Andrey Kolmogorov

Andrey Kolmogorov
Born	(1903-04-25)25 April 1903 Tambov, Russian Empire
Died	20 October 1987(1987-10-20) (aged 84) Moscow, Soviet Union
Citizenship	Soviet Union
Nationality	Soviet Union
Fields	Mathematics
Institutions	Moscow State University
Alma mater	Moscow State University
Doctoral advisor	Nikolai Luzin
Doctoral students	Vladimir Arnold Sergei Artemov Grigory Barenblatt Roland Dobrushin Eugene B. Dynkin Israil Gelfand Boris V. Gnedenko Leonid Levin Per Martin-Löf Sergey Nikolsky Yuri Prokhorov Yakov G. Sinai Albert N. Shiryaev Anatoli G. Vitushkin Andrei Monin Alexander Obukhov Akiva Yaglom
Known for	Probability theory, topology, intuitionistic logic, turbulence, classical mechanics, mathematical analysis
Notable awards	Stalin Prize (1941) Balzan prize (1962) Lenin Prize (1965) Wolf prize (1980) Lobachevsky Prize (1986) Fellow of the Royal Society
Spouse	Anna Dmitrievna Egorova

Andrey Nikolaevich Kolmogorov (Russian: Андре́й Никола́евич Колмого́ров) (25 April 1903 – 20 October 1987) was a Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.

Biography

Early life

Andrey Kolmogorov was born in Tambov, about 500 kilometers south-southeast of Moscow, in 1903. His unmarried mother, Maria Y. Kolmogorova, died giving him birth. Andrey was raised by two of his aunts in Tunoshna (near Yaroslavl) at the estate of his grandfather, a well-to-do nobleman.

Little is known about Andrey's father. He was supposedly named Nikolai Matveevich Kataev and had been an agronomist. Nikolai had been exiled from St. Petersburg to the Yaroslavl province after his participation in the revolutionary movement against the czars. He disappeared in 1919 and he was presumed to have been killed in the Russian Civil War.

Andrey Kolmogorov was educated in his aunt's village school, and his earliest literary efforts and mathematical papers were printed in the school newspaper. As a teenager, 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 they moved to Moscow, where he graduated from high school in 1920. Later that same year, 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 student in college, he attended the seminars of the Russian historian S.V. Bachrushin, and he published his first research paper on the fifteenth and sixteenth centuries' landholding practices in the Novgorod Republic. During the same period (1921 — 22), Kolmogorov worked out and proved several results in set theory and in the theory of Fourier series.

Adulthood

In 1922, Kolmogorov gained international recognition for constructing a Fourier series that diverges almost everywhere. Around this time, he decided to devote his life to mathematics.

In 1925, Kolmogorov graduated from the Moscow State University and began to study under the supervision of Nikolai Luzin. He made a lifelong friendship with Pavel Alexandrov. (Both were later involved in the political persecution of their common teacher Nikolai Luzin, in the so-called Luzin affair in 1936.) According to some researchers, Kolmogorov and Alexandrov were involved in a homosexual relationship, while others deny this and suppose that this rumor was spread in the 1950s in order to rehabilitate the participants of the Luzin affair. Kolmogorov (together with Aleksandr 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 which he proved that under a certain interpretation, all statements of classical formal logic can be formulated as those of intuitionistic logic. In 1929, Kolmogorov earned his Doctor of Philosophy (Ph.D.) degree, from the Moscow State University.

In 1930, Kolmogorov went on his first long trip abroad, traveling to Göttingen and Munich, and then to Paris. His pioneering work, About the Analytical Methods of Probability Theory, was published (in German) in 1931. Also in 1931, he became a professor at the Moscow State University.

In 1933, Kolmogorov published his book, Foundations of the Theory of Probability, laying the modern axiomatic foundations of probability theory and establishing his reputation as the world's leading expert in this field. In 1935, Kolmogorov became the first chairman of the department of probability theory at the Moscow State University. Around the same years (1936) Kolmogorov contributed to the field of ecology and generalized the Lotka–Volterra model of predator-prey systems. 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. In 1939, he was elected a full member (academician) of the USSR Academy of Sciences.

In his study of stochastic processes (random processes), especially Markov processes, Kolmogorov and the British mathematician Sydney Chapman independently developed the pivotal set of equations in the field, which have been given the name of the Chapman–Kolmogorov equations.

Kolmogorov (left) delivers a talk at a Soviet information theory symposium. (Tallinn, 1973).

Kolmogorov works on his talk (Tallinn, 1973).

Later, Kolmogorov focused his research on turbulence, where his publications (beginning in 1941) significantly influenced 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, working jointly with his student, V. I. Arnold, he solved a particular interpretation of Hilbert's thirteenth problem. Around this time he also began to develop, and was considered a founder of, algorithmic complexity theory - often referred to as Kolmogorov complexity theory.

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, music, and mathematics). At the Moscow State University, Kolmogorov occupied different positions, including the heads of several departments: probability, statistics, and random processes; mathematical logic. He also served as the Dean of the Moscow State University Department 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.

Kolmogorov died in Moscow in 1987, and his remains were buried in the Novodevichy cemetery.

A quotation attributed to Kolmogorov is [translated into English]: "Every mathematician believes that he is ahead over all others. The reason why they don't say this in public, is because they are intelligent people."

Bibliography

A bibliography of his works appeared in "Publications of A. N. Kolmogorov". Annals of Probability 17 (3): 945–964. July 1989. doi:10.1214/aop/1176991252. 

• Kolmogorov, Andrey (1933). Grundbegriffe der Wahrscheinlichkeitsrechnung (in German). Berlin: Julius Springer. 
  • Translation: Kolmogorov, Andrey (1956). Foundations of the Theory of Probability (2nd ed.). New York: Chelsea. ISBN 0-8284-0023-7. 
• 1991–93. Selected works of A.N. Kolmogorov, 3 vols. Tikhomirov, V. M., ed., Volosov, V. M., trans. Dordrecht:Kluwer Academic Publishers. ISBN 90-277-2796-1
• 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.
• Kolmogorov, Andrei N. (1963). "On Tables of Random Numbers". Sankhyā Ser. A. 25: 369–375. MR 178484. 
• Kolmogorov, Andrei N. (1963). "On Tables of Random Numbers". Theoretical Computer Science 207 (2): 387–395. doi:10.1016/S0304-3975(98)00075-9. MR 1643414. 

See also

• Kolmogorov axioms
• Kolmogorov equations (also known as the Fokker–Planck equations in the context of diffusion and in the forward case)
• Kolmogorov dimension (upper box dimension)
• Kolmogorov continuity theorem
• Kolmogorov’s criterion
• Kolmogorov extension theorem
• Kolmogorov's inequality
• Landau–Kolmogorov inequality
• Kolmogorov integral
• Brouwer–Heyting–Kolmogorov interpretation
• Kolmogorov microscales
• Kolmogorov space
• Kolmogorov complexity
• Kolmogorov–Smirnov test
• Kolmogorov's characterization of reversible diffusions
• Borel–Kolmogorov paradox
• Chapman–Kolmogorov equation
• Sydney Chapman (mathematician)
• Hahn–Kolmogorov theorem
• Astronomical seeing described by Kolmogorov's turbulence law
• Kolmogorov structure function
• Kolmogorov's zero-one law

External links

• Biography at Scholarpedia
• O'Connor, John J.; Robertson, Edmund F., "Andrey Kolmogorov", MacTutor History of Mathematics archive, University of St Andrews .
• 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
• Vitanyi, P.M.B., Andrey Nikolaevich Kolmogorov. Scholarpedia, 2(2):2798; 2007
• Collection of links to Kolmogorov resources
• Interview with Kolmogorov (1958, Moscow), Eugene Dynkin Collection of Mathematics Interviews, Cornell University Library.
• 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.; Robertson, Edmund F., "The 1936 Luzin affair", MacTutor History of Mathematics archive, University of St Andrews .
• Lorentz G. G., Mathematics and Politics in the Soviet Union from 1928 to 1953
• Kutateladze S. S., The Tragedy of Mathematics in Russia
• Video recording of the G. Falkovich's lecture: "Andrey Nikolaevich Kolmogorov (1903–1987) and the Russian school"