April 25, 1903: Andrey Kolmogorov is born
Andrey Nikolayevich Kolmogorov (1903-1987)
Scientific field: Mathematics
Known for: Information theory, Harmonic analysis, Number theory, Probability theory, Set theory
Andrey Kolmogorov was a Russian mathematician whose work influenced many branches of modern mathematics, and best remembered for a brilliant series of papers on the theory of probability.
Of the many areas of pure and applied mathematical research to which Kolmogorov contributed, probability theory is unquestionably the most important, in terms of both the depth and breadth of his contributions. In addition to his work on the foundations of probability, he contributed profound papers on stochastic processes, especially Markov processes. In Markov processes only the present state has any bearing upon the probability of future states; states are therefore said to retain no “memory” of past events. Kolmogorov invented a pair of functions to characterize the transition probabilities for a Markov process and showed that they amount to what he called an “instantaneous mean” and an “instantaneous variance”. Using these functions, he was able to write a set of partial differential equations to determine the probabilities of transition from one state to another. These equations provided an entirely new approach to the application of probability theory in physics, chemistry, civil engineering, and biology.
Kolmogorov’s interest in problems of turbulence in fluids (turbulent flow) arose in the late 1930s, when he realized that the recently developed stochastic field theory would be relevant to these problems. In 1941 and 1942 he contributed four papers to this area, in which his contributions were multiplied by a talented group of collaborators working under his direction.
During the 1930s, while continuing a prolific output of papers on particular mathematical topics, Kolmogorov began to write articles on methodological questions involving the theories of real analysis and probability. He also began to write expository articles for encyclopedias and journals aimed at a popular audience. After the end of World War II, established as one of the leading Soviet mathematicians, he began writing articles of historical and philosophical content. During the 1950s he contributed more than 80 articles to the second edition of the Great Soviet Encyclopedia.
In the mid-1950s Kolmogorov began to work on problems of information theory. He was inspired, in part, by the earlier nonrigorous work of the American engineer Claude Shannon. Working with Israil Gelfand and Akiva Yaglom, he was able to give a mathematical definition of the notion of quantity of information. In the 1960s he began writing articles on automata theory and theory of algorithms. The breadth of his culture and interests is shown by articles that he wrote at this time on the metrical structure of some of the masterpieces of Russian poetry.
The late 1960s marked Kolmogorov’s entrance into the theory of pedagogy, in which he was enormously influential through his textbooks and his service as a member of the U.S.S.R. Academy of Pedagogical Sciences. He cowrote and reviewed school textbooks and actively participated in reforming the mathematics curriculum in Soviet schools. Though suffering from Parkinson’s disease and nearly blind during the last few years of his life, he continued to take an active interest in the mathematical world until he died.
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