Andrey Kolmogorov was born inTambov, about 500 kilometers southeast ofMoscow, in 1903. His unmarried mother, Maria Yakovlevna Kolmogorova, died giving birth to him.[8] Andrey was raised by two of his aunts inTunoshna (nearYaroslavl) at the estate of his grandfather, a well-to-donobleman.
Little is known about Andrey's father. He was supposedly named Nikolai Matveyevich Katayev and had been anagronomist. Katayev had been exiled fromSaint Petersburg to the Yaroslavl province after his participation in the revolutionary movement against thetsars. He disappeared in 1919 and was presumed to have been killed in theRussian Civil War.
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 interest in mathematics was spurred when he noticed, at the age of six, the regularity in the sum of the series of odd numbers: etc.[9]
In 1910, his aunt adopted him, and they moved to Moscow, where he graduated fromhigh school in 1920. Later that same year, Kolmogorov began to study atMoscow State University and at the same timeMendeleev Moscow Institute of Chemistry and Technology.[10] Kolmogorov writes about this time: "I arrived at Moscow University with a fair knowledge of mathematics. I knew in particular the beginning ofset theory. I studied many questions in articles in theEncyclopedia of Brockhaus and Efron, filling out for myself what was presented too concisely in these articles."[11]
Kolmogorov gained a reputation for his wide-ranging erudition. While an undergraduate student in college, he attended the seminars of the Russian historianS. V. Bakhrushin, and he published his first research paper on the fifteenth and sixteenth centuries'landholding practices in theNovgorod Republic.[12] During the same period (1921–22), Kolmogorov worked out and proved several results inset theory and in the theory ofFourier series.
In 1925, Kolmogorov graduated fromMoscow State University and began to study under the supervision ofNikolai Luzin.[3] He formed a lifelong close friendship withPavel Alexandrov, a fellow student of Luzin; indeed, several researchers have concluded that the two friends were sexually involved,[15][16][17] although neither acknowledged this openly. Kolmogorov (together withAleksandr Khinchin) became interested inprobability theory. Also in 1925, he published his work inintuitionistic 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 degree from Moscow State University. In 1929, Kolmogorov and Alexandrov during a long travel stayed about a month in an island in lakeSevan in Armenia.[18]
In 1930, Kolmogorov went on his first long trip abroad, traveling toGöttingen andMunich and then toParis. He had various scientific contacts in Göttingen, first withRichard Courant and his students working on limit theorems, wherediffusion processes proved to be the limits of discrete random processes, then withHermann Weyl in intuitionistic logic, and lastly withEdmund Landau in function theory. His pioneering workAbout the Analytical Methods of Probability Theory was published (in German) in 1931. Also in 1931, he became a professor atMoscow State University.
In 1933, Kolmogorov published his bookFoundations of the Theory of Probability, laying the modern axiomaticfoundations 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 theLotka–Volterra model ofpredator–prey systems.
During theGreat Purge in 1936, Kolmogorov's doctoral advisorNikolai Luzin 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 theAcademy of Sciences of the Soviet Union.[19][20] 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 mathematicianSemën 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.[21] Soviet historian of mathematicsA.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.[22]
In a 1938 paper, Kolmogorov "established the basic theorems for smoothing and predicting stationarystochastic processes"—a paper that had major military applications during theCold War.[23] In 1939, he was elected a full member (academician) of theUSSR Academy of Sciences.
DuringWorld War II Kolmogorov contributed to the Soviet war effort by applying statistical theory to artillery fire, developing a scheme of stochastic distribution ofbarrage balloons intended to help protect Moscow from German bombers during theBattle of Moscow.[24]
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 apedagogy for gifted children in literature, music, and mathematics. At Moscow State University, Kolmogorov occupied different positions including the heads of several departments:probability,statistics, andrandom processes;mathematical logic. He also served as the Dean of the Moscow State University Department of Mechanics and Mathematics.
In 1971, Kolmogorov joined anoceanographic expedition aboard the research vesselDmitri Mendeleev. He wrote a number of articles for theGreat Soviet Encyclopedia. In his later years, he devoted much of his effort to the mathematical and philosophical relationship betweenprobability theory in abstract and applied areas.[25]
Kolmogorov died in Moscow in 1987 and his remains were buried in theNovodevichy cemetery.
A quotation attributed to Kolmogorov is [translated 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."
1925. "On the principle of the excluded middle" inJean van Heijenoort, 1967.A Source Book in Mathematical Logic, 1879–1931. Harvard Univ. Press: 414–37.
Kolmogorov, Andrey Nikolaevich; Fomin, Sergei Vasilyevich (1975) [1970]Introductory Real Analysis, New York: Dover Publications.ISBN978-0-486-61226-3..
^Gessen, Masha (2011).Perfect Rigour: A Genius and the Mathematical Breakthrough of a Lifetime. Icon Books Ltd. p. 17.Kolmogorov alone among the top Soviet mathematicians avoided being drafted into the postwar military effort. His students always wondered why-and the only likely explanation seems to be Kolmogorov's homosexuality. His lifelong partner, with whom he shared a home starting in 1929, was the topologist Pavel Alexandrov.
