Address: Mathematics 25337
 Caltech  Pasadena, CA 91125
Telephone: (626) 3954335  Fax: (626) 5851728
The 13th Annual Charles
R. DePrima Memorial
Undergraduate Mathematics Lecture
Tuesday, January 11, 2005
4:15 p.m. 151 Sloan
JORDAN ELLENBERG
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
A^{n}
+ B^{n}
= C^{n}
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.
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.
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.
