Moscow Mathematical Society
The Legacy of A. N. Kolmogorov

April 25, 1903 - October 20, 1987

Addresses by Kolmogorov at meetings of the Moscow Mathematical Society

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.

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