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
— 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
Springer-Verlag London, 2002, viii + 158 pages, hardcover, ISBN 1-85233-549-1.
Barnes & Noble.
Review of Modern Logic,
American Mathematical Monthly,
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
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)
Recommended further reading
- Page 1, line 2, ``twenty-three'' should read ``twenty-two''.
- 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
- Page 52, the anecdote about Feynman is not in Gleick's biography.
I cannot determine the original source.
- 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.
- Page 140, lines 14 and 15 from the bottom: ``Note 1'' should read ``Note 2''.