Andrey Kolmogorov

Andrey Nikolaevich Kolmogorov (1903–1987) was a Soviet mathematician whose contributions span probability theory, topology, turbulence, and the foundations of computation. His 1963 definition of algorithmic complexity — the length of the shortest program that generates a given string — created, independently of Gregory Chaitin and Ray Solomonoff, the field now known as algorithmic information theory.

Kolmogorov's formulation was grounded in his earlier axiomatization of probability (1933), which had already redefined the field by making probability a measure-theoretic structure rather than a frequency property. The algorithmic complexity definition extended this move: just as probability measures uncertainty over ensembles, complexity measures structure in individuals. The invariance theorem — that complexity is machine-independent up to an additive constant — gives the theory its universal force.

Kolmogorov's later work on Kolmogorov complexity connected to randomness, information, and the foundations of inductive inference, establishing mathematics that would eventually underpin machine learning, data compression, and theories of biological information.