Born April 25, 1903 in Tambov,Andrey Nikolayevich Kolmogorovwas a Russian mathematician whose work influenced many branches of modern mathematics, especially harmonic analysis, probability, set theory, information theory, and number theory. A man of broad culture, interested in technology, history and education, he played an active role in the reform of education in the Soviet Union. He is best remembered for a brilliant series of articles on probability theory.
The mother ofKolmogorovdied giving birth; He was raised by his sister and took the surname of his maternal grandfather. His aunt moved with him to Moscow when he was seven years old, where he showed an early interest in biology and history. In 1920, still undecided about a career, he simultaneously enrolled at Moscow State University to study history and mathematics and at Mendeleev’s Institute of Chemical Engineering to study metallurgy. However, he soon revealed a remarkable talent for mathematics and specialized in that subject. When he was 19 years old, he was entrusted with teaching courses in mathematics and physics at the Experimental School of Potylikhin, and by the time he graduated in 1925 he had already published 10 mathematical papers, most of them on trigonometric series, an extraordinary result for a student. . This amazing burst of mathematical creativity continued as a graduate student with eight more articles written until 1928. He later expanded upon the most important of these articles, “General theory of measurement and probability theory“, whose objective was to develop a rigorous and axiomatic basis for probability in an influential monograph,Grundbegriffe der Wahrscheinlichkeitsrechnung(1933; Foundations of probability theory, 1950).
In 1929, after completing his doctorate,Kolmogorovhe was elected to the Institute of Mathematics and Mechanics of Moscow State University, with which he remained associated for the rest of his life. In 1931, after a radical restructuring of the Moscow mathematical community, he was elected professor. Two years later he was appointed director of the University’s Institute of Mathematical Research, a position he held until 1939 and again from 1951 to 1953. In 1938 he was elected to head the new department of probability and statistics at the Steklov Mathematical Institute of the Academy of Sciences of the USSR in Moscow (now Russian Academy of Sciences), a position he held until 1958. He was elected to the Academy of Sciences in 1939, and between 1946 and 1949 he was also head of the Turbulence Laboratory of the Institute of Theoretical Geophysics of the USSR Academy of Sciences in Moscow.
Among the many areas of pure and applied mathematical research to which he contributedKolmogorov, the theory of probability is without a doubt the most important, both for its depth and for the breadth of its contributions. In addition to his work on the fundamentals of probability, he contributed in-depth articles on stochastic processes, especially Markov processes. In Markov processes, only the present state has any relation to the probability of future states; therefore, states are said not to retain “memory“from past events.Kolmogorovinvented a couple of functions to characterize the transition probabilities for a Markov process and showed that they amount to what he called a “instant average” and one “instantaneous varianceUsing 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 a completely new approach for the application of probability theory in physics, chemistry, civil engineering, and biology. To point out just two examples, in 1937Kolmogorovpublished an article on the use of statistical theory to study the crystallization process, and the following year published an article on mathematical biology using a branched stochastic process to describe the asymptotic probability of extinction of a species over a large number of generations.
Interest ofKolmogorovproblems of turbulence in fluids (turbulent flow) arose in the late 1930s, when it was realized that the recently developed stochastic field theory would be relevant to these problems. In 1941 and 1942 he contributed four articles in this area, in which his contributions were multiplied by a talented group of collaborators who worked under his direction.
During the 1930s, while continuing a prolific production of articles on particular mathematical topics,Kolmogorovbegan writing articles on methodological issues involving the theories of real analysis and probability. He also began writing expository articles for encyclopedias and magazines aimed at a more popular audience. After the end of World War II, already established as one of the main Soviet mathematicians, he began to write 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,Kolmogorovbegan to work on problems of information theory. It was inspired, in part, by the earlier non-rigorous 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 algorithm theory. The breadth of his culture and interests is shown in the articles he wrote at the time on the metric structure of some of the masterpieces of Russian poetry.
The 1960s marked the entry ofKolmogorovin the theory of pedagogy, in which he had enormous influence through his textbooks and his service as a member of the Academy of Pedagogical Sciences of the U.S.S.R. He co-wrote and revised school textbooks and was active in reforming the mathematics curriculum in Soviet schools. Although he suffered from Parkinson’s disease and was almost blind during the last years of his life, he continued to take an active interest in the mathematical world until he died.