School of Computer Science Distinguished Lecture, Carnegie-Mellon University, Pittsburg, Pennsylvania, 2000 Historical Introduction --- A Century of Controversy Over the Foundations of Mathematics G.J. Chaitin's 2 March 2000 Carnegie Mellon University School of Computer Science Distinguished Lecture. The speaker was introduced by Manuel Blum. The lecture was videotaped; there is an edited transcript which appeared on pp. 12-21 of a special issue of Complexity magazine on Limits in Mathematics and Physics'' (Vol. 5, No. 5, May/June 2000). http://www.cs.auckland.ac.nz/~chaitin