**Andrey Kolmogorov** was one of the developers of probability theory. He later used this work to study the motion of the planets and the turbulent flow of air from a jet engine.

- After Kolmogorov left school he worked for a while as a conductor on the railway.
- Then, in 1920, Kolmogorov entered Moscow State University but at this stage he was far from committed to mathematics.
- Kolmogorov may have told this story as a joke but nevertheless jokes are only funny if there is some truth in them and undoubtedly this is the case here.
- In mathematics Kolmogorov was influenced at an early stage by a number of outstanding mathematicians.
- P S Aleksandrov was beginning his research (for the second time) at Moscow around the time Kolmogorov began his undergraduate career.
- However the person who made the deepest impression on Kolmogorov at this time was Stepanov who lectured to him on trigonometric series.
- It is remarkable that Kolmogorov, although only an undergraduate, began research and produced results of international importance at this stage.
- This was wholly unexpected by the experts and Kolmogorov's name began to be known around the world.
- Kolmogorov graduated from Moscow State University in 1925 and began research under Luzin's supervision in that year.
- It is remarkable that Kolmogorov published eight papers in 1925, all written while he was still an undergraduate.
- Another milestone occurred in 1925, namely Kolmogorov's first paper on probability appeared.
- In 1929 Kolmogorov completed his doctorate.
- An important event for Kolmogorov was his friendship with Aleksandrov which began in the summer of 1929 when they spent three weeks together.
- There Aleksandrov worked on the topology book which he co-authored with Hopf, while Kolmogorov worked on Markov processes with continuous states and continuous time.
- Kolmogorov's results from his work by the Lake were published in 1931 and mark the beginning of diffusion theory.
- In the summer of 1931 Kolmogorov and Aleksandrov made another long trip.
- They visited Berlin, Göttingen, Munich, and Paris where Kolmogorov spent many hours in deep discussions with Paul Lévy.
- Aleksandrov and Kolmogorov bought a house in Komarovka, a small village outside Moscow, in 1935.
- Among them were Aleksandrov, Gelfand, Kolmogorov, Petrovsky, and Khinchin.
- The Department of Probability and Statistics was set up at the Institute and Kolmogorov was appointed as Head of Department.
- Kolmogorov later extended his work to study the motion of the planets and the turbulent flow of air from a jet engine.
- We must mention just a few of the numerous other major contributions which Kolmogorov made in a whole range of different areas of mathematics.
- In topology Kolmogorov introduced the notion of cohomology groups at much the same time, and independently of, Alexander.
- In 1934 Kolmogorov investigated chains, cochains, homology and cohomology of a finite cell complex.
- In further papers, published in 1936, Kolmogorov defined cohomology groups for an arbitrary locally compact topological space.
- At this conference both Kolmogorov and Alexander lectured on their independent work on cohomology.
- In 1953 and 1954 two papers by Kolmogorov, each of four pages in length, appeared.
- These papers mark the beginning of KAM-theory, which is named after Kolmogorov, Arnold and Moser.
- Kolmogorov addressed the International Congress of Mathematicians in Amsterdam in 1954 on this topic with his important talk General theory of dynamical systems and classical mechanics.
- If Kolmogorov made a major contribution to Hilbert's sixth problem, he completely solved Hilbert's Thirteenth Problem in 1957 when he showed that Hilbert was wrong in asking for a proof that there exist continuous functions of three variables which could not be represented by continuous functions of two variables.
- Such an outstanding scientist as Kolmogorov naturally received a whole host of honours from many different countries.
- In addition to the prizes mentioned above, Kolmogorov was awarded the Balzan International Prize in 1962.
- Kolmogorov had many interests outside mathematics, in particular he was interested in the form and structure of the poetry of the Russian author Pushkin.

Born 25 April 1903, Tambov, Tambov province, Russia. Died 20 October 1987, Moscow, Russia.

View full biography at MacTutor

Origin Russia, Statistics, Topology, Prize Wolf

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive