# Gregory Chaitin

Gregory Chaitin
Born November 15, 1947
Chicago[1]
Residence United States
Nationality American
Fields Biology
Mathematics
Computer science
Institutions Federal University of Rio de Janeiro
IBM Thomas J. Watson Research Center
Known for Chaitin-Kolmogorov complexity
Chaitin's constant
Chaitin's algorithm
Influences Gottfried Wilhelm Leibniz

Gregory John Chaitin (/ˈtn/ CHY-tən; born 15 November 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 computer-theoretic result equivalent to Gödel's incompleteness theorem. He is considered to be one of the founders of what is today known as Kolmogorov (or Kolmogorov-Chaitin) complexity together with Andrei Kolmogorov and Ray Solomonoff. Today, algorithmic information theory is a common subject in any computer science curriculum.

## Mathematics and computer science

He attended the Bronx High School of Science and City College of New York, where he (still in his teens) developed the theory that led to his independent discovery of Kolmogorov complexity.[2][3]

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 followed after the work of Solomonoff, Kolmogorov, and Martin-Löf.

Chaitin is also the originator of using graph coloring to do register allocation in compiling, a process known as Chaitin's algorithm.[4]

He was formerly a researcher at IBM's Thomas J. Watson Research Center in New York and remains an emeritus researcher. He has written more than 10 book titles that have been translated to about 15 languages. He is today interested in questions of metabiology and information-theoretic formalizations of the theory of evolution.

## Other scholarly contributions

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).

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".[5] Chaitin proposes that mathematicians must abandon any hope of proving those mathematical facts and adopt a quasi-empirical methodology.

## Honors

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. In 2007 he was given a Leibniz Medal[6] by Wolfram Research. In 2009 he was given the degree of doctor of philosophy honoris causa by the National University of Córdoba. He was formerly a researcher at IBM's Thomas J. Watson Research Center and is now a professor at the Federal University of Rio de Janeiro.

## Criticism

Some philosophers and logicians strongly disagree with the philosophical conclusions that Chaitin has drawn from his theorems.[7] The logician Torkel Franzén[8] criticized Chaitin’s interpretation of Gödel's incompleteness theorem and the alleged explanation for it that Chaitin’s work represents.

## Notes

1. Li; Vitanyi (1997), An Introduction to Kolmogorov Complexity and Its Applications, Springer, p. 92, G.J.Chaitin had finished the Bronx High School of Science, and was an 18-year-old undergraduate student at City College of the City University of New York, when he submitted two papers.... In his [second] paper, Chaitin puts forward the notion of Kolmogorov complexity....
2. Chaitin, G. J. (October 1966), "On the Length of Programs for Computing Finite Binary Sequences", Journal of the ACM, 13 (4): 547–569, doi:10.1145/321356.321363
3. G.J. Chaitin, Register Allocation and Spilling via Graph Coloring, US Patent 4,571,678 (1986) [cited from Register Allocation on the Intel® Itanium® Architecture, p.155]
4. "Professor Gregory John Chaitin". IT History Society. Retrieved 2016-07-12.
5. Zenil, Hector "Leibniz medallion comes to life after 300 years" Anima Ex Machina, The Blog of Hector Zenil, November 3rd, 2007.
6. Panu Raatikainen, "Exploring Randomness and The Unknowable" Notices of the American Mathematical Society Book Review October 2001.
7. Franzén, Torkel (2005), Gödel's Theorem: An Incomplete Guide to its Use and Abuse, Wellesley, Massachusetts: A K Peters, Ltd., ISBN 1-56881-238-8