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 to be one of the pre-eminent mathematicians of the 20th century.

Biography

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 disappeared and was presumed to be killed in the Russian Civil War.

Kolmogorov was educated in his aunt's 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 (necessary) defects so cleverly that his secondary-school teachers could not discover them. In 1910, his aunt adopted him and then they moved to Moscow, where he went to a gymnasium (the equivalent of a American high school), graduating from it in 1920.

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

Maturity

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 Doctor of Philosophy degree, Ph.D., at the Moscow State University.

In 1930, Kolmogorov went on his first long trip abroad, traveling to Göttingen and Munich, Germany, and then to Paris, France. His pioneering work About the Analytical Methods of Probability Theory was published (in German) in 1931. Also in 1931, he became a professor at Moscow University. In 1933, Kolmogorov published the book, Foundations of the Theory of Probability, laying the modern axiomatic foundations of probability theory and establishing his reputation the world's leading living expert in this field. In 1935, Kolmogorov became the first chairman of probability theory at the Moscow State University. In 1939, he was elected a full member (academician) of the USSR Academy of Sciences. In a 1938 paper, Kolmogorov "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.

In his study of stochastic processes (random processes), especially Markov processes, Komolgorov and the Briton Sydney Chapman independently developed the pivotal set of equations in the field, the Chapman-Kolmogorov equations.

Later on, Kolmogorov changed his research interests to the area of turbulence, where his publications beginning in 1941 had a significant influence on the field. In classical mechanics, he is best known for the Kolmogorov–Arnold–Moser theorem (first presented in 1954 at 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 was married to 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 in music, as well as in mathematics. At the Moscow State University, Kolmogorov occupied different positions, including the heads of several departments: probability, statistics, and random processes; mathematical logic; and he also served as the Dean of the Moscow State University Faculty of Mechanics and Mathematics.

In 1971, Kolmogorov 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.

Andrey Kolmogorov passed away in Moscow in 1987.

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
• Sydney Chapman
• Chaitin-Kolmogorov randomness
• Hahn-Kolmogorov theorem
• Astronomical seeing described by Kolmogorov's turbulence law

Bibliography

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.

References

• 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).

External links

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