Kolmogorov

Andrey Nikolaevich Kolmogorov (April 25, 1903 – October 20, 1987) was a Russian mathematician whose work spanned probability theory, statistical mechanics, turbulence, and the theory of algorithmic information. He is regarded as one of the most influential mathematicians of the 20th century and played a central role in advancing modern formalism and rigor in several disciplines.

In probability theory, Kolmogorov formulated the axioms of probability in 1933, providing a rigorous measure-theoretic foundation. He defined probability as a measure on a σ-algebra of events, requiring non-negativity, normalization (the probability of the sure event equals 1), and countable additivity. His framework unified and clarified the field and underpins much of modern statistics and stochastic analysis. He also contributed to the theory of stochastic processes, including the Kolmogorov extension theorem, which allows the construction of processes from specified finite-dimensional distributions.

In statistical physics and turbulence, Kolmogorov proposed the 1941 theory of turbulence (often called K41), describing universal scaling laws for velocity fluctuations in high-Reynolds-number flows. The theory predicts, among other things, the −5/3 power law for the energy spectrum and the existence of an energy cascade from large to small scales.

In the 1960s, Kolmogorov helped inaugurate algorithmic information theory with the notion of Kolmogorov complexity, defining the information content of a finite object as the length of the shortest description that generates it. This concept provides a formal measure of randomness and has influenced computer science, mathematics, and information theory.

Kolmogorov spent much of his career at Moscow State University and the Steklov Institute, shaping generations of mathematicians and leaving a lasting impact on multiple domains.