A Course on Information Theory and the Limits of Formal Reasoning

G J Chaitin, IBM Research

Published by Springer-Verlag Singapore, 1998, xii + 148 pages, hardcover, ISBN 981-3083-59-X.

Published by Springer-Verlag London, 2003, xii + 148 pages, hardcover, ISBN 1-85233-668-4.

Order from Springer-Verlag, Amazon, Barnes & Noble.

Reviewed in Complexity, SIAM News, J Sci Expl.

Translated in Japanese

This book presents the final version of Chaitin's course on the limits of mathematical reasoning. This course uses algorithmic information theory to show that mathematics has serious limitations, and features a new more didactic approach to algorithmic information theory using LISP and Mathematica software. The thesis of the book is that the incompleteness phenomenon discovered by Gödel is much more widespread and serious than hitherto suspected. Also Gödel and Einstein's views on the foundations of mathematics are discussed, and it is suggested that mathematics is quasi-empirical and that experimental mathematics should be used more freely. The software for this book can be downloaded from MathSource at Wolfram Research at by querying for ``0208-820''. [New! Software available below.]

``The Limits of Mathematics is a very personal and idiosyncratic account of Greg Chaitin's entire career in developing algorithmic information theory. The combination of the edited transcripts of his three introductory lectures maintains all the energy and content of the oral presentations, while the material on AIT itself gives a full explanation of how to implement Greg's ideas on real computers for those who want to try their hand at furthering the theory.''
--- John Casti, Santa Fe Institute

Vienna, 1991

``He thought he had THE TRUTH!''

--- Gwen, the literary agent in Norman Chaitin's play Off Broadway.