Gregory J. Chaitin

Conversations with a Mathematician

Math, Art, Science and the Limits of Reason

A collection of his most wide-ranging
and non-technical lectures and interviews

G. J. Chaitin is at the IBM Thomas J. Watson Research Center in New York. He has shown that God plays dice not only in quantum mechanics, but even in the foundations of mathematics, where Chaitin discovered mathematical facts that are true for no reason, that are true by accident. This book collects his most wide-ranging and non-technical lectures and interviews, and it will be of interest to anyone concerned with the philosophy of mathematics, with the similarities and differences between physics and mathematics, or with the creative process and mathematics as an art.

``Chaitin has put a scratch on the rock of eternity.''
— Jacob T. Schwartz, Courant Institute, New York University, USA

``[Chaitin is] one of the great ideas men of mathematics and computer science.''
— Marcus Chown, author of The Magic Furnace, in NEW SCIENTIST

``Finding the right formalization is a large component of the art of doing great mathematics.''
— John Casti, author of Mathematical Mountaintops, on Gödel, Turing and Chaitin in NATURE

``What mathematicians over the centuries — from the ancients, through Pascal, Fermat, Bernoulli, and de Moivre, to Kolmogorov and Chaitin — have discovered, is that it [randomness] is a profoundly rich concept.''
— Jerrold W. Grossman in the MATHEMATICAL INTELLIGENCER

Published by Springer-Verlag London, 2002, viii + 158 pages, hardcover, ISBN 1-85233-549-1.

Order from Springer-Verlag, Amazon, Barnes & Noble.

Reviewed in Review of Modern Logic, American Mathematical Monthly, MAA Online, Zadig, New Scientist, SIAM News, Folha de São Paulo, Times Higher Education Supplement:

``This book is wonderful in both senses of the word: superlatively good and full of wonder. Nonmathematicians could read it, too, but as I read it, I felt glad (and proud) to be a mathematician!''
— Marion D. Cohen in the AMERICAN MATHEMATICAL MONTHLY

``funny, witty, and delightfully informal and irreverent''
— George Englebretsen in the REVIEW OF MODERN LOGIC

Translated in Japanese and in Portuguese

Contents

Preface
Introduction

A century of controversy over the foundations of mathematics (Lecture)
How to be a mathematician (TV interview)
The creative life: science vs. art (Interview)

Algorithmic information theory and the foundations of mathematics (Lecture)
Randomness in arithmetic (TV interview)
The reason for my life (Interview)

Undecidability and randomness in pure mathematics (Lecture)
Math, science and fantasy (Interview)
Sensual mathematics (TV interview)

Final thoughts
Recommended further reading

Errata

  1. Page 1, line 2, ``twenty-three'' should read ``twenty-two''.

  2. Page 46, the source of Einstein's remark on the positive integers is incorrect. Einstein's exact words are: ``Thus, for example, the series of integers is obviously an invention of the human mind, a self-created tool which simplifies the ordering of certain sensory experiences.'' The source is actually Einstein's essay ``Remarks on Bertrand Russell's theory of knowledge.'' It was published in 1944 in the volume on The Philosophy of Bertrand Russell edited by Paul Arthur Schilpp, and it was reprinted in 1954 in Einstein's Ideas and Opinions. However, in his Autobiographical Notes Einstein repeats the main point of his Bertrand Russell essay in a paragraph on Hume and Kant in which Einstein states that ``all concepts, even those closest to experience, are from the point of view of logic freely chosen posits.''

  3. Page 52, the anecdote about Feynman is not in Gleick's biography. I cannot determine the original source.

  4. Page 111, Werner DePauli-Schimanovich informs me that the job that Gödel's wife actually had at the nightclub where they met was coat-check girl, not dancer.

  5. Page 140, lines 14 and 15 from the bottom: ``Note 1'' should read ``Note 2''.