Andrey Kolmogorov

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In this Eastern Slavic name, the patronymic is Nikolaevich and the family name is Kolmogorov. Andrey Kolmogorov_sentence_0

Andrey Kolmogorov_table_infobox_0

Andrey KolmogorovAndrey Kolmogorov_header_cell_0_0_0
BornAndrey Kolmogorov_header_cell_0_1_0 Andrey Nikolaevich Kolmogorov

(1903-04-25)25 April 1903 Tambov, Russian EmpireAndrey Kolmogorov_cell_0_1_1

DiedAndrey Kolmogorov_header_cell_0_2_0 20 October 1987(1987-10-20) (aged 84)

Moscow, Russian SFSR, Soviet UnionAndrey Kolmogorov_cell_0_2_1

CitizenshipAndrey Kolmogorov_header_cell_0_3_0 Soviet UnionAndrey Kolmogorov_cell_0_3_1
Alma materAndrey Kolmogorov_header_cell_0_4_0 Moscow State University (Ph.D.)Andrey Kolmogorov_cell_0_4_1
Known forAndrey Kolmogorov_header_cell_0_5_0 Andrey Kolmogorov_cell_0_5_1
Spouse(s)Andrey Kolmogorov_header_cell_0_6_0 Anna Dmitrievna Egorova

​ ​(m. 1942⁠–⁠1987)​Andrey Kolmogorov_cell_0_6_1

AwardsAndrey Kolmogorov_header_cell_0_7_0 Andrey Kolmogorov_cell_0_7_1
FieldsAndrey Kolmogorov_header_cell_0_8_0 MathematicsAndrey Kolmogorov_cell_0_8_1
InstitutionsAndrey Kolmogorov_header_cell_0_9_0 Moscow State UniversityAndrey Kolmogorov_cell_0_9_1
Doctoral advisorAndrey Kolmogorov_header_cell_0_10_0 Nikolai LuzinAndrey Kolmogorov_cell_0_10_1
Doctoral studentsAndrey Kolmogorov_header_cell_0_11_0 Andrey Kolmogorov_cell_0_11_1

Andrey Nikolaevich Kolmogorov (Russian: Андре́й Никола́евич Колмого́ров, IPA: [ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf (listen), 25 April 1903 – 20 October 1987) was a Soviet mathematician who made significant contributions to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity. Andrey Kolmogorov_sentence_1

Biography Andrey Kolmogorov_section_0

Early life Andrey Kolmogorov_section_1

Andrey Kolmogorov was born in Tambov, about 500 kilometers south-southeast of Moscow, in 1903. Andrey Kolmogorov_sentence_2

His unmarried mother, Maria Y. Kolmogorova, died giving birth to him. Andrey Kolmogorov_sentence_3

Andrey was raised by two of his aunts in Tunoshna (near Yaroslavl) at the estate of his grandfather, a well-to-do nobleman. Andrey Kolmogorov_sentence_4

Little is known about Andrey's father. Andrey Kolmogorov_sentence_5

He was supposedly named Nikolai Matveevich Kataev and had been an agronomist. Andrey Kolmogorov_sentence_6

Nikolai had been exiled from St. Andrey Kolmogorov_sentence_7 Petersburg to the Yaroslavl province after his participation in the revolutionary movement against the czars. Andrey Kolmogorov_sentence_8

He disappeared in 1919 and was presumed to have been killed in the Russian Civil War. Andrey Kolmogorov_sentence_9

In 1910, his aunt adopted him, and they moved to Moscow, where he graduated from high school in 1920. Andrey Kolmogorov_sentence_10

Later that same year, Kolmogorov began to study at the Moscow State University and at the same time Mendeleev Moscow Institute of Chemistry and Technology. Andrey Kolmogorov_sentence_11

Kolmogorov writes about this time: "I arrived at Moscow University with a fair knowledge of mathematics. Andrey Kolmogorov_sentence_12

I knew in particular the beginning of set theory. Andrey Kolmogorov_sentence_13

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." Andrey Kolmogorov_sentence_14

Kolmogorov gained a reputation for his wide-ranging erudition. Andrey Kolmogorov_sentence_15

While 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. Andrey Kolmogorov_sentence_16

During the same period (1921–22), Kolmogorov worked out and proved several results in set theory and in the theory of Fourier series. Andrey Kolmogorov_sentence_17

Adulthood Andrey Kolmogorov_section_2

In 1922, Kolmogorov gained international recognition for constructing a Fourier series that diverges almost everywhere. Andrey Kolmogorov_sentence_18

Around this time, he decided to devote his life to mathematics. Andrey Kolmogorov_sentence_19

In 1925, Kolmogorov graduated from the Moscow State University and began to study under the supervision of Nikolai Luzin. Andrey Kolmogorov_sentence_20

He formed a lifelong close friendship with Pavel Alexandrov, a fellow student of Luzin. Andrey Kolmogorov_sentence_21

Kolmogorov (together with Aleksandr Khinchin) became interested in probability theory. Andrey Kolmogorov_sentence_22

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. Andrey Kolmogorov_sentence_23

In 1929, Kolmogorov earned his Doctor of Philosophy (Ph.D.) degree, from Moscow State University. Andrey Kolmogorov_sentence_24

In 1930, Kolmogorov went on his first long trip abroad, traveling to Göttingen and Munich, and then to Paris. Andrey Kolmogorov_sentence_25

He had various scientific contacts in Göttingen, first with Richard Courant and his students working on limit theorems, where diffusion processes turned out to be the limits of discrete random processes, then with Hermann Weyl in intuitionistic logic, and lastly with Edmund Landau in function theory. Andrey Kolmogorov_sentence_26

His pioneering work, About the Analytical Methods of Probability Theory, was published (in German) in 1931. Andrey Kolmogorov_sentence_27

Also in 1931, he became a professor at the Moscow State University. Andrey Kolmogorov_sentence_28

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. Andrey Kolmogorov_sentence_29

In 1935, Kolmogorov became the first chairman of the department of probability theory at the Moscow State University. Andrey Kolmogorov_sentence_30

Around the same years (1936) Kolmogorov contributed to the field of ecology and generalized the Lotka–Volterra model of predator-prey systems. Andrey Kolmogorov_sentence_31

In 1936, Kolmogorov and Alexandrov were involved in the political persecution of their common teacher Nikolai Luzin, in the so-called Luzin affair. Andrey Kolmogorov_sentence_32

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. Andrey Kolmogorov_sentence_33

In 1939, he was elected a full member (academician) of the USSR Academy of Sciences. Andrey Kolmogorov_sentence_34

During World War II Kolmogorov contributed to the Russian 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. Andrey Kolmogorov_sentence_35

In his study of stochastic 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. Andrey Kolmogorov_sentence_36

Later, Kolmogorov focused his research on turbulence, where his publications (beginning in 1941) significantly influenced the field. Andrey Kolmogorov_sentence_37

In classical mechanics, he is best known for the Kolmogorov–Arnold–Moser theorem, first presented in 1954 at the International Congress of Mathematicians. Andrey Kolmogorov_sentence_38

In 1957, working jointly with his student Vladimir Arnold, he solved a particular interpretation of Hilbert's thirteenth problem. Andrey Kolmogorov_sentence_39

Around this time he also began to develop, and was considered a founder of, algorithmic complexity theory – often referred to as Kolmogorov complexity theory. Andrey Kolmogorov_sentence_40

Kolmogorov married Anna Dmitrievna Egorova in 1942. Andrey Kolmogorov_sentence_41

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). Andrey Kolmogorov_sentence_42

At the Moscow State University, Kolmogorov occupied different positions, including the heads of several departments: probability, statistics, and random processes; mathematical logic. Andrey Kolmogorov_sentence_43

He also served as the Dean of the Moscow State University Department of Mechanics and Mathematics. Andrey Kolmogorov_sentence_44

In 1971, Kolmogorov joined an oceanographic expedition aboard the research vessel Dmitri Mendeleev. Andrey Kolmogorov_sentence_45

He wrote a number of articles for the Great Soviet Encyclopedia. Andrey Kolmogorov_sentence_46

In his later years, he devoted much of his effort to the mathematical and philosophical relationship between probability theory in abstract and applied areas. Andrey Kolmogorov_sentence_47

Kolmogorov died in Moscow in 1987, and his remains were buried in the Novodevichy cemetery. Andrey Kolmogorov_sentence_48

A quotation attributed to Kolmogorov is [translated into English]: "Every mathematician believes that he is ahead of the others. Andrey Kolmogorov_sentence_49

The reason none state this belief in public is because they are intelligent people." Andrey Kolmogorov_sentence_50

Vladimir Arnold once said: "Kolmogorov – PoincaréGaussEulerNewton, are only five lives separating us from the source of our science". Andrey Kolmogorov_sentence_51

Awards and honours Andrey Kolmogorov_section_3

Kolmogorov received numerous awards and honours both during and after his lifetime: Andrey Kolmogorov_sentence_52

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The following are named in Kolmogorov's honour: Andrey Kolmogorov_sentence_53

Credits to the contents of this page go to the authors of the corresponding Wikipedia page: Kolmogorov.