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

TL;DR

This book explores the intersection of information theory, mathematics, and physics, arguing that mathematics is quasi-empirical and discussing the limitations of formal reasoning through the perspectives of Einstein and Godel.

Contribution

It presents a comprehensive course on algorithmic information theory and its implications for understanding the epistemology of mathematics and physics, emphasizing the quasi-empirical nature of mathematics.

Findings

Mathematics is shown to be quasi-empirical based on information theory.

Discusses the views of Einstein and Godel on mathematical nature.

Highlights the limits of formal reasoning in mathematics.

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