APL Colloquium

March 10, 2000

Colloquium Topic: A Century of Controversy over the Foundations of Mathematics

The speaker will outline the work of Cantor, Russell, Hilbert, Gödel, Turing, and his own, leading to the tentative conclusion that mathematics is quasi-empirical. The talk will show that the computer is not just a practical tool, but is in fact also a fundamental theoretical concept with deep philosophical significance in epistemology.

Colloquium Speaker: Gregory Chaitin

Dr. Gregory Chaitin is at the IBM Watson Research Center in New York. In the mid 1960s, while still a teenager, he created algorithmic information theory, which combines, among other elements, Shannon's information theory and Turing's theory of computability. In the three decades since then he has been the principal architect of the theory. Among his contributions are the definition of a random sequence via algorithmic incompressibility, and his information-theoretic approach to Gödel's incompleteness theorem. His work on Hilbert's 10th problem has shown that in a sense there is randomness in arithmetic, in other words, that God not only plays dice in quantum mechanics and nonlinear dynamics, but even in elementary number theory. He is the author of five books: Algorithmic Information Theory published by Cambridge University Press; Information, Randomness & Incompleteness and Information-Theoretic Incompleteness, both published by World Scientific Press; and The Limits of Mathematics and The Unknowable, both published by Springer-Verlag Press. In 1995 he was awarded the degree of doctor of science honoris causa by the University of Maine, and was elected to the IBM Academy of Technology. In 1998 he was named visiting professor at the University of Buenos Aires.