Math symbols
About us
Contact us
Site map
Search The Site
   Program of Lessons
Study Guide
Topics of problems
Tests & exams
www.bymath.com Study Guide - Arithmetic Study Guide - Algebra Study Guide - Geometry Study Guide - Trigonometry Study Guide - Functions & Graphs Study Guide - Principles of Analysis Study Guide - Sets Study Guide - Probability Study Guide - Analytic Geometry Select topic of problems Select test & exam


Andrey Nikolaevich Kolmogorov (1903 – 1987) was a great Soviet mathematician, preeminent in the 20th century, who advanced various scientific fields, among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity.
Foreign member of the National academy of sciences of the USA (1967), the London royal society (1964), a member of the German academy of scientists «Leopoldina» (1959), the French (Parisian) academy of sciences (1968), the honorary member of the American academy of arts and sciences (1959), a foreign member of the Hungarian academy of sciences (1965), the Polish academy of sciences (1956), the Netherlands royal academy of sciences (1963), the Academy of sciences of Finland (1985), the honorary member of the Romanian academy. A member of the London mathematical society (1962), the Indian mathematical society (1962), a foreign member of the American philosophical society (1961). Kolmogorov – the honourable doctor of the Parisian university (Ñîðáîííû) (1955), the Stockholm university (1960), the Indian statistical college in Calcutta (1962).
A.N.Kolmogorov – the founder of the big scientific school, among its disciples: V.I.Arnold, I.M.Gelfand, V.M.Alekseev, G.I.Barenblatt, A.A.Borovkov, A.G.Vitushkin, B.V.Gnedenko, R.L.Dobrushin, E.B.Dynkin, A.I.Maltsev, M.D.Millionshchikov, V.S.Mihalevich, A.S.Monin, S.M.Nikolsky, A.M.Obuhov, J.V.Prohorov, J.G.Sinaj, V.M.Tihomirov, J.N.Tjurin, A.N.Shirjaev, V.A.Uspensky, C.Â.Ôîìèí, A.M.Jaglom and many other things known mathematicians.
Andrey Nikolaevich Kolmogorov was born at Tambov in 1903. His unwed mother died in childbirth and he was raised by his aunts in Tunoshna near Yaroslavl at the estate of his grandfather, a wealthy nobleman. His father, an agronomist by trade, was deported from Saint-Petersburg for participation in the revolutionary movement. He disappeared and was presumed to have been killed in the Russian Civil War.
Andrey Nikolaevich Kolmogorov was brought up in Yaroslavl by sisters of mother, one of them, Vera Jakovlevna Kolmogorov, has officially adopted Andrey and per 1910 has moved with it to Moscow for definition in a grammar school. Andrey's aunts have organized in the house a school for children of different age who lived nearby, were engaged with them, for children hand-written magazine «Spring swallows» was published. Creative works of disciples were published In it — pictures, verses, stories. In it appeared and «scientific works» Andrey — the arithmetic problems thought up by it. Here the boy has published the first work on the mathematician in five years. Andrey Nikolaevich recalled: «Pleasure mathematical" opening "I ïîçíàë early, having noticed in the age of five-six years law: 1 = 12, 1 + 3 = 22, 1 + 3 + 5 = 32... ». 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 University and 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. At the same time (1921–1922), Kolmogorov derived and proved several results in set theory and in the theory of Fourier series (trigonometrical series).
In 1921 Kolmogorov does the first scientific report to a mathematical study group in which denies one improvised N.N.Luzina's statement which it has applied at lecture at the proof of Caushi's theorem. When Kolmogorov has made the first opening in the field of trigonometrical numbers, and in the beginning of 1922 — under the descriptive theory of sets, Luzin has suggested it to become its disciple — so Kolmogorov has entered numbers "Luzitania" - so Luzin's school was named. In 1922 Kolmogorov constructed a Fourier series that diverges almost everywhere, gaining international recognition. This work has brought to the 19th years of old student world popularity. Discussed in the middle of the 1920th years everywhere, including in Moscow, questions of the bases of the mathematical analysis and it is close with them the associated researches on mathematical logic have drawn Kolmogorov's attention almost right at the beginning of his work. He has taken part in discussions between two the basic resisted then methodological schools – is formal-axiomatic (D.Gilbert) and intuitionistic one (L.Brauer and G.Weil). Thus it has received absolutely unexpected first class result, having proved, that known offers of classical formal logic at the certain interpretation pass all in offers intuitionistic logic — his famous work «On the principle of the excluded middle» was dated in 1925 year. The great interest in philosophy of mathematics Kolmogorov has kept for ever.
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 Nikolaevich Luzin. He made lifelong friends with Pavel Alexandrov. Both were involved in 1936 in political persecution of their common teacher Nikolai Luzin, the so-called "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, where 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, Ph.D., at the Moscow State University.
In 1930, Kolmogorov went on his first long trip abroad, traveling to Gottingen and 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 War to come. Around the same years (1936) Kolmogorov contributed to the field of ecology and generalized the Lotka–Volterra model of predator-prey systems.
In his study of stochastic processes (random processes), especially Markov processes, Kolmogorov and the British mathematician Sydney Chapman independently 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 1946, after war, it again comes back to these questions. He has organized laboratory of atmospheric turbulence in Institute of theoretical geophysics of the USSR Academy of Sciences. In parallel with works on this problem Kolmogorov continues successful activity in many areas of mathematics – the researches devoted to accidental processes, algebraic topology, etc.
In the end of 1940s A.N.Kolmogorov was the first lecturer of a rate of the theory of functions and functional analysis at Mechanical-and-Mathematical faculty of the Moscow State University. Together with S.V.Fomin he has written the textbook «Elements of the theory of functions and the functional analysis», the sustained seven editions (the 7th edit. – 2012), as well as translated on foreign languages: English, French, German, Spanish, Japanese, Czech, etc.
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 a particular interpretation of Hilbert's 13th 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 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 theory in abstract and applied areas.
In 1963 A.N.Kolmogorov acts as one of initiators of creation of a boarding school at the Moscow State University and itself starts to teach there. In 1970 together with academician I.K.Kikoinym creates magazine "Quantum". In recent years Kolmogorov managed faculty of mathematical logic in the Moscow State University and taught at physical and mathematical school ¹18 at the Moscow State University (nowadays – the Special Study Research Centre of the Moscow State University of a name of A.N.Kolmogorov). On neat expression of Stefan Banach: «The mathematician is the one who is able to find analogies between statements. The best mathematician – who establishes analogies of proofs. The stronger mathematician can notice analogies of theories. But is also such mathematician who between analogies sees analogies». Andrey Nikolaevich Kolmogorov concerns to these rare representatives of the last – one of the largest mathematicians of the 20th century also.
Kolmogorov died in Moscow in 1987 and is buried at the Novodevichy cemetery.
A quotation attributed to him is: "Every mathematician believes he is ahead over all others. The reason why they don't say this in public is because they are intelligent people."

| Math symbols | Jokes | Responses About us | Links | Contact us | Site map |

Copyright © 2002-2012 Dr. Yury Berengard.  All rights reserved.
Last updated: August 10, 2012