Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet mathematician who played a central role in the creation of modern

probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...

. He also contributed to the mathematics of

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

intuitionistic logic Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems ...

turbulence In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to laminar flow, which occurs when a fluid flows in parallel layers with no disruption between ...

classical mechanics Classical mechanics is a Theoretical physics, physical theory describing the motion of objects such as projectiles, parts of Machine (mechanical), machinery, spacecraft, planets, stars, and galaxies. The development of classical mechanics inv ...

, algorithmic information theory and

computational complexity In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations ...

Biography

Early life

Andrey Kolmogorov was born in

Tambov Tambov ( , ; rus, Тамбов, p=tɐmˈbof) is a types of inhabited localities in Russia, city and the administrative center of Tambov Oblast, Central Federal District, central Russia, at the confluence of the Tsna River (Moksha basin), Tsna ...

, about 500 kilometers southeast of

Moscow Moscow is the Capital city, capital and List of cities and towns in Russia by population, largest city of Russia, standing on the Moskva (river), Moskva River in Central Russia. It has a population estimated at over 13 million residents with ...

, in 1903. His unmarried mother, Maria Yakovlevna Kolmogorova, died giving birth to him. Andrey was raised by two of his aunts in Tunoshna (near

Yaroslavl Yaroslavl (; , ) is a city and the administrative center of Yaroslavl Oblast, Russia, located northeast of Moscow. The historic part of the city is a World Heritage Site, and is located at the confluence of the Volga and the Kotorosl rivers. ...

) at the estate of his grandfather, a well-to-do

nobleman Nobility is a social class found in many societies that have an aristocracy. It is normally appointed by and ranked immediately below royalty. Nobility has often been an estate of the realm with many exclusive functions and characteristics. T ...

. Little is known about Andrey's father. He was supposedly named Nikolai Matveyevich Katayev and had been an

agronomist An agriculturist, agriculturalist, agrologist, or agronomist (abbreviated as agr.) is a professional in the science, practice, and management of agriculture and agribusiness. It is a regulated profession in Canada, India, the Philippines, the Uni ...

. Katayev had been exiled from

Saint Petersburg Saint Petersburg, formerly known as Petrograd and later Leningrad, is the List of cities and towns in Russia by population, second-largest city in Russia after Moscow. It is situated on the Neva, River Neva, at the head of the Gulf of Finland ...

to the Yaroslavl province after his participation in the revolutionary movement against the

tsar Tsar (; also spelled ''czar'', ''tzar'', or ''csar''; ; ; sr-Cyrl-Latn, цар, car) is a title historically used by Slavic monarchs. The term is derived from the Latin word '' caesar'', which was intended to mean ''emperor'' in the Euro ...

s. He disappeared in 1919 and was presumed to have been killed in the

Russian Civil War The Russian Civil War () was a multi-party civil war in the former Russian Empire sparked by the 1917 overthrowing of the Russian Provisional Government in the October Revolution, as many factions vied to determine Russia's political future. I ...

. Andrey Kolmogorov was educated in his aunt Vera's village school, and his earliest literary efforts and mathematical papers were printed in the school journal "The Swallow of Spring". Andrey (at the age of five) was the "editor" of the mathematical section of this journal. Kolmogorov's first mathematical discovery was published in this journal: at the age of five he noticed the regularity in the sum of the series of odd numbers:

1 = 1^2; 1 + 3 = 2^2; 1 + 3 + 5 = 3^2,

etc. In 1910, his aunt adopted him, and they moved to Moscow, where he graduated from

high school A secondary school, high school, or senior school, is an institution that provides secondary education. Some secondary schools provide both ''lower secondary education'' (ages 11 to 14) and ''upper secondary education'' (ages 14 to 18), i.e., ...

in 1920. Later that same year, Kolmogorov began to study at

Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...

and at the same time Mendeleev Moscow Institute of Chemistry and Technology. Kolmogorov writes about this time: "I arrived at Moscow University with a fair knowledge of mathematics. I knew in particular the beginning of

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

. I studied many questions in articles in the '' Encyclopedia of Brockhaus and Efron'', filling out for myself what was presented too concisely in these articles." Kolmogorov gained a reputation for his wide-ranging erudition. While an undergraduate student in college, he attended the seminars of the Russian historian S. V. Bakhrushin, and he published his first research paper on the fifteenth and sixteenth centuries' landholding practices in the

Novgorod Republic The Novgorod Republic () was a medieval state that existed from the 12th to 15th centuries in northern Russia, stretching from the Gulf of Finland in the west to the northern Ural Mountains in the east. Its capital was the city of Novgorod. The ...

. During the same period (1921–22), Kolmogorov worked out and proved several results in

and in the theory of

Fourier series A Fourier series () is an Series expansion, expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series. By expressing a function as a sum of sines and cosines, many problems ...

Adulthood

In 1922, Kolmogorov gained international recognition for constructing a

that diverges

almost everywhere In measure theory (a branch of mathematical analysis), a property holds almost everywhere if, in a technical sense, the set for which the property holds takes up nearly all possibilities. The notion of "almost everywhere" is a companion notion to ...

. Around this time, he decided to devote his life to

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

. In 1925, Kolmogorov graduated from

and began to study under the supervision of

Nikolai Luzin Nikolai Nikolayevich Luzin (also spelled Lusin; rus, Никола́й Никола́евич Лу́зин, p=nʲɪkɐˈlaj nʲɪkɐˈlajɪvʲɪtɕ ˈluzʲɪn, a=Ru-Nikilai Nikilayevich Luzin.ogg; 9 December 1883 – 28 February 1950) was a Sov ...

. He formed a lifelong close friendship with

Pavel Alexandrov Pavel Sergeyevich Alexandrov (), sometimes romanized ''Paul Alexandroff'' (7 May 1896 – 16 November 1982), was a Soviet mathematician. He wrote roughly three hundred papers, making important contributions to set theory and topology. In topol ...

, a fellow student of Luzin; indeed, several researchers have concluded that the two friends were sexually involved, although neither acknowledged this openly. Kolmogorov (together with Aleksandr Khinchin) became interested in

. Also in 1925, he published his work in

, "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 degree from Moscow State University. In 1929, Kolmogorov and Alexandrov during a long travel stayed about a month in an island in lake Sevan in Armenia. In 1930, Kolmogorov went on his first long trip abroad, traveling to

Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...

and

Munich Munich is the capital and most populous city of Bavaria, Germany. As of 30 November 2024, its population was 1,604,384, making it the third-largest city in Germany after Berlin and Hamburg. Munich is the largest city in Germany that is no ...

and then to

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

. He had various scientific contacts in Göttingen, first with

Richard Courant Richard Courant (January 8, 1888 – January 27, 1972) was a German-American mathematician. He is best known by the general public for the book '' What is Mathematics?'', co-written with Herbert Robbins. His research focused on the areas of real ...

and his students working on limit theorems, where

diffusion process In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Diffusion process is stochastic in nature and hence is used to model many real-life stochastic sy ...

es proved to be the limits of discrete random processes, then with

Hermann Weyl Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, ...

in intuitionistic logic, and lastly with

Edmund Landau Edmund Georg Hermann Landau (14 February 1877 – 19 February 1938) was a German mathematician who worked in the fields of number theory and complex analysis. Biography Edmund Landau was born to a Jewish family in Berlin. His father was Leopo ...

in function theory. His pioneering work ''About the Analytical Methods of Probability Theory'' was published (in German) in 1931. Also in 1931, he became a professor at

. 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 Moscow State University. Around the same years (1936) Kolmogorov contributed to the field of ecology and generalized the Lotka–Volterra model of

predator–prey Predation is a biological interaction in which one organism, the predator, kills and eats another organism, its prey. It is one of a family of common List of feeding behaviours, feeding behaviours that includes parasitism and micropredation ...

systems. During the

Great Purge The Great Purge, or the Great Terror (), also known as the Year of '37 () and the Yezhovshchina ( , ), was a political purge in the Soviet Union that took place from 1936 to 1938. After the Assassination of Sergei Kirov, assassination of ...

in 1936, Kolmogorov's doctoral advisor

became a high-profile target of Stalin's regime in what is now called the "Luzin Affair." Kolmogorov and several other students of Luzin testified against Luzin, accusing him of plagiarism, nepotism, and other forms of misconduct; the hearings eventually concluded that he was a servant to "fascistoid science" and thus an enemy of the Soviet people. Luzin lost his academic positions, but curiously he was neither arrested nor expelled from the Academy of Sciences of the Soviet Union. The question of whether Kolmogorov and others were coerced into testifying against their teacher remains a topic of considerable speculation among historians; all parties involved refused to publicly discuss the case for the rest of their lives. Soviet-Russian mathematician Semën Samsonovich Kutateladze concluded in 2013, after reviewing archival documents made available during the 1990s and other surviving testimonies, that the students of Luzin had initiated the accusations against Luzin out of personal acrimony; there was no definitive evidence that the students were coerced by the state, nor was there any definitive evidence to support their allegations of academic misconduct. Soviet historian of mathematics A.P. Yushkevich surmised that, unlike many of the other high-profile persecutions of the era, Stalin did not personally initiate the persecution of Luzin and instead eventually concluded that he was not a threat to the regime, which would explain the unusually mild punishment relative to other contemporaries. In a 1938 paper, Kolmogorov "established the basic theorems for smoothing and predicting stationary

stochastic processes In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stoc ...

"—a paper that had major military applications during the

Cold War The Cold War was a period of global Geopolitics, geopolitical rivalry between the United States (US) and the Soviet Union (USSR) and their respective allies, the capitalist Western Bloc and communist Eastern Bloc, which lasted from 1947 unt ...

. In 1939, he was elected a full member (academician) of the

USSR Academy of Sciences The Academy of Sciences of the Soviet Union was the highest scientific institution of the Soviet Union from 1925 to 1991. It united the country's leading scientists and was subordinated directly to the Council of Ministers of the Soviet Union (u ...

. During

World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...

Kolmogorov contributed to the Soviet war effort by applying statistical theory to artillery fire, developing a scheme of stochastic distribution of

barrage balloon A barrage balloon is a type of airborne barrage, a large uncrewed tethered balloon used to defend ground targets against aircraft attack, by raising aloft steel cables which pose a severe risk of collision with hostile aircraft, making the atta ...

s intended to help protect Moscow from German bombers during the

Battle of Moscow The Battle of Moscow was a military campaign that consisted of two periods of strategically significant fighting on a sector of the Eastern Front during World War II, between October 1941 and January 1942. The Soviet defensive effort frustrated H ...

. In his study of

, especially

Markov process In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, ...

es, Kolmogorov and the British mathematician Sydney Chapman independently developed a pivotal set of equations in the field that have been given the name of the Chapman–Kolmogorov equations. Kolm complexity lect

Later, Kolmogorov focused his research on

, beginning his publications in 1941. In

, he is best known for the Kolmogorov–Arnold–Moser theorem, first presented in 1954 at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the IMU Abacus Medal (known before ...

. In 1957, working jointly with his student Vladimir Arnold, he solved a particular interpretation of Hilbert's thirteenth problem. Around this time he also began to develop, and has since been considered a founder of,

algorithmic complexity theory In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that prod ...

– often referred to as Kolmogorov complexity theory. Kolmogorov married Anna Dmitrievna Egorova in 1942. He pursued a vigorous teaching routine throughout his life both at the university level and also with younger children, as he was actively involved in developing a

pedagogy Pedagogy (), most commonly understood as the approach to teaching, is the theory and practice of learning, and how this process influences, and is influenced by, the social, political, and psychological development of learners. Pedagogy, taken ...

for gifted children in literature, music, and mathematics. At Moscow State University, Kolmogorov occupied different positions including the heads of several departments:

probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...

statistics Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

, and

random process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stoc ...

es;

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

. He also served as the Dean of the Moscow State University Department of Mechanics and Mathematics. In 1971, Kolmogorov joined an

oceanographic Oceanography (), also known as oceanology, sea science, ocean science, and marine science, is the scientific study of the ocean, including its physics, chemistry, biology, and geology. It is an Earth science, which covers a wide range of top ...

expedition aboard the research vessel ''

Dmitri Mendeleev Dmitri Ivanovich Mendeleev ( ; ) was a Russian chemist known for formulating the periodic law and creating a version of the periodic table of elements. He used the periodic law not only to correct the then-accepted properties of some known ele ...

.'' He wrote a number of articles for the ''

Great Soviet Encyclopedia The ''Great Soviet Encyclopedia'' (GSE; , ''BSE'') is one of the largest Russian-language encyclopedias, published in the Soviet Union from 1926 to 1990. After 2002, the encyclopedia's data was partially included into the later ''Great Russian Enc ...

.'' In his later years, he devoted much of his effort to the mathematical and philosophical relationship between

in abstract and applied areas. Kolmogorov died in Moscow in 1987 and his remains were buried in the

Novodevichy cemetery Novodevichy Cemetery () is a cemetery in Moscow. It lies next to the southern wall of the 16th-century Novodevichy Convent, which is the city's third most popular tourist site. History The cemetery was designed by Ivan Mashkov and inaugurated ...

. A quotation attributed to Kolmogorov is ranslated into English "Every mathematician believes that he is ahead of the others. The reason none state this belief in public is because they are intelligent people." Vladimir Arnold once said: "Kolmogorov –

Poincaré Poincaré is a French surname. Notable people with the surname include: * Henri Poincaré Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philos ...

–

Gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observat ...

–

Euler Leonhard Euler ( ; ; ; 15 April 170718 September 1783) was a Swiss polymath who was active as a mathematician, physicist, astronomer, logician, geographer, and engineer. He founded the studies of graph theory and topology and made influential ...

– Newton, are only five lives separating us from the source of our science."

Awards and honours

Kolmogorov received numerous awards and honours both during and after his lifetime: * Member of the

Russian Academy of Sciences The Russian Academy of Sciences (RAS; ''Rossíyskaya akadémiya naúk'') consists of the national academy of Russia; a network of scientific research institutes from across the Russian Federation; and additional scientific and social units such ...

* Awarded the Stalin Prize in 1941 * Elected an Honorary Member of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

in 1959 * Elected member of the

American Philosophical Society The American Philosophical Society (APS) is an American scholarly organization and learned society founded in 1743 in Philadelphia that promotes knowledge in the humanities and natural sciences through research, professional meetings, publicat ...

in 1961 * Awarded the Balzan Prize in 1962 * Elected a Foreign Member of the

Royal Netherlands Academy of Arts and Sciences The Royal Netherlands Academy of Arts and Sciences (, KNAW) is an organization dedicated to the advancement of science and literature in the Netherlands. The academy is housed in the Trippenhuis in Amsterdam. In addition to various advisory a ...

in 1963 * Elected a Foreign Member of the Royal Society (ForMemRS) in 1964. * Awarded the

Lenin Prize The Lenin Prize (, ) was one of the most prestigious awards of the Soviet Union for accomplishments relating to science, literature, arts, architecture, and technology. It was originally created on June 23, 1925, and awarded until 1934. During ...

in 1965 * Elected member of the United States

National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit, NGO, non-governmental organization. NAS is part of the National Academies of Sciences, Engineering, and Medicine, along with the National Academy of Engineering (NAE) and the ...

in 1967 * Awarded the

Wolf Prize The Wolf Prize is an international award granted in Israel, that has been presented most years since 1978 to living scientists and artists for "achievements in the interest of mankind and friendly relations among people ... irrespective of natio ...

in 1980 * Awarded the Lobachevsky Prize in 1986 The following are named in Kolmogorov's honour: * Fisher–Kolmogorov equation * Johnson–Mehl–Avrami–Kolmogorov equation * 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–Arnold theorem * Kolmogorov–Arnold–Moser theorem * Kolmogorov continuity theorem * Kolmogorov's criterion * Kolmogorov extension theorem * Kolmogorov's three-series theorem *

Convergence of Fourier series In mathematics, the question of whether the Fourier series of a given periodic function converges to the given function is researched by a field known as classical harmonic analysis, a branch of pure mathematics. Convergence is not necessarily gi ...

* Gnedenko-Kolmogorov central limit theorem * Quasi-arithmetic mean (it is also called Kolmogorov mean) * Kolmogorov homology * Kolmogorov's inequality * Landau–Kolmogorov inequality * Kolmogorov integral *

Brouwer–Heyting–Kolmogorov interpretation In mathematical logic, the Brouwer–Heyting–Kolmogorov interpretation, or BHK interpretation, is an explanation of the meaning of proof in intuitionistic logic, proposed by L. E. J. Brouwer and Arend Heyting, and independently by Andrey Kolmogor ...

* Kolmogorov microscales *

Kolmogorov's normability criterion In mathematics, Kolmogorov's normability criterion is a theorem that provides a necessary and sufficient condition for a topological vector space to be ; that is, for the existence of a norm on the space that generates the given topology. The nor ...

* Fréchet–Kolmogorov theorem *

Kolmogorov space In topology and related branches of mathematics, a topological space ''X'' is a T0 space or Kolmogorov space (named after Andrey Kolmogorov) if for every pair of distinct points of ''X'', at least one of them has a neighborhood not containing th ...

Kolmogorov complexity In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest computer program (in a predetermined programming language) that prod ...

Kolmogorov–Smirnov test In statistics, the Kolmogorov–Smirnov test (also K–S test or KS test) is a nonparametric statistics, nonparametric test of the equality of continuous (or discontinuous, see #Discrete and mixed null distribution, Section 2.2), one-dimensional ...

* Wiener filter (also known as Wiener–Kolmogorov filtering theory) * Wiener–Kolmogorov prediction * Kolmogorov automorphism * Kolmogorov's characterization of reversible diffusions * Borel–Kolmogorov paradox * Chapman–Kolmogorov equation * Hahn–Kolmogorov theorem * Johnson–Mehl–Avrami–Kolmogorov equation * Kolmogorov–Sinai entropy *

Astronomical seeing In astronomy, seeing is the degradation of the real image, image of an astronomical object due to turbulence in the atmosphere of Earth that may become visible as blurring, twinkling or variable Distortion (optics), distortion. The origin of this ...

described by Kolmogorov's turbulence law *

Kolmogorov structure function In 1973, Andrey Kolmogorov proposed a non-probabilistic approach to statistics and model selection. Let each datum be a finite binary string and a model be a finite set of binary strings. Consider model classes consisting of models of given maxim ...

* Kolmogorov–Uspenskii machine model * Kolmogorov's zero–one law * Kolmogorov–Zurbenko filter * Kolmogorov's two-series theorem * Rao–Blackwell–Kolmogorov theorem * Khinchin–Kolmogorov theorem * Kolmogorov population model * Kolmogorov's Strong

Law of Large Numbers In probability theory, the law of large numbers is a mathematical law that states that the average of the results obtained from a large number of independent random samples converges to the true value, if it exists. More formally, the law o ...

Bibliography

A bibliography of his works appeared in * ** Translation: * 1991–93. ''Selected works of A.N. Kolmogorov'', 3 vols. Tikhomirov, V. M., ed., Volosov, V. M., trans.

Dordrecht Dordrecht (), historically known in English as Dordt (still colloquially used in Dutch, ) or Dort, is a List of cities in the Netherlands by province, city and List of municipalities of the Netherlands, municipality in the Western Netherlands, lo ...

Kluwer Academic Publishers Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

. * 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. (2005) ''Selected works''. In 6 volumes. Moscow (in Russian) Textbooks: * A. N. Kolmogorov and B. V. Gnedenko. ''"Limit distributions for sums of independent random variables"'', 1954. * A. N. Kolmogorov and S. V. Fomin. ''"Elements of the Theory of Functions and Functional Analysis"''
Publication 1999Publication 2012
* Kolmogorov, Andrey Nikolaevich; Fomin, Sergei Vasilyevich (1975) 970 Introductory real analysis. New York: Dover Publications. ..

References

External links

Portal dedicated to AN Kolmogorov
(his scientific and popular publications, articles about him).
The Legacy of Andrei Nikolaevich Kolmogorov

Biography at Scholar''pedia''

* ttp://www.probabilityandfinance.com/articles/04.pdf 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 Professor A. M. Yaglom about Kolmogorov, Gelfand and other (1988, Ithaca, New York

Kolmogorov School
at Moscow University

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

* ttp://www.math.nsc.ru/LBRT/g2/english/ssk/case_e.html 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"
* {{DEFAULTSORT:Kolmogorov, Andrey 1903 births 1987 deaths 20th-century Russian educators 20th-century Russian mathematicians People from Tambov People from Tambovsky Uyezd Academicians of the USSR Academy of Pedagogical Sciences Corresponding members of the Romanian Academy Data compression researchers Fellows of the American Academy of Arts and Sciences Foreign associates of the National Academy of Sciences Foreign members of the Royal Society Full Members of the USSR Academy of Sciences Members of the American Philosophical Society Members of the French Academy of Sciences Members of the German Academy of Sciences at Berlin Members of the German National Academy of Sciences Leopoldina Members of the Royal Netherlands Academy of Arts and Sciences Moscow State University alumni Academic staff of Moscow State University Heroes of Socialist Labour Recipients of the Stalin Prize Recipients of the Lenin Prize Recipients of the Order of Lenin Recipients of the Order of the Red Banner of Labour Wolf Prize in Mathematics laureates Approximation theorists Control theorists Dynamical systems theorists Fluid dynamicists Historians of mathematics Measure theorists Probability theorists Soviet systems scientists Textbook writers Topologists Russian information theorists Russian logicians Russian statisticians Soviet educators Soviet logicians Soviet mathematicians Burials at Novodevichy Cemetery Russian scientists LGBTQ in Russia 20th-century Russian LGBTQ people