書誌事項

The unknowable

by Gregory J. Chaitin

(Springer series in discrete mathematics and theoretical computer science)

Springer, c1999

  • : hc

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注記

Bibliography: p. 111-122

内容説明・目次

内容説明

This essential companion to Chaitins highly successful The Limits of Mathematics, gives a brilliant historical survey of important work on the foundations of mathematics. The Unknowable is a very readable introduction to Chaitins ideas, and includes software (on the authors website) that will enable users to interact with the authors proofs. "Chaitins new book, The Unknowable, is a welcome addition to his oeuvre. In it he manages to bring his amazingly seminal insights to the attention of a much larger audience His work has deserved such treatment for a long time." JOHN ALLEN PAULOS, AUTHOR OF ONCE UPON A NUMBER

目次

I. A Hundred Years of Controversy Regarding the Foundations of Mathematics.- II. LISP: A Formalism for Expressing Mathematical Algorithms.- III. Goedel'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.

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