Andrey Kolmogorov gave probability its rules in a single 1933 book
At six, Andrey Kolmogorov noticed that 1, then 1 plus 3, then 1 plus 3 plus 5 always add up to a perfect square. By 30 he had written the axioms modern probability still rests on, and he went on to reshape turbulence, mechanics, logic and the theory of randomness itself.
Kolmogorov was born in Tambov in 1903. His unmarried mother died giving birth to him, and his father, reputedly an agronomist exiled for revolutionary activity, vanished in 1919. Two aunts raised him on his grandfather's estate near Yaroslavl, where his aunt Vera's village school printed a magazine called The Swallow of Spring; at five he edited its mathematics section. In 1910 an aunt adopted him and moved to Moscow.
He entered Moscow State University in 1920 with a taste for everything. His first research paper was actually history, on land ownership in medieval Novgorod, written for S. V. Bakhrushin's seminar. In 1922, while still an undergraduate, he won international notice by constructing a Fourier series that diverges almost everywhere, and chose mathematics for life. Under Nikolai Luzin he became lifelong companions with fellow student Pavel Alexandrov, and in 1925 showed that classical logic can be recast in intuitionistic terms.
His 1933 Foundations of the Theory of Probability set the subject on an axiomatic footing and made him its leading authority. Independently of Sydney Chapman he derived the Chapman-Kolmogorov equations for Markov processes. He also extended the Lotka-Volterra predator-prey model, analysed turbulence from 1941, presented the Kolmogorov-Arnold-Moser theorem in 1954, and with his student Vladimir Arnold solved a version of Hilbert's thirteenth problem in 1957. He is regarded as a founder of algorithmic complexity, the measure of randomness that now bears his name. During the war he applied statistics to artillery and to placing barrage balloons over Moscow.
There is a darker episode. In 1936, during the Great Purge, Kolmogorov and other students testified against Luzin, accusing him of plagiarism and misconduct. Luzin lost his posts but was not arrested. Whether the students were coerced is still debated; one 2013 archival review concluded they acted from personal acrimony. Kolmogorov married Anna Egorova in 1942, devoted decades to teaching gifted children, and died in Moscow in 1987. He once quipped that every mathematician privately believes he is ahead of the rest, and stays quiet only because he is intelligent.
Source: Andrey Kolmogorov
