Lecture — Undecidability & Randomness in Pure Mathematics

Abstract

I have shown that God not only plays dice in physics, but even in pure mathematics, in elementary number theory, in arithmetic! My work is a fundamental extension of the work of Gödel and Turing on undecidability in pure mathematics. I show that not only does undecidability occur, but in fact sometimes there is complete randomness, and mathematical truth becomes a perfect coin toss.

Originally published in G. J. Chaitin, Information, Randomness & Incompleteness, 2nd Edition, World Scientific, 1990, pp. 307–313.

This lecture was given at a Solvay physics conference on complexity in Brussels in 1989, one of the historic series of meetings that originally involved such great names as Madame Curie, Rutherford and Poincaré. This was in fact my second Solvay conference on complexity, both of them extremely stimulating, both organized by Ilya Prigogine. At them I had the pleasure of speaking in the same place where the historic Solvay conferences were held, and of meeting the then King and Queen of Belgium and also Mr. Honda, the founder of the Japanese auto company, who provided funding for the meetings.