THE LIMITS OF MATHEMATICS---
A course on information theory & the limits of formal reasoning
G. J. Chaitin (IBM Research)
To be published by Springer-Verlag Singapore.
Currently at http://www.cs.auckland.ac.nz/CDMTCS/chaitin/lm.html
together with information on how to order it from Springer-Verlag.
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 Goedel is much more widespread
and serious than hitherto suspected. Also Goedel 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 http://www.wolfram.com
by querying for "0208-820".