SCS DISTINGUISHED LECTURE, Monday, January 15, 4 pm, Wean 7500 PROFESSOR STEVE SMALE City University of Hong Kong TITLE: "On the Mathematical Foundations of Learning Theory" ABSTRACT: We will give an exposition of what we see as some of the universal laws of learning in human and artificial intelligence. For appointments contact Phyllis Pomerantz, plp@cs.cmu.edu or 268-7897 ABOUT THE SPEAKER From the Review of the biography of Stephen Smale, "The Mathematician Who Broke the Dimension Barrier" by Steve Batterson: "In 1957 Stephen Smale startled the mathematical world by showing that, in a theoretical sense, it is possible to turn a sphere inside out. A few years later, from the beaches of Rio, he introduced the horseshoe map, demonstrating that simple functions could have chaotic dynamics. His next stunning mathematical accomplishment was to solve the higher-dimensional Poincar conjecture*, thus demonstrating that higher dimensions are simpler than the more familiar three. In 1966 in Moscow, he was awarded the Fields Medal, the most prestigious prize in mathematics. Smale's vision and influence extended beyond mathematics into two vastly different realms. In 1965 in Berkeley, he initiated a program with Jerry Rubin of civil disobedience directed at ending the Vietnam War. And as a mineral collector, he accumulated a museum-quality collection that ranks among the finest in the world...." In late sixties Smale moved into applications. He modelled physical processes by dynamical systems, opening new lines of inquiry. The n-body problem and electric circuit theory were among the applications that Smale framed in the language of dynamical systems. For much of the seventies he focused on economics, injecting topology and dynamics into the study of general economic equilibria. Having established the nature of equilibria, Smale began to think of algorithms for their computation. While traditional approaches to the convergence theory of algorithms were local, Smale introduced a global perspective to the problems. Was the algorithm reasonably reliable, and how many iterations were to be expected? Smale's recent work has been on theoretical computer science. With co-workers L Blum and M Shub, he has developed a model of computation which includes both the Turing machine approach and the numerical methods of numerical analysis. For the past 2 years he has focused his attention on mathematical foundations for learning theory. Born in Michigan, Professor Smale received his PhD degree from the University of Michigan in 1957, and within four years became a full Professor at Columbia University. In 1964, he was named a Professor at the University of California, Berkeley and held the post for 30 years before joining City University of Hong Kong as a Distinguished University Professor. Professor Smale is a member of both the National Academy of Sciences and the American Academy of Arts and Sciences. In 1996 he was awarded the US National Medal of Science. In 2000, in recognition of Smale's significant contributions to science and mathematics, the Institute of Applied Astronomy of the Russian Academy of Sciences named a minor planet in his honor.