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 Unknowable
is 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
TheUnknowable
can be downloaded from the author' s Web site.
Inhaltsverzeichnis
I. A Hundred Years of Controversy Regarding the Foundations of Mathematics. - II. LISP: A Formalism for Expressing Mathematical Algorithms. - III. Gödel's Proof of his Incompleteness Theorem. - IV. Turing's Proof of the Unsolvability of the Halting Problem. - V. My Proof that You Can Show that a LISP Expression is Elegant. - VI. Information & Randomness: A Survey of Algorithmic Information Theory. - VII. Mathematics in the Third Millennium? - Bibliography.
