One of the most important scientists of the past century: who is Andrey Kolmogorov?

This makes him one of the most important scientists of the past century.

Andrei Nikolaevich Kolmogorov (25 April 1903 – 20 October 1987) was born in Tambov, Russia had an aristocratic family and was raised by his aunt when he lost his mother at an early age. In 1910, his aunt adopted him, and in 1920 they moved to Moscow, where he graduated from high school. Later that year, he began working at Moscow State University, as well as at the Mendeleev Moscow Institute of Chemistry and Technology. After graduating in 1925, he extended his stay at the university for another four years as a research student and completed his doctorate in 1929.

This year has a special significance in Kolmogorov's life. Their friendship that started with Pavel Sergeevich Alexandrov (1896 – 1982), a mathematician like himself, turned into one of the most important events of his life. Taking long vacations together, these two mathematicians bought a house in Komarovka, a small village outside of Moscow, in 1935, and this house also hosted other famous mathematicians.

Andrey Nikolaevich Kolmogorov (25 April 1903 – 20 October 1987) was a Soviet mathematician who contributed to the mathematics of probability theory, topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity.

Kolmogorov, who became a Professor at Moscow University in 1931, besides his hard work in mathematics and science, devoted most of his time to improving the teaching of mathematics in secondary schools in the Soviet Union and creating special schools for mathematics-gifted students. He married Anna Dmitriyevna Egorov in 1942. Especially after the search for meaning and formal structure in the background of Pushkin's works, Kolmogorov is also very interested in studies of Russian poetry.

Early Years: 1903-1933

Kolmogorov is interested in Russian history and mathematics from the earliest times. In mathematics, Kolmogorov's early topics included set theory, projective geometry, and the theory of analytic functions. Between 1921 and 1922, he achieved his first independent mathematical success as a result of his work on the Fourier (French Mathematician, 1768 -1830) Series (the existence of the Fourier-Lebesgue series with arbitrarily slowly decreasing Fourier coefficients) and Nikolai Luzin (Russian Mathematician, 1883 – 1950) becomes his student.

Kolmogorov became interested in mathematical logic and in 1925 published an article on the theory of "the law of the excluded middle", which became a constant source for later work in this field. This publication is the first Soviet publication containing (very important) new results on mathematical logic and the first systematic research in the world on intuitive logic.

Kolmogorov established a more precise relationship between classical and intuitive mathematics, largely anticipating the intuitive reasoning formatting of A Heyting (Dutch Mathematician and Logician, 1898 – 1980). Thus he defined an operation to "embed" one logical theory into another.

His interest in probability theory began in 1924. He took the first steps in this field together with Aleksandr Yakovlevich Khinchin (Russian Mathematician, 1894 – 1959). In 1928 he succeeded in finding the necessary and sufficient conditions for the preservation of the "strong law of large numbers" and proved the iterated law of logarithms for sums of independent random variables on sums under very general conditions.

In 1929, he put forward the first draft of the "general measure theory and calculus of probabilities", that is, the axiom system for probability theory, based on the theory of functions of a real variable and measure theory. Such a theory was first proposed by E Borel (French Mathematician, 1871 – 1956) in 1909, was further developed by Lomnicki (Polish Mathematician, 1881 – 1941) in 1923, and was very successfully finalized by Kolmogorov's analysis in 1933. took shape.

There are already very important studies on probability theory; However, he showed the formulation of the subject in his book "Foundations of the Calculus of Probabilities" published in 1933. This book not only marked a new stage in the development of probability theory as a branch of mathematics; he also explained the basis of the "theory of random processes", which was the subject of Kolmogorov's article published in 1931.

In 1931, Kolmogorov's article “Analytical Methods in Probability Theory” is published, in which he laid the foundations of the modern theory of Markov (Russian Mathematician, 1856 – 1922) processes. In Markov processes, only the current state has any bearing on the probability of future states; therefore 'situations' are said to hold no 'memory' of past events. Kolmogorov invented a pair of functions to characterize transition probabilities in a Markov process and showed that they correspond to what he calls "instantaneous mean" and "instantaneous variance".

Between 1930 and 1940 Kolmogorov, especially probability theory, which affected the history of philosophy and mathematics; published more than sixty articles on projective geometry, mathematical statistics, theory of functions of a real variable, topology, harmonic analysis, mathematical logic, and mathematical biology.

Subsequent Years: 1960-1987

While Kolmogorov initially used the concepts of information theory in mathematical sciences, in the following years he tried to reconstruct information theory on the theory of algorithms. It creates a research circle by giving logical-algorithmic foundations to the theory of random probability. With “Algorithmic Information Theory”- “Kolmogorov complexity”, Kolmogorov is the pioneer of the development of today's computers.

Perhaps the last mathematical innovation of his outstanding scientific career was Kolmogorov's discovery of a statistical theory in 1973 on independent finite combinatorial principles. The new statistics to be obtained by the technique of this study are expressed in terms of Kolmogorov complexity.

Perspective on Teaching

Kolmogorov's pedagogical activities began in 1922 when he became a teacher at the Experimental Model School of the People's Commissariat of Education. He taught there until 1925, and then immediately worked as a lecturer at the university from 1925 to 1929.

Scientific Career

Kolmogorov graduated from his university education, which he started in 1920, in 1925, and received his doctorate in 1929. By 1931, at the age of 28, he became a professor at Moscow University.

Between 1933 and 1939, he worked as the "Director of Scientific Research Mathematics Institute" at the same university. During this duty, he also deals with the scientific research of all graduate students and the Sunday walks he organizes with both graduates and students in the academy become a classic. In 1939, Kolmogorov was elected to the All-Union Academies of the Sciences and Physics-Mathematics Department. He does tremendous work as chairman of the mathematics editorial board of the Foreign Literary Publishing House and editor of the mathematics section of the Great Soviet Encyclopedia.

From 1964 to 1966 and from 1976 to 1983 Kolmogorov, President of the Moscow Mathematical Society; was the Editor-in-Chief of Uspekhi Math from 1946 until his death. From 1938 to 1966 he was the head of the branch of probability theory at Moscow University. He was head of the Interdepartmental Statistical Methods Laboratory from 1966 to 1976 and chaired the branch of mathematical statistics from 1976 to 1980. He left this post in 1980 to head the branch of mathematical logic.

Although he suffered from Parkinson's disease and spent the last few years of his life almost blind, he continued to take an active interest in the world of mathematics until his death. Undoubtedly, a name beyond his time with his scientific understanding and educator identity, far from political life, Kolmogorov also deserves respect for his idealistic personality and continues to be a source of inspiration for many people.