Andrey Nikolaevich Kolmogorov (1903-1987) was a Soviet mathematician widely regarded as one of the most important figures of twentieth-century mathematics. In his 1933 monograph “Grundbegriffe der Wahrscheinlichkeitsrechnung” he built up probability theory rigorously from a small set of axioms, in a way the MacTutor biography compares to Euclid’s treatment of geometry. That axiomatization turned probability from a collection of heuristics into a precise branch of measure theory and underpins essentially all modern statistics and machine learning.
Beyond probability, Kolmogorov made deep contributions to topology, turbulence, dynamical systems, and classical mechanics. In the 1960s he helped found what is now called algorithmic information theory by proposing that the complexity of an object can be measured as the length of the shortest program that produces it. This idea, now known as Kolmogorov complexity, formalizes the intuition that a simple, regular object is “compressible” while a random one is not.
Kolmogorov complexity is a foundation for modern thinking about learning, compression, and Occam’s razor: simpler hypotheses are those with shorter descriptions, a notion that runs through theories of inductive inference and generalization in AI. For a general reader, Kolmogorov matters because the mathematics that lets us reason about uncertainty and about what counts as a “simple” explanation both trace back substantially to his work.