The Unknowable

1999
ISBN: 978-981-4021-72-2
Verlag: Springer Nature Singapore

Buch, Englisch, 124 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 383 g

Reihe: Discrete Mathematics and Theoretical Computer Science

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 The Unknowable can be downloaded from the author's Web site.

Zielgruppe

Professional/practitioner

Autoren/Hrsg.

Chaitin, Gregory J.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Philosophie der Mathematik
• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten
• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik
• Geisteswissenschaften Philosophie Philosophie der Mathematik, Philosophie der Physik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik

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.