Computers and Mathematics: Problems and Prospects

RONALD LEWIS GRAHAM

TUESDAY, MARCH 31, 2009

There is no question that the recent advent of the modern computer has had a dramatic impact on what mathematicians do and on how they do it. However, there is increasing evidence that many apparently simple problems may in fact be forever beyond any conceivable computer attack. In this talk, Professor Ronald Lewis Graham will describe a variety of mathematical problems in which computers either have had, may have or will probably never have a significant role in their solutions.

Professor Graham is one of the world's best-known mathematicians, computer theorists, and technology visionaries. In math, he pioneered worst-case analysis in scheduling theory, online algorithms, quasi-randomness, and Ramsey Theory--a branch of pure math that states that complete disorder is impossible. Graham is in the Guinness Book of World Records for using the largest number ever used in a mathematical proof (so large, there isn't even a standard notation for it), now known as "Graham's number.". During his long career at AT&T Graham's work on "hard problems" in mathematics led him to focus on the complexity of routing millions of telephone calls. And his work on routing was influential in the early architecture of the Internet, as well as the vision of "anywhere/anytime access to the wireless Web" pursued by Cal-(IT)2.

Ronald Graham holds the Irwin and Joan Jacobs Endowed Chair in Computer and Information Science at the University of California- San Diego (UCSD) and is Chief Scientist of the California Institute for Telecommunications and Information Technology. He joined the UCSD faculty in 1999, after a 37-year career with AT&T. Graham received his Ph.D. in mathematics from U.C. Berkeley in 1962. From 1962-95, he was director of information sciences at (AT&T) Bell Labs, and from 1996-99 Chief Scientist of AT&T Labs. Graham is the Treasurer of the National Academy of Sciences, a Fellow of American Academy of Arts and Sciences, a Fellow of the Association of Computing Machinery, and a past President of both the American Mathematical Society, and the Mathematical Association of America. He has won numerous awards in the field of mathematics, including the Polya Prize in Combinatorics and the Steele Prize for Lifetime Achievement awarded in 2003 by the American Mathematical Society.