Early life Andrey Kolmogorov was born in
Tambov, about 500 kilometers southeast of
Moscow, 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) at the estate of his grandfather, a well-to-do
nobleman. Little is known about Andrey's father. He was supposedly named Nikolai Matveyevich Katayev and had been an
agronomist. Katayev had been exiled from
Saint Petersburg to the Yaroslavl province after his participation in the revolutionary movement against the
tsars. He disappeared in 1919 and was presumed to have been killed in the
Russian 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: 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 in 1920. Later that same year, Kolmogorov began to study at
Moscow State University 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. 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. 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
Moscow State University and began to study under the supervision of
Nikolai Luzin. He formed a lifelong close friendship with
Pavel Alexandrov, 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
probability theory. Also in 1925, he published his 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 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 and
Munich and then to
Paris. He had various scientific contacts in Göttingen, first with
Richard Courant and his students working on limit theorems, where
diffusion processes proved to be the limits of discrete random processes, then with
Hermann Weyl in intuitionistic logic, and lastly with
Edmund Landau 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
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 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. During the
Great Purge in 1936, Kolmogorov's doctoral advisor
Nikolai 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 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"—a paper that had major military applications during the
Cold War. In 1939, he was elected a full member (academician) of the
USSR Academy of Sciences. During
World War II Kolmogorov contributed to the Soviet war effort by applying statistical theory to artillery fire, developing a scheme of stochastic distribution of
barrage balloons intended to help protect Moscow from German bombers during the
Battle of Moscow. In his study of
stochastic processes, especially
Markov processes, 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. , 1973) , 1973) Later, Kolmogorov focused his research on
turbulence, beginning his publications in 1941. In
classical mechanics, he is best known for the
Kolmogorov–Arnold–Moser theorem, first presented in 1954 at the
International Congress of Mathematicians. 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 of the others. The reason none state this belief in public is because they are intelligent people."
Vladimir Arnold once said: "Kolmogorov –
Poincaré –
Gauss –
Euler –
Newton, are only five lives separating us from the source of our science." ==Awards and honours==