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Gregory John Chaitin (born 1947) is an Argentine-American mathematician and computer scientist.

Beginning in the late 1960s, Chaitin made contributions to algorithmic information theory and metamathematics, in particular a new incompleteness theorem similar in spirit to Gödel's incompleteness theorem. He attended the Bronx High School of Science and City College of New York, where he first developed his theorem while still in his teens.

Chaitin has defined Chaitin's constant Ω, a real number whose digits are equidistributed and which is sometimes informally described as an expression of the probability that a random program will halt. Ω has the mathematical property that it is definable but not computable.

Chaitin's early work on algorithmic information theory paralleled the earlier work of Kolmogorov.

Chaitin also writes about philosophy, especially metaphysics and philosophy of mathematics (particularly about epistemological matters in mathematics). In metaphysics, Chaitin claims that algorithmic information theory is the key to solving problems in the field of biology (obtaining a formal definition of ‘life’, its origin and evolution) and neuroscience (the problem of consciousness and the study of the mind). Indeed, in recent writings, he defends a position known as digital philosophy. In the epistemology of mathematics, he claims that his findings in mathematical logic and algorithmic information theory show there are “mathematical facts that are true for no reason, they're true by accident. They are random mathematical facts”. Chaitin proposes that mathematicians must abandon any hope of proving those mathematical facts and adopt a quasi-empirical methodology.

Chaitin is also the originator of using graph coloring to do register allocation in compiling, a process known as Chaitin's algorithm.

In 1995 he was given the degree of doctor of science honoris causa by the University of Maine. In 2002 he was given the title of honorary professor by the University of Buenos Aires in Argentina, where his parents were born and where Chaitin spent part of his youth. He is a research staff member at IBM's Thomas J. Watson Research Center and also a visiting professor at the Computer Science Department of the University of Auckland, and on the international committee of the Valparaíso Complex Systems Institute.

Some philosophers and logicians strongly disagree with the philosophical conclusions that Chaitin has drawn from his theorems. ^[1] The logician Torkel Franzén ^[2] criticizes Chaitin’s interpretation of Gödel's Incompleteness Theorem and the alleged explanation for it that Chaitin’s work represents. One criticism is that although Chaitin has frequently talked of the "unknowable" and the "limits of reason", he has not given one instance of a mathematical fact or question which is unknowable or beyond the limits of reason/mathematics. In fact, there is no limit, in principle, to the number and location of bits of omega one could work out.

• Algorithmic Information Theory, (Cambridge University Press, 1987),
• Information, Randomness & Incompleteness, (World Scientific, 1987),
• Information-Theoretic Incompleteness, (World Scientific, 1992),
• The Limits of Mathematics, (Springer-Verlag 1998),
• The Unknowable, (Springer-Verlag 1999),
• Exploring Randomness, (Springer-Verlag 2001),
• Conversations with a Mathematician, (Springer-Verlag 2002),
• From Philosophy to Program Size, (Tallinn Cybernetics Institute 2003),
• Meta Math!: The Quest for Omega, (Pantheon 2005).

1. ^ Panu Raatikainen "Exploring Randomness and The Unknowable" Notices of the American Mathematical Society Book Review October 2001
2. ^ Torkel Franzén Gödel's Theorem: An Incomplete Guide to its Use and Abuse. Wellesley, Massachusetts: A K Peters, Ltd., 2005. x + 172 pp. ISBN 1-56881-238-8.

• G J Chaitin Home Page
• List of publications of G J Chaitin
• New Scientist article (March, 2001) on Chaitin, Omegas and Super-Omegas
• A short version of Chaitin's proof