Kolmogorov: Life and Creative Activities

Abstract

Mathematics and MechanicsProbability Theory and Mathematical StatisticsInformation Theory and the Theory of AlgorithmsThough these three volumes [MM, PS, IA] contain as many as 60, 53 and 13 papers, respectively (author’s selection), they cover far from all that he accomplished in these areas of science (see the list of Andrei Nikolaevich Kolmogorov’s works on pages 945-964). However, even a brief review of the lists of contents astonishes the reader with the breadth and profoundness of the material therein. Topics in the theory of trigonometric series, theory of measure and sets, studies in the theory of integration, approximation theory, constructive logic, topology, theory of superposition of functions and Hilbert’s 13th problem, topics in classical mechanics, ergodic theory, theory of turbulence, diffusion and patterns (models) in the dynamics of populations, papers on the foundations of probability theory, limit theorems, theory of stochastic (Markov, stationary, branching, ...) processes, mathematical statistics, theory of algorithms, information theory,…–even this is hardly a complete list of all the branches of science in which Andrei Nikolaevich obtained fundamentally important results, which determined the state of many fields of 20th century mathematics and possible directions for their development.