# Andrei Kolmogorov

Andrei Nikolaevich Kolmogorov (April 25, 1903 - October 20, 1987) was a Russian mathematician who made major advances in different scientific fields (among them probability theory, the theory of algorithms, topology, analysis, and intuitionistic logic).

He was born in 1903 (at Tambov, where his mother stopped on her way to Crimea). 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 St Petersburg for participation in the revolutionary movement. He went missing in the Russian Civil War.

Kolmogorov was educated in his aunts' village school. In 1910 his aunt adopted him and they moved to Moscow, where he went to a gymnasium, graduating from it in 1920.

In 1920 Kolmogorov began to study at Moscow University and the Chemistry Technological Institute. As an undergraduate, he participated in the seminar of Russian historian Bachrushin and published his first research paper on landholding practices in the Novgorod Republic in the fifteenth and sixteenth centuries. At the same time (1921 - 1922), Kolmogorov obtained several results in set theory and the theory of trigonometrical series.

In 1922 Kolmogorov constructed a Fourier series that diverges almost everywhere, gaining international recognition. 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 made lifelong friends with Pavel Alexandrov, who involved Kolmogorov in 1936 in an ugly political persecution of their mutual teacher, the so-called Luzin affair. Kolmogorov (together with Khinchin) became interested in probability theory. Also in 1925, he published his famous work in intuitionistic logic, *On the principle of the excluded middle*. In 1929 Kolmogorov earned his PhD at Moscow State University.

In 1930 Kolmogorov went on his first long trip abroad, traveling to Göttingen, Munich, and then to Paris. His pioneering work *About the analytical methods of probability theory* was published (in German) in 1931, the same year he became a professor at Moscow University. In 1933 Kolmogorov published his book *Foundations of the theory of probability* (known as Grundbegriffe, after its original German title), laying the modern measure-theoretic foundations of probability theory. In 1935, Kolmogorov became the first chair of probability theory at the Faculty of Mathematics and Mechanics of Moscow State University. In 1939 he was elected a full member (academician) of the USSR Academy of Sciences. In a 1938 paper he "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.

Kolmogorov married Anna Dmitrievna Egorova in 1942. 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 and music as well as mathematics. At the university, he occupied different positions, including the head of several departments (probability, statistics and random processes, mathematical logic) and also served as dean of the Faculty of Mechanics and Mathematics.

Kolmogorov was a founder of algorithmic complexity theory, often referred to as Kolmogorov complexity theory, which he began to develop around 1960. The theory of algorithmic complexity served for Kolmogorov as the foundation for his theories of algorithmic randomness and algorithmic information.

Kolmogorov 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 theoretical probability (for which, in his opinion, his measure-theoretic axioms were sufficient) and the applications of probability (where he preferred von Mises's version of game-theoretic probability).

For further information, see Kolmogorov's Wikipedia entry (on which this article is partly based).