The Limits of Mathematics -- A course on information theory and the limits of formal reasoning

Abstract

This book is the final version of a course on algorithmic information theory and the epistemology of mathematics and physics. This is camera-ready copy prepared for publication as a book, but at the last minute I decided to publish it electronically instead. This book discusses Einstein and Godel's views on the nature of mathematics in the light of information theory, and sustains the thesis that mathematics is quasi-empirical. There is a foreword by Cris Calude of the University of Auckland, and a remark on the back cover by John Casti of the Santa Fe Institute. Supplementary material is available at the author's web site -- The frontispiece photograph is at http://www.cs.auckland.ac.nz/CDMTCS/chaitin/index.html, and the software not included in the book is at http://www.cs.auckland.ac.nz/CDMTCS/chaitin/rov.html