# Mathematician:Andrey Nikolaevich Kolmogorov

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## Mathematician

Russian mathematician active in various fields, including probability theory, topology and intuitionistic logic.

### Wolf Prize

Andrey Nikolaevich Kolmogorov was awarded a Wolf Prize for Mathematics in $\text {1980}$:

*For deep and original discoveries in Fourier analysis, probability theory, ergodic theory and dynamical systems.*

## Nationality

Russian

## History

- Born: April 25, 1903, Tambov, Russia
- Died: October 20, 1987, Moscow, Russia

## Theorems and Definitions

- Kolmogorov Complexity
- Kolmogorov Dimension (upper box dimension)
- Kolmogorov Microscales
- Kolmogorov Space (also known as a $T_0$ Space)

- Kolmogorov Backward Equation
- Kolmogorov's Characterization of Reversible Diffusions
- Kolmogorov Continuity Theorem
- Kolmogorov's Criterion
- Kolmogorov Forward Equation (also known as the Fokker-Planck Equation)
- Kolmogorov Extension Theorem
- Kolmogorov's Inequality
- Kolmogorov's Law, also known as the Strong Law of Large Numbers
- Kolmogorov's Submartingale Inequality, also known as Doob's Maximal Inequality or Doob's Martingale Inequality for Joseph Leo Doob
- Kolmogorov's Zero-One Law

- Kolmogorov-Arnold-Moser Theorem (with Vladimir Igorevich Arnold and Jürgen Kurt Moser)
- Kolmogorov-Smirnov Test (with Nikolai Vasilyevich Smirnov)

- Borel-Kolmogorov Paradox (with Émile Borel)
- Brouwer-Heyting-Kolmogorov Interpretation (independently of Bertus Brouwer and Arend Heyting)
- Chapman-Kolmogorov Equation (with Sydney Chapman)
- Chaitin-Kolmogorov Randomness (with Gregory John Chaitin)
- Fisher-Kolmogorov Equation (with Ronald Aylmer Fisher)
- Hahn-Kolmogorov Theorem (with Hans Hahn)
- Landau-Kolmogorov Inequality (with Edmund Landau)
- Rao-Blackwell-Kolmogorov Theorem (with Calyampudi Radhakrishna Rao and David Harold Blackwell)

Results named for **Andrey Nikolaevich Kolmogorov** can be found here.

Definitions of concepts named for **Andrey Nikolaevich Kolmogorov** can be found here.

Axioms named for **Andrey Nikolaevich Kolmogorov** can be found here.

## Publications

- 1925:
*On the principle of the excluded middle* - 1931:
*About the Analytical Methods of Probability Theory* - 1933:
*Grundbegriffe der Wahrscheinlichkeitsrechnung*(*Foundations of the Theory of Probability*) - 1938:
*Analytic methods in probability theory* - 1954:
*Limit distributions for sums of independent random variables*(with Boris Vladimirovich Gnedenko) - 1957:
*Elements of the Theory of Functions and Functional Analysis, Volume 1*(with S.V. Fomin (translated by Leo F. Boron) - 1961:
*Elements of the Theory of Functions and Functional Analysis, Volume 2*(with S.V. Fomin (translated by Leo F. Boron) - 1968:
*Introductory Real Analysis*(with Sergei Fomin) (translated into English, and rather severely and less-than-successfully edited, in 1970 by Richard A. Silverman, Dover Publications: ISBN 0-486-61226-0)

## Also known as

In Russian: **Андрей Николаевич Колмогоров**).

Various formulations can be seen in Latin script, for example **Andrei** for **Andrey**.

## Sources

- John J. O'Connor and Edmund F. Robertson: "Andrey Nikolaevich Kolmogorov": MacTutor History of Mathematics archive

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**Kolmogorov, Andrei Nikolaevich**(1903-87) - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**Kolmogorov, Andrei Nikolaevich**(1903-87) - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**Kolmogorov, Andrei Nikolaevich**(1903-87)