Andrey Kolmogorov

Andrey Nikolaevich Kolmogorov (1903 - 1987) was a Soviet mathematician widely regarded as one of the most influential figures of twentieth-century mathematics, best known for placing probability theory on a rigorous axiomatic foundation.^[1]

Early life and education

Kolmogorov was born in Tambov, in the Russian Empire, in 1903 and was raised largely by his aunt. In 1920 he entered Lomonosov Moscow State University, where he studied mathematics under Nikolai Luzin and soon produced original results, including work on Fourier series and set theory, before joining the university as a researcher.^[2]

Foundations of probability

In 1933 Kolmogorov published Grundbegriffe der Wahrscheinlichkeitsrechnung (Foundations of the Theory of Probability), in which he used measure theory to give probability a rigorous axiomatic basis. The framework became the standard foundation of the modern discipline and underlies fields ranging from statistics to mathematical finance.^[3] His name is attached to the Chapman-Kolmogorov equations and the Kolmogorov-Smirnov test.

Breadth of contributions

Kolmogorov worked across an unusually wide range of fields. In 1941 he formulated an influential statistical theory of turbulence. With his student Vladimir Arnold he helped resolve Hilbert's thirteenth problem, and their work, together with that of Jurgen Moser, gave rise to the Kolmogorov-Arnold-Moser (KAM) theory in dynamical systems. In the 1960s he helped found algorithmic information theory, and the measure of the complexity of an object by the length of its shortest description is now known as Kolmogorov complexity. He also contributed to topology, classical mechanics, intuitionistic logic and information theory.

Teaching and legacy

A dedicated educator, Kolmogorov supervised many students who became leading mathematicians and helped establish specialized physics and mathematics schools for gifted children.^[4] His honours included the Wolf Prize in Mathematics, the Balzan Prize and the Lenin Prize, and he was elected a Foreign Member of the Royal Society. He died in Moscow in 1987.