# Gregory Chaitin

**Gregory Chaitin**, American contemporary mathematician and computer scientist who, beginning in the late 1960s, has made important contributions to algorithmic information theory, in particular a new incompleteness theorem similar in spirit
to Gödel's incompleteness theorem. 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 where born and where Chaitin spent part of his youth. He is also a visiting professor at the Computer Science Department of the University of Auckland.

Chaitin's work has profound consequences for our ideas of randomness.

Chaitin has defined Chaitin's constant **Ω**, a real number whose digits are randomly distributed and which expresses the probability that a random program will halt. **Ω** has numerous remarkable mathematical properties, including the fact that it is definable but not computable.

Chaitin's work on algorithmic information theory paralleled the work of Kolmogorov in many respects.

*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: math, art, science and the limits of reason*, (Springer-Verlag 2002),
*From Philosophy to Program Size*, (Tallinn Cybernetics Institute 2003).

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