Gregory John Chaitin (// CHY-tin; born 25 June 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 algorithmic (Solomonoff–Kolmogorov–Chaitin, Kolmogorov or program-size) complexity together with Andrei Kolmogorov and Ray Solomonoff. Along with the works of e.g. Solomonoff, Kolmogorov, Martin-Löf, and Leonid Levin, algorithmic information theory became a foundational part of theoretical computer science, information theory, and mathematical logic. It is a common subject in several computer science curricula. Besides computer scientists, Chaitin's work draws attention of many philosophers and mathematicians to fundamental problems in mathematical creativity and digital philosophy.
Mathematics and computer science
Gregory Chaitin is Jewish and 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 algorithmic complexity.
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, with asymptotic approximations from below (but not from above), but not computable.
He was formerly a researcher at IBM's Thomas J. Watson Research Center in New York. He has written more than 10 books 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, and is a member of the Institute for Advanced Studies at Mohammed VI Polytechnic University.
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, that are true by accident". Chaitin proposes that mathematicians must abandon any hope of proving those mathematical facts and adopt a quasi-empirical methodology.
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 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 a professor at the Federal University of Rio de Janeiro.
Some philosophers and logicians disagree with the philosophical conclusions that Chaitin has drawn from his theorems related to what Chaitin thinks is a kind of fundamental arithmetic randomness. The logician Torkel Franzén criticized Chaitin's interpretation of Gödel's incompleteness theorem and the alleged explanation for it that Chaitin's work represents.
- Information, Randomness & Incompleteness (World Scientific 1987) (online)
- Algorithmic Information Theory (Cambridge University Press 1987) (online)
- Information-theoretic Incompleteness (World Scientific 1992) (online)
- The Limits of Mathematics (Springer-Verlag 1998) (online)
- The Unknowable (Springer-Verlag 1999) (online)
- Exploring Randomness (Springer-Verlag 2001) (online)
- Conversations with a Mathematician (Springer-Verlag 2002) (online)
- From Philosophy to Program Size (Tallinn Cybernetics Institute 2003)
- Meta Math!: The Quest for Omega (Pantheon Books 2005) (reprinted in UK as Meta Maths: The Quest for Omega, Atlantic Books 2006) (arXiv:math/0404335)
- Teoria algoritmica della complessità (G. Giappichelli Editore 2006)
- Thinking about Gödel & Turing (World Scientific 2007) (online)
- Mathematics, Complexity and Philosophy (Editorial Midas 2011)
- Gödel's Way (CRC Press 2012)
- Proving Darwin: Making Biology Mathematical (Pantheon Books 2012) (online)
- Building the World from Information & Computation (Academia.edu 2023) (online)
- Philosophical Mathematics: Infinity, Incompleteness, Irreducibility (Academia.edu 2023) (online)
- Gregory Chaitin (2007), Algorithmic information theory: "Chaitin Research Timeline" Archived 23 March 2012 at the Wayback Machine
- Review of Meta Math!: The Quest for Omega, By Gregory Chaitin SIAM News, Volume 39, Number 1, January/February 2006
- Calude, C.S. (2002). Information and Randomness: An Algorithmic Perspective. Texts in Theoretical Computer Science. An EATCS Series. Springer-Verlag.
- R. Downey, and D. Hirschfeldt (2010), Algorithmic Randomness and Complexity, Springer-Verlag.
- Li; Vitanyi (1997), An Introduction to Kolmogorov Complexity and Its Applications, Springer, p. 92, ISBN 9780387948683,
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....
- 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, S2CID 207698337
- 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]
- Chaitin, G. J. (2003). "From Philosophy to Program Size". arXiv:math/0303352.
- Zenil, Hector "Leibniz medallion comes to life after 300 years" Anima Ex Machina, The Blog of Hector Zenil, 3 November 2007.
- Panu Raatikainen, "Exploring Randomness and The Unknowable" Notices of the American Mathematical Society Book Review October 2001.
- Franzén, Torkel (2005), Gödel's Theorem: An Incomplete Guide to its Use and Abuse, Wellesley, Massachusetts: A K Peters, Ltd., ISBN 978-1-56881-238-0
- Pagallo, Ugo (2005), Introduzione alla filosofia digitale. Da Leibniz a Chaitin [Introduction to Digital Philosophy: From Leibniz to Chaitin] (in Italian), G. Giappichelli Editore, ISBN 978-88-348-5635-2, archived from the original on 22 July 2011, retrieved 16 April 2008
- Calude, Cristian S., ed. (2007), Randomness and Complexity. From Leibniz to Chaitin, World Scientific, ISBN 978-981-277-082-0
- Wuppuluri, Shyam; Doria, Francisco A., eds. (2020), Unravelling Complexity: The Life and Work of Gregory Chaitin, World Scientific, doi:10.1142/11270, ISBN 978-981-12-0006-9, S2CID 198790362
- G J Chaitin Home Page from academia.edu
- G J Chaitin Home Page from UMaine.edu in the Internet Archive Archived 29 October 2013 at the Wayback Machine
- List of publications of G J Chaitin
- on YouTube
- Video of lecture on "Leibniz, complexity and incompleteness"
- New Scientist article (March, 2001) on Chaitin, Omegas and Super-Omegas
- A short version of Chaitin's proof
- Gregory Chaitin extended film interview and transcripts for the 'Why Are We Here?' documentary series
- Chaitin Lisp on github