The Limits of Mathematics: A Course on Information Theory and the Limits of Formal Reasoning
Inhaltsverzeichnis
Reference
Chaitin, G.J. (2002). The Limits of Mathematics: A Course on Information Theory and the Limits of Formal Reasoning. Discrete Mathematics and Theoretical Computer Science. Springer.
DOI
http://www.springer.com/mathematics/book/978-1-85233-668-4
Abstract
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.
Extended Abstract
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Full Text
https://www.cs.auckland.ac.nz/~chaitin/lm.html