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Andrey Kolmogorov

Andrey Nikolaevich Kolmogorov (Russian: Андре́й Никола́евич Колмого́ров) (April 25, 1903 - October 20, 1987) was a Soviet mathematician who made major advances in different scientific fields (among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity). Kolmogorov is widely considered one of the prominent mathematicians of the 20th century.


Early life

Kolmogorov was born at Tambov in 1903. His unwed mother died in childbirth and he was raised by his aunts in Tunoshna near Yaroslavl at the estate of his grandfather, a wealthy nobleman. His father, an agronomist by trade, was deported from Saint-Petersburg for participation in the revolutionary movement. He went missing in the Russian Civil War.

Kolmogorov was educated in his aunts' village school, and his earliest literary efforts and mathematical papers were printed in the school newspaper. As an adolescent he designed perpetual motion machines, concealing their defects so cleverly that his secondary-school teachers could not discover them. In 1910 his aunt adopted him and they moved to Moscow, where he went to a gymnasium (the equivalent of a United States high school), graduating from it in 1920.

In 1920 Kolmogorov began to study at Moscow University and the Chemistry Technological Institute. Kolmogorov gained a reputation for his wide-ranging erudition. As an undergraduate, he participated in the seminar of Russian historian S.V. Bachrushin and published his first research paper on landholding practices in the Novgorod Republic in the fifteenth and sixteenth centuries.[1] At the same time (1921-1922), Kolmogorov obtained several results in set theory and the theory of trigonometrical series.


In 1922 Kolmogorov constructed a Fourier series that diverges almost everywhere, gaining international recognition. Around this time he decided to devote his life to mathematics. In 1925 Kolmogorov graduated from Moscow State University, and began to study under the supervision of Nikolai Luzin. He made lifelong friends with Pavel Alexandrov who involved Kolmogorov in 1936 in an ugly political persecution of their mutual teacher, the so-called Luzin case or Luzin affair. Kolmogorov (together with A. Khinchin) became interested in probability theory. Also in 1925, he published his famous work in intuitionistic logic - On the principle of the excluded middle. In 1929 Kolmogorov earned his Ph.D. at Moscow State University.

In 1930 Kolmogorov went on his first long trip abroad, traveling to Göttingen, Munich, and then to Paris. His pioneering work About the Analytical Methods of Probability Theory was published (in German) in 1931, the same year he became a professor at Moscow University. In 1933 Kolmogorov published Foundations of the Theory of Probability, laying the modern foundations of probability theory and establishing his reputation as one of the world's experts in this field. In 1935, Kolmogorov became the first chair of probability theory at the Faculty of Mathematics and Mechanics of Moscow State University. In 1939 he was elected a full member (academician) of the USSR Academy of Sciences. In a 1938 paper he "established the basic theorems for smoothing and predicting stationary stochastic processes" — a paper that would have major military applications during the Cold War to come.[2]

Later on, Kolmogorov switched his research interests to the area of turbulence, where his 1941 works had significant influence on the field. In classical mechanics he is best known for the KAM theory (first presented in 1954 in Amsterdam, during the International Congress of Mathematicians). In 1957 he solved Hilbert's thirteenth problem (a joint work with his student V. I. Arnold). He was a founder of algorithmic complexity theory, often referred to as Kolmogorov complexity theory, which he began to develop around this time.

Kolmogorov married Anna Dmitrievna Egorova in 1942. He pursued a vigorous teaching routine throughout his life, not only at the university level but also with younger children, as he was actively involved in developing a pedagogy for gifted children, in literature and music as well as mathematics. At the University, he occupied different positions, including the head of several departments (probability, statistics and random processes, mathematical logic) and also served as dean of the Faculty of Mechanics and Mathematics.

In 1971 he joined an oceanographic expedition aboard the research vessel Dmitri Mendeleev. He wrote a number of articles for the Great Soviet Encyclopedia. In his later years he devoted much of his effort to the mathematical and philosophical relationship between probability theory in abstract and applied areas.[3]

See also

* Kolmogorov axioms
* Kolmogorov backward equation
* Kolmogorov forward equation (also known as the Fokker-Planck equation)
* Kolmogorov dimension (upper box dimension)
* Kolmogorov complexity
* Kolmogorov continuity theorem
* Kolmogorov extension theorem
* Kolmogorov's inequality
* Landau-Kolmogorov inequality
* Brouwer-Heyting-Kolmogorov interpretation
* Kolmogorov microscales
* Kolmogorov space
* Kolmogorov-Smirnov test
* Kolmogorov-Arnold-Moser theorem
* Kolmogorov's zero-one law
* Kolmogorov's characterization of reversible diffusions
* Borel-Kolmogorov paradox
* Chapman-Kolmogorov equation
* Chaitin-Kolmogorov randomness
* Hahn-Kolmogorov theorem
* Astronomical seeing described by Kolmogorov's turbulence law

Math 574, Lesson 4-3: Kolmogorov Complexity


A bibliography of his works appeared in The Annals of Probability, 17(3): 945--964 (July 1989).

* 1956. Foundations of the Theory of Probability by A. N. Kolmogorov, Second English Edition, translation edited by Nathan Morrison, Chelsea Publishing Company, New York

* 1991-93. Selected works of A.N. Kolmogorov, 3 vols. Tikhomirov, V. M., ed., Volosov, V. M., trans. Dordrecht:Kluwer Academic Publishers. ISBN 9027727961

* 1925. "On the principle of the excluded middle" in Jean van Heijenoort, 1967. A Source Book in Mathematical Logic, 1879-1931. Harvard Univ. Press: 414-37.


1. ^ David Salsburg, The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century, New York, W. H. Freeman, 2001; pp. 137-50.

2. ^ Salsburg, p. 139.

3. ^ Salsburg, pp. 145-7.

* Kendall, D. G., "Andrei Nikolaevich Kolmogorov. 25 April 1903 - 20 October 1987," Biographical Memoirs of Fellows of the Royal Society, Vol. 37, pages 300 - 319 (November 1991).


* O'Connor, John J; Edmund F. Robertson "Andrey Kolmogorov". MacTutor History of Mathematics archive.

* Andrey Kolmogorov at the Mathematics Genealogy Project

* The Legacy of Andrei Nikolaevich Kolmogorov Curriculum Vitae and Biography. Kolmogorov School. Ph.D. students and descendants of A.N. Kolmogorov. A.N. Kolmogorov works, books, papers, articles. Photographs and Portraits of A.N. Kolmogorov.

* The origins and legacy of Kolmogorov's Grundbegriffe

* A Short Biography of A.N. Kolmogorov, national research institute for Mathematics and Computer Science in the Netherlands

* Collection of links to Kolmogorov resources

* Andrei Nikolaevich Kolmogorov (in Russian)
* Kolmogorov School at Moscow University

* Annual Kolmogorov Lecture at the Computer Learning Research Centre at Royal Holloway, University of London

* O'Connor, John J; Edmund F. Robertson "The 1936 Luzin affair". MacTutor History of Mathematics archive.

* Lorentz G.G., Mathematics and Politics in the Soviet Union from 1928 to 1953

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