In 1975, Chaitin 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, where he wrote more than 10 books that have been translated into about 15 languages.
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".[8] Chaitin proposes that mathematicians must abandon any hope of proving those mathematical facts and adopt a quasi-empirical methodology.
↑Li; Vitanyi (1997), An Introduction to Kolmogorov Complexity and Its Applications, Springer, p.92, ISBN9780387948683, 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, S2CID207698337
Gusfield, Dan (2024), Proven Impossible: Elementary Proofs of Profound Impossibility from Arrow, Bell, Chaitin, Gödel, Turing and More, Cambridge University Press, doi:10.1017/9781009349451, ISBN978-1-009-34950-5
