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.