The Unknowable

by Chaitin, Gregory J.

• ISBN13: 9789814021722
• ISBN10: 9814021725
• Format: Hardcover
• Copyright: 1999-05-01
• Publisher: Springer Verlag

Summary

This essential companion volume to Chaitin's highly successful "The Limits of Mathematics", also published by Springer, gives a brilliant historical survey of the work of this century on the foundations of mathematics, in which the author was a major participant. The Unknowableis a very readable and concrete introduction to Chaitin's ideas, and it includes a detailed explanation of the programming language used by Chaitin in both volumes. It will enable computer users to interact with the author's proofs and discover for themselves how they work. The software for TheUnknowablecan be downloaded from the author's Web site.

Table of Contents

Preface	v
A Hundred Years of Controversy Regarding the Foundations of Mathematics	1	(28)
LISP: A Formalism for Expressing Mathematical Algorithms	29	(22)
Godel's Proof of his Incompleteness Theorem	51	(8)
Turing's Proof of the Unsolvability of the Halting Problem	59	(8)
My Proof that You Can't Show that a LISP Expression is Elegant	67	(16)
Information & Randomness: A Survey of Algorithmic Information Theory	83	(18)
Mathematics in the Third Millennium?	101	(10)
Bibliography	111