Mathematician:Andrey Nikolaevich Kolmogorov

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 Axioms

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

• Kolmogorov-Sinai Entropy (with Yakov Grigorevich Sinai)
• Kolmogorov-Smirnov Test (with Nikolai Vasilyevich Smirnov)

• Kolmogorov Backward Equation
• Kolmogorov's Characterization of Reversible Diffusions
• Kolmogorov Continuity Theorem
• Kolmogorov's Criterion
  • Kolmogorov's Generalized 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)

• 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
  • 1950: 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

Kolmogoroff for Kolmogorov

and so on.

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)