# Andrei Kolmogorov

## Kolmogorov, Andrei Nikolaevich

Born Apr. 12 (25), 1903, in Tambov. Soviet mathematician. Academician of the Academy of Sciences of the USSR (1939); Hero of Socialist Labor (1963).

Kolmogorov graduated from Moscow University in 1925 and became a professor there in 1931. He began his scientific work on the theory of functions of a real variable, where he is credited with fundamental work on trigonometric series, measure theory, set theory, integration theory, and the theory of approximation of functions. He also made substantial contributions to the development of constructive logic, topology (cohomology theory), mechanics (theory of turbulence), the theory of differential equations, and functional analysis.

Kolmogorov’s work in probability theory is of fundamental importance. In this field, together with A. Ia. Khinchin, he began (1925) to apply the methods of the theory of functions of a real variable. This enabled him to solve a number of difficult problems and to construct the widely known axiomatic basis of probability theory (1933) and to lay the foundations of the theory of continuous-time random Markov processes. He later developed (in conjunction with the studies of A. Ia. Khinchin) the theory of stationary random processes, processes with stationary increments, and branching processes. Kolmogorov has made important contributions to information theory. He has done research on the theory of firing, statistical inspection methods for mass production, applications of mathematical methods in biology, and mathematical linguistics.

Kolmogorov was the editor of the mathematical section of the first edition of the *Great Soviet Encyclopedia* and a member of the Main Editorial Board of the second edition. He is active in working out problems of mathematical education in secondary schools and universities. Kolmogorov founded a large school of probability theory and the theory of functions. Among his students are Academicians of the Academy of Sciences of the USSR A. I. Mal’tsev, M. D. Millionshchikov, S. M. Nikol’skii, and Iu. V. Prokhorov; corresponding members of the Academy of Sciences of the USSR I. M. Gel’fand and A. S. Monin; Academician of the Academy of Sciences of the Ukrainian SSR B. V. Gnedenko; Academician of the Academy of Sciences of the Uzbek SSR S. Kh. Sirazhdinov; and Lenin Prize laureates I. V. Arnol’d and Iu. A. Rozanov.

Kolmogorov is a foreign member of the Paris Academy of Sciences, the Royal Society of London, and a number of other foreign academies (the Netherlands, Poland, Rumania, the USA), scientific institutions and societies. A recipient of the Bolzano International Prize (1963), the State Prize of the USSR (1941), and the Lenin Prize (1965), he has been awarded six Orders of Lenin, the Order of the Red Banner of Labor, and various medals.

### WORKS

*Osnovnye poniatiia teorii veroiatnostei.*Moscow-Leningrad, 1936.

*Vvedenie v teoriiu funktsii deistvitel’nogo peremennogo,*3rd ed. Moscow-Leningrad, 1938. (With P. S. Aleksandrov.)

*Predel’nye raspredeleniia dlia summ nezavisimykh sluchainykh velichin.*Moscow-Leningrad, 1949. (With B. V. Gnedenko.)

*Elementy teorii funktsii i funktsional’nogo analiza,*3rd ed. Moscow, 1972. (With S. V. Fomin.)

### REFERENCES

Aleksandrov, P. S., and A. Ia. Khinchin. “A. N. Kolmogorov.”*Uspekhi matematicheskikh nauk,*1953, vol. 8, issue 3. (Contains a bibliography.)

*Uspekhi matematicheskikh nauk,*1963, vol. 18, issue 5. (The issue is devoted to A. N. Kolmogorov on the occasion of his 60th birthday.)

B. V. GNEDENKO