Andrey Kolmogorov

Andrey Nikolaevich Kolmogorov was born in 1903 in Tambov, Russia, and raised by his aunt after his unmarried mother died in childbirth. He was a restlessly curious child — he published his first mathematical paper at seventeen — and went up to Moscow University in 1920, at a moment when the city was starving and the new Soviet state was half-collapsed. He never left. By the end of that decade he had already rewritten the logical foundations of his subject; by the end of the next he was one of the defining mathematicians of the twentieth century.

His 1933 monograph Grundbegriffe der Wahrscheinlichkeitsrechnung gave probability theory the measure-theoretic axioms it still uses today — a single, clean framework that made the subject a respectable branch of mathematics rather than a collection of gambler's heuristics. From probability he moved to stochastic processes, from there to dynamical systems (the K in KAM theorem stands for Kolmogorov), to information theory (Kolmogorov complexity), to algorithmic randomness, to classical and celestial mechanics.

In the summer of 1941, with German armies advancing on Moscow, the academy evacuated to Kazan, and Kolmogorov turned his attention to the one problem every fluid dynamicist had given up on. In three short papers he laid out what is now called the K41 theory: an argument, by pure dimensional analysis, that the energy spectrum in the inertial range of fully-developed turbulence must go as E(k) ∝ ε^(2/3) k^(−5/3). He had not solved the Navier-Stokes equations. He had solved, in a sense, the scaling of the Navier-Stokes equations. Measured ever since, in every turbulent flow in every medium, the spectrum is a straight line with slope −5/3.