- Andrey Kolmogorov
name = Andrey Kolmogorov
birth_date = birth date|1903|4|25
Tambov, Imperial Russia
death_date = death date and age|1987|10|20|1903|4|25
Moscow State University
Moscow State University
Vladimir Arnold Roland Dobrushin
Eugene B. Dynkin
Israil Gelfand Leonid Levin Per Martin-Löf
Yakov G. Sinai
Albert N. Shiryaev
Anatoli G. Vitushkin
probability theory, topology, intuitionistic logic, turbulence, classical mechanics, mathematical analysis
USSR State Prize(1941) Balzan prize(1963) Lenin Prize(1965) Wolf prize(1980) Lobachevsky Prize(1987)
Andrey Nikolaevich Kolmogorov ( _ru. Андрей Николаевич Колмогоров) (
April 25, 1903- October 20, 1987) was a Soviet mathematician, preeminent in the 20th century who advanced various scientific fields (among them probability theory, topology, intuitionistic logic, turbulence, classical mechanicsand computational complexity).
Kolmogorov was born at
Tambovin 1903. His unwed mother died in childbirth and he was raised by his aunts in Tunoshnanear Yaroslavlat the estate of his grandfather, a wealthy nobleman. His father, an agronomistby trade, was deported from Saint-Petersburgfor 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 motionmachines, 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, graduating from it in 1920.
In 1920, Kolmogorov began to study at the
Moscow State Universityand 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. [David Salsburg, "The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century," New York, W. H. Freeman, 2001; pp. 137-50.] At the same time (1921-1922), Kolmogorov derived and proved several results in set theoryand in the theory of Fourier series(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 Alexandrovwho involved Kolmogorov in 1936 in an ugly political persecution of their mutual teacher, the so-called Luzin caseor 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
Göttingenand 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 as 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 Warto come. [Salsburg, p. 139.]
In his study of stochastic processes (random processes), especially
Markov processes, Komolgorov and the Briton Sydney Chapmanindependently 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 theoryin abstract and applied areas. [Salsburg, pp. 145-7.]
Kolmogorov passed away in Moscow in 1987. A quotation, "Every mathematician believes he is a head over all others. The reason why they don't say this in public, is because they are intelligent persons" is attributed to him.
Kolmogorov backward equation
Kolmogorov forward equation(also known as the Fokker-Planck equation)
* Kolmogorov dimension (
upper box dimension)
Kolmogorov continuity theorem
Kolmogorov extension theorem
Kolmogorov's zero-one law
Kolmogorov's characterization of reversible diffusions
Astronomical seeingdescribed by Kolmogorov's turbulence law
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.
* 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).
* [http://www.kolmogorov.com/ 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.
* [http://www.probabilityandfinance.com/articles/04.pdf The origins and legacy of Kolmogorov's Grundbegriffe]
* [http://homepages.cwi.nl/~paulv/KOLMOGOROV.BIOGRAPHY.html A Short Biography of A.N. Kolmogorov] , national research institute for Mathematics and Computer Science in the Netherlands
* [http://www.geometry.net/scientists/kolmogorov_andrey.php Collection of links to Kolmogorov resources]
* [http://www.kolmogorov.info/ Andrei Nikolaevich Kolmogorov] (in Russian)
* [http://www.pms.ru/ Kolmogorov School] at Moscow University
* [http://www.clrc.rhul.ac.uk/events/eventsoverview.htm Annual Kolmogorov Lecture] at the Computer Learning Research Centre at Royal Holloway, University of London
*MacTutor Biography|class=Extras|id=Luzin|title=The 1936 Luzin affair
* [http://www.math.ohio-state.edu/AT/LORENTZ/JAT02-0001_final.ps Lorentz G.G., Mathematics and Politics in the Soviet Union from 1928 to 1953]
NAME= Kolmogorov, Andrey
DATE OF BIRTH=
April 25, 1903
PLACE OF BIRTH=
Tambov, Imperial Russia
DATE OF DEATH=
October 20, 1987
PLACE OF DEATH=
Wikimedia Foundation. 2010.
Look at other dictionaries:
Andrey Kolmogorov — Andreï Kolmogorov Andreï Kolmogorov Andreï Nikolaïevitch Kolmogorov (en russe : Андрей Николаевич Колмогоров ; 25 avril 1903 à Tambov 20 octobre 1987 à … Wikipédia en Français
Andrey Kolmogorov — Andrei Nikolajewitsch Kolmogorow Andrei Nikolajewitsch Kolmogorow (russisch Андрей Николаевич Колмогоров, wiss. Transliteration Andrej Nikolaevič Kolmogorov; * 12.jul./ 25. April 1903 … Deutsch Wikipedia
Kolmogorov's theorem — is any of several different results by Andrey Kolmogorov:;In statistics * Kolmogorov Smirnov test;In probability theory * Hahn Kolmogorov theorem * Kolmogorov existence theorem * Kolmogorov continuity theorem * Kolmogorov s three series theorem * … Wikipedia
Kolmogorov complexity — In algorithmic information theory (a subfield of computer science), the Kolmogorov complexity of an object, such as a piece of text, is a measure of the computational resources needed to specify the object. It is named after Soviet Russian… … Wikipedia
Kolmogorov-Smirnov test — In statistics, the Kolmogorov ndash;Smirnov test (also called the K S test for brevity) is a form of minimum distance estimation used as a nonparametric test of equality of one dimensional probability distributions used to compare a sample with a … Wikipedia
Kolmogorov space — In topology and related branches of mathematics, the T0 spaces or Kolmogorov spaces, named after Andrey Kolmogorov, form a broad class of well behaved topological spaces.The T0 condition is one of the separation axioms. Definition A T0 space is a … Wikipedia
Kolmogorov backward equation — The Kolmogorov backward equation (KBE) and its adjoint the Kolmogorov forward equation (KFE) are partial differential equations (PDE) that arise in the theory of continuous time continuous state Markov processes. Both were published by Andrey… … Wikipedia
Kolmogorov–Arnold–Moser theorem — The Kolmogorov–Arnold–Moser theorem is a result in dynamical systems about the persistence of quasi periodic motions under small perturbations. The theorem partly resolves the small divisor problem that arises in the perturbation theory of… … Wikipedia
Kolmogorov's inequality — In probability theory, Kolmogorov s inequality is a so called maximal inequality that gives a bound on the probability that the partial sums of a finite collection of independent random variables exceed some specified bound. The inequality is… … Wikipedia
Kolmogorov’s criterion — In probability theory, Kolmogorov s criterion, named after Andrey Kolmogorov, is a theorem in Markov processes which states that a stationary Markov chain with transition matrix P and state space S is reversible if and only if its transition… … Wikipedia