Gregory J. Chaitin is a mathematician at the IBM Watson Research Center in Yorktown Heights, New York. He is also a visiting professor at the University of Buenos Aires and at the University of Auckland. For the past 35 years, he has been the principal architect of algorithmic information theory, which he invented as a teenager. His latest advance has been to transform algorithmic information theory so that it offers predictions about the size of real computer programs. Chaitin has written seven books: Algorithmic Information Theory (Cambridge University Press);Information, Randomness & Incompleteness and Information-Theoretic Incompleteness (both World Scientific); and The Limits of Mathematics, The Unknowable, Exploring Randomness and (most recently) Conversations with a Mathematician (all Springer-Verlag). This article is excerpted from a lecture that he delivered at the University of Massachusetts, Lowell, in 1999, which appears in full in Conversations with a Mathematician. This material is reproduced here with the permission of Springer-Verlag. Address: IBM Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598. Internet: chaitin@us.ibm.com