Andrey Kolmogorov

Andrey Kolmogorov was a Soviet mathematician who, in his 1933 monograph Grundbegriffe der Wahrscheinlichkeitsrechnung, Foundations of the Theory of Probability, established the modern axiomatic framework for probability theory, defining probability rigorously in terms of measure theory and providing the formal foundation on which nearly all later probability theory has been built. Kolmogorov also made significant contributions to the mathematical theory of turbulence in fluid flow, proposing statistical laws describing how energy is distributed across different scales of motion in turbulent fluids that remain influential in the field. Later in his career he contributed to the theory now called algorithmic information theory, developing the concept of what is now called Kolmogorov complexity, a way of measuring the intrinsic complexity of an object such as a string of data by the length of the shortest computer program that could produce it. Kolmogorov led an influential school of mathematics in Moscow, training a large number of students across probability, topology and other fields, and worked across an unusually wide range of mathematics over the course of his career.