinguished contribution to mathematics and Caltech, where he served as a faculty member for over forty years, with a lecture each year by an outstanding mathematician.