The Legacy of A. N. Kolmogorov

April 25, 1903 - October 20, 1987

**8 October 1922**

Example of a Fourier-Lebesque trigonometric series that diverges almost everywhere.

**
5 April 1925**

On the possibility of a general definition of derivative, integral, and sum of a series.

**
16 November 1926**

The Fourier series that diverges everywhere.

**
7 December 1926**

The double negation principle and the definition of a function.

**
6 December 1927**

A generalization of Chebyshev's theorem.

**
20 March 1928**

On a general scheme in probability theory.

**
18 December 1928**

A new interpretation of intuitionistic logic.

**
4 April 1931**

A scientific trip to Berlin and Goettingen.

**
29 April 1931**

Modern problems of probability theory.

**
11 December 1932**

On geometry ideas of Plücker and Klein.

**
11 November 1934**

On contingencies, jointly with I. Ya. Verchenko.

**
11 December 1934**

A supplementary communication (see 11/Nov/1934)

**
5 January 1935**

Markov chains and reversibility of laws of nature.

**
16 February 1937**

The statistical theory of crystallization of hardening metals.

**
22 April 1937**

On differentiability properties of functions of two variables.

**
10 November 1937**

The development in the USSR of mathematical methods for learning about nature
(differential and integral equations and probability theory).

**
22, 28 November 1937**

Meetings devoted to a discussion of a plan to put together
a new elementary algebra textbook
(by P. S. Aleksandrov and A. N. Kolmogorov). Two meetings.

**
10 or 16 March 1938** (exact date uncertain)

Meeting devoted to a discussion of the draft of Kolmogorov's article
"Mathematics"
for the *Great Soviet Encyclopedia*.

**
22 December 1938**

Contemporary questions in set-theoretic geometry (servey report).

**
16 February 1939**

On principles for estimating the reliability of statistical hypotheses (survey report).

**
22 March 1939**

On the extrapolation of stationary series in dependence on the nature of their spectra.

**
4 June 1939**

Stationary sequences of elements of a Hilbert space.

**
22 November 1939**

On the definition of the stationary property for an individual function.

**
22 March 1940**

A mathematical study of deterministic and random processes.

**
18 March 1941**

On two forms of an axiomatic method (first survey report).

**
1 April 1941**

On two forms of an axiomatic method (second survey report).

**
16 April 1941**

On measures invariant under a group of transformations.

**
7 March 1942**

On a variational problem.

**
3 November 1943**

Report at the meeting dedicated to the memory of Lobachevskii.

**
2 February 1944**

Unitary representations of infinite groups.

**
3 October 1944**

A mathematical theory of turbulence.

**
31 October 1944**

The contemporary state of the theory of Markov chains and unsolved problems
in this area (survey report).

**
11 December 1944**

Problems in probability theory.

**
4 December 1945**

Computable sequences and their significance in investigations
of the foundations of mathematics (survey report).

**
7 May 1946**

The work of P. S. Aleksandrov on set theory and the theory of functions
(on his fiftieth birthday).

**
10 June 1947**

On some new work in probability theory (survey report).

**
17 June 1947**

An address at the meeting dedicated to the memory of Aleksei Konstantinovich Vlasov.

**
9 December 1947**

The structure of complete metric Boolean algebras.

**
17 February 1948**

On a draft of curricula for secondary schools.

**
24 February 1948**

Best approximation of complex functions.

**
30 March 1948**

A local limit theorem for Markov chains.

**
28 September 1948**

On Ostrogradskii's critique of the work of Lobachevskii.

**
30 November 1948**

Measures and probability distributions in function spaces (survey report).

**
4 October 1949**

A presentation of the foundations of Lebesque measure theory.

**
18 October 1949**

"Axiom", "Infinitesimal"
(articles for a new edition of the *Great Soviet Encyclopedia*).

**
6 December 1949**

Basic types of Markov processes.

**
23 December 1949**

The development of mathematics during the Soviet epoch.

**
9 January 1951**

On some mathematical problems connected with control and production (survey report).

**
15 May 1951**

The work of V. V. Stepanov on the theory of functions.

**
27 November 1951**

Two-valued functions of two-valued variables and their application
to relay-contact networks.

**
20 May 1952**

D. E. Men'shov's work on the theory of functions of a real variable
(on his sixtieth birthday).

**
30 September 1952**

On the spectra of dynamical systems on a torus.

**
25 February 1953**

the research direction of the Probability Theory Branch.

**
17 March 1953**

On the concept of algorithm.

**
26 May 1953**

On almost periodic motions of a heavy rigid body about a fixed point.

**
8 December 1953**

The concept of "information" in mathematical statistics
and in the Shannon theory of information transmission.

**
27 April 1954**

Estimates of the minimal number of elements in
-nets in various function
classes and their application to the question of representability of functions of
several variables as superpositions of functions of a smaller number of variables.

**
25 May 1954**

On stability of conditionally periodic motions in conservative dynamical systems.

**
28 September 1954**

On the International Congress of Mathematicians in Amsterdam.

**
25 October 1955**

A few words about a trip to Stockholm, jointly with P. S. Aleksandrov.

**
28 February 1956**

On a scientific trip to France, the German Democratic Republic, and Poland.

**
17 April 1956**

The representation of continuous functions of several variables by several continuous
functions of a smaller number ov variables.

**
29 May 1956**

"Éléments de Mathématique" by Nicolas Bourbaki.

**
5 June 1956**

On some asymptotic characteristics of a totally bounded metric space.

**
18 December 1956**

Uniform limit theorems for sums of independent terms.

**
25 December 1956**

On D. F. Egorov's work in the theory of functions and integral equations
(on the twentieth anniversary of his death).

**
2 April 1957**

What is cybernetics?
(on a draft of an article for the *Great Soviet Encyclopedia*).

**
24 September 1957**

On the representation of a continuous function of several variables
by means of continuous functions of a single variable and addition.

**
17 October 1957**

On the approximate representation of functions of several variables by superpositions
of functions of a smaller number of variables and
-entropy of function classes.

**
7 October 1958**

On the training of workers for the physical and mathematical sciences
and the new technologies.

**
13 January 1959**

"Small denominators" in problems of mechanics and analysis (survey report).

**
21 April 1959**

On some features of the contemporary stage of development of mathematics.

**
17 May 1960**

Solved and unsolved problems associated with Hilbert's thirteenth problem.

**
7 December 1960**

An experimental method of estimation of language entropy.

**
13 December 1960**

A. Ya. Khinchin's work in the theory of functions.

**
27 December 1960**

Mathematical methods in the study of Russian poetry (survey report).

**
4 April 1961**

What is 'information'?

**
16 May 1961**

An estimation of the difficulty of defining and computing finite sequences
and discrete functions.

**
21 November 1961**

Self-constructing apparatuses.

**
26 December 1961**

N. K. Bari's work in the representation of superposition functions.

**
26 March 1963**

On uniform limit theorems for sums of independent terms.

**
25 April 1963**

Sharing work experience.

**
28 May 1963**

An introductory address to the specialized meeting on the theory of random processes.

**
19 November 1963**

Computable functions and the foundations in information theory and probability theory.

**
24 October 1964**

On the influence of the ideas of information theory on the development of mathematics.

**
15 December 1964**

The asymptotic behavior of the complexity of finite segments of an infinite sequence.

**
18 May 1965**

Experiment and mathematical theory in the study of turbulence.

**
7 December 1965**

The calculus of finite problems of Yu. T. Medvedev.

**
3 March 1966**

On a draft of a mathematics curriculum for secondary school.

**
10 May 1966**

An introductory word dedicated to P. S. Aleksandrov's seventieth birthday.

**
14 February 1967**

On elective studies in mathematics in secondary school for 1967/68.

**
28 March 1967**

Logic, intuitionism, and the foundations of mathematics in the work L. E. J. Brouwer.

**
31 October 1967**

Some theorems on algorithmic entropy and the algorithmic amount of information.

**
24 February 1970**

The statistical hydrodynamics of the ocean.

**
23 November 1971**

The complexity of determining and the complexity of constructing mathematical objects.

**
14 December 1971**

On P. L. Chebyshev's work in probability theory.

**
25 April 1972**

On D. E. Men'shov's work in the theory of orthogonal series.

**
16 April 1974**

The complexity of algorithms and an objective definition of randomness.

**
15 February 1977**

An introductory word dedicated to the sixtieth birthday of G. E. Shilov.

**
18 January 1978**

Remarks on statistical solutions of the Navier-Stokes equations.

**
13 December 1983**

An introductory word dedicated to the 100th birthday of N. N. Luzin.

**
2 April 1985**

The first Moscow school mathematical olympiad.

A. N. Kolmogorov was President of the Moscow Mathematical Society from 1964 to 1966 and from 1973 to 1985. P. S. Aleksandrov was President of the Moscow Mathematical Society from 1932 to 1964. Current President of the Moscow Mathematical Society is V. I. Arnol'd who is Kolmogorov's student.

Kolmogorov Library Project

http://kolmogorov.com

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