Support Kolmogorov.com
Ph.D. students and descendants of A. N. Kolmogorov
(Moscow, April 29, 2003)
INTERNATIONAL CONFERENCE
KOLMOGOROV AND CONTEMPORARY MATHEMATICS(Moscow, June 16  21, 2003)
of Andrei Nikolaevich Kolmogorov (25.IV.1903  20.X.1987)
Scopes and Themes


The conference is devoted to memory of outstanding mathematician of modernity Andrei Nikolaevich Kolmogorov 

International Science Students Conference
Kolmogorov Specialized Physics and Mathematics School  Internat #18, Moscow
Lomonosov
Moscow State University
May 57, 2003, Moscow
ICTPINFM Summer School
Transport, Reaction and Propagation in Fluids
812 September 2003, ICTP, Trieste, Italy
followed by conference on
Kolmogorov's Legacy in Physics:
One Century of Chaos, Turbulence and Complexity
1517 September 2003, ICTP, Trieste, Italy
Complexity, Information, and Randomness:
The Legacy of Andrei Kolmogorov
Sunday, July 6, 2003, University of Aarhus, Denmark
in conjunction with
18th Annual IEEE Conference on Computational Complexity
Monday, July 7th, to Thursday, July 10th, 2003, University of Aarhus, Denmark
INTERNATIONAL CONFERENCE AND RESEARCH CENTER FOR COMPUTER SCIENCE
2003, April 27  May 5, Schloss Dagstuhl, D66687 Wadern, Saarbrücken, Germany
organizzano una Giornata su
L'EREDITA' CULTURALE di A.N. KOLMOGOROV
La Conferenza si terra' presso l'Edificio Fermi del Dip di Fisica
p.le Aldo Moro 2, 00185, Roma
AULA 1 ore 16 del 9 Maggio 2003
Speaker: Professor Ray Solomonoff
27th February 2003 5:30pm, Main Lecture Theatre Royal Holloway, University of London
Discussion Leader: Israel M. Gelfand
January 21, 2003 4:30pm, Courant Institute of Mathematical Sciences, New York University
Report to the mathematical circle on covering by squares (1921)
On operations on sets. II (1922)
A. Kolmogoroff, Une série de FourierLebesgue divergente presqne partout (1923)
Sur l'ordre de grandeur des coéfficients de la série de FourierLebesgue (1923)
A. Kolmogoroff, Une contribution à l'étude de la convergence des séries de Fourier (1924)
Sur la convergence des séries de Fourier (1924), jointly with G. A. Seliverstov
La définition axiomatique de l'intégrale (1925)
Sur le bornes de la généralisation de l'intégrale (1925)
Sur la possibilité de la définition générale de la dérivée, de l'intégrale et de lasommation des séries divergentes (1925)
A. Kolmogoroff, Sur les fonctions harmoniques conjuguées et les séries de Fourier (1925)
On the tertium non datur principle (1925)
Über Convergenz von Reihen, deren Glieder durch den Zufall bestimmt werden (1925), jointly with A. Ya. Khintchin
Sur la convergence des séries de Fourier (1926), jointly with G. A. Seliverstov
Une série de FourierLebesgue divergente partout (1926)
Sur la loi des grands nombres (1927)
A. Kolmogoroff et D. Menchoff, Sur la convergence des series de fonctions ortogonales (1927)
On operations on sets (1928) (in Russian)
Sur une formule limite de M. A. Khintchine (1928)
Sur un procédé d'intégration de M. Denjoy (1928)
A. Kolmogoroff, Über die Summen durch den Zufall bestimmter unabhängiger Größen (1928)
Bemerkungen zu meiner Arbeit "Über die Summen durch den Zufall bestimmter unabhängiger Größen" (1929)
General measure theory and the calculus of probabilities (1929) (in Russian)
Presentday controversies on the nature of mathematics (1929) (in Russian)
A. Kolmogoroff, Über das Gesetz des iterierten Logarithmus (1929)
Sur la loi des grands nombres (1929)
Sur la loi forte des grands nombres (1930)
A. Kolmogoroff, Zur topologisch gruppentheoretischen Begründung der Geometrie" (1930)
A. Kolmogoroff, Untersuchungen über den Integralbegriff (1930)
Sur la notion de la moyenne (1930)
A. Kolmogoroff, Bemerkungen zu meiner Arbeit "Über die Summen zufälliger Größen" (1930)
A. Kolmogoroff, Über die analytischen Methoden in der Wahrscheinlichkeitsrechnung (1931)
Sur la probléme d'attente (1931)
The method of medians in the theory of errors (1931) (in Russian)
Eine Verallgemeinerung des LaplaceLiapunoffschen Satzes (1931)
A. Kolmogoroff, Über Kompaktheit der Funktionenmengen bei der Konvergenz im Mittel" (1931)
The theory of functions of a real variable (1932) (in Russian)
Sulla forma generale di un processo stocastico omogeneo (Un problema di Bruno di Finetti) (1932)
Ancora sulla forma generale di un processo stocastico omogeneo (1932)
A. Kolmogoroff, Zur Deutung der intuitionistischen Logik (1932)
Zur Begründung der projektiven Geometrie (1932)
Introduction to the theory of functions of a real variable (1932), jointly with P. S. Aleksandrov (in Russian)
Introduction to the theory of functions of a real variable, 2nd ed. (1933), jointly with P. S. Aleksandrov (in Russian)
Grundbegriffe der Wahrscheinlichkeitrechnung (1933)
A. Kolmogoroff, Beiträge zur Maßtheorie (1933)
Zur Berechung der mittleren Brownschen Fläche (1933), jointly with M. A. Leontovich
Sulla determinazione empirica di una legge di distribuzione (1933)
Über die Grenzwertsätze der Wahrscheinlichkeitsrechnung (1933)
A. Kolmogoroff, Zur Theorie der stetigen zufälligen Prozesse (1933)
Sur la détermination empirique d'une loi de distribution (1933)
On the question of suitability of forecast formulas found statistically (1933) (in Russian)
10 papers in 1934
4 papers in 1935
17 papers in 1936
A. Kolmogoroff, Zur Theorie der Markoffschen Ketten (1936)
9 papers in 1937
A. Kolmogoroff, Zur Umkehrkeit der statistischen Naturgesetze (1937)
16 papers in 1938
.................
Complete list of Kolmogorov's works is published in the book
Kolmogorov in Perspective.
Most of published scientific papers and monographs of A.N. Kolmogorov are reproduced in a 3 Volume Set  Selected Works of A.N. Kolmogorov.
See also more than a dozen of A. N. Kolmogorov's articles in Russian popular science journal for students Kvant (Quantum).
The editorial board for the History of Mathematics series has selected for this volume a series of translations from two Russian publications, Kolmogorov in Remembrance and Mathematics and its Historical Development. This book, Kolmogorov in Perspective, includes articles written by Kolmogorov's students and colleagues and his personal accounts of shared experiences and lifelong mathematical friendships. Specifically, the article, "Andrei Nikolaevich Kolmogorov. A Biographical Sketch of His Life and Creative Paths" by A. N. Shiryaev, gives an excellent personal and scientific biography of Kolmogorov. The volume also includes the following articles: "On A. N. Kolmogorov" by V. I. Arnol'd, "In Memory of A. N. Kolmogorov" by S. M. Nikol'skii, "Remembrances of A. N. Kolmogorov" by Ya. G. Sinai, "The Influence of Andrei Nikolaevich Kolmogorov on My Life" by P. L. Ul'yanov, "A Few Words on A. N. Kolmogorov" by P. S. Aleksandrov, "Memories of P. S. Aleksandrov" by A. N. Kolmogorov, "Newton and Contemporary Mathematical Thought" by A. N. Kolmogorov, and an extensive bibliography with the complete list of Kolmogorov's worksincluding the articles written for encyclopedias and newspapers. The book is illustrated with photographs and includes quotations from Kolmogorov's letters and conversations, uniquely reflecting his mathematical tastes and opinions.
Copublished with the London Mathematical Society. Members of the LMS may order directly from the AMS at the AMS member price. The LMS is registered with the Charity Commissioners.
Full text of this book could be downloaded from MCCME (free).
Click on any picture to enlarge.
This edition reprints in one volume the second edition of this title, which was published in three volumes by The MIT Press in 1969. The original edition was published in 1964, translated from the Russian. Eighteen Russian mathematicians survey the scope of math, from elementary to the advanced levels, writing to educate a lay audience (those with "secondary school mathematics") who are motivated to know more. Discussion includes both the origins and the development of analytic geometry, algebra, ordinary differential equations, partial differential equations, curve and surface theories, prime numbers, probability, functions of a complex variable, linear algebra, nonEuclidean geometry, topology, functional analysis, and groups and other algebraic systems.
The material appearing in each volume was selected by A.N. Kolmogorov himself and is accompanied by short introductory notes and commentaries which reflect upon the influence of this work on the development of modern mathematics. All papers appear in English  some for the first time  and in chronological order. The volume contains a significant legacy which will find many grateful beneficiaries amongst researchers and students of mathematics and mechanics, as well as historians of mathematics.
Volume I: Mathematics and Mechanics
This first volume contains papers in mathematics (excluding probability theory and information theory, which are the subject of the following two volumes), turbulence and classical mechanics. They include his famous paper on everywheredivergent Fourier series, the concluding work on Hilbert's 13th problem, the fundamentals of the KolmogorovArnoldMoser theory in classical mechanics, the fundamentals of the theory of upper homologies, an original construction of the integral, papers on approximation theory and turbulence, and much more.
Volume II: Probability Theory and Mathematical Statistics
This second volume contains papers on probability theory and mathematical statistics, and embraces topics such as limit theorems, axiomatics and logical foundations of probability theory, Markov chains and processes, stationary processes and branching processes.
Volume III: Information Theory and the Theory of Algorithms
This third volume contains original papers dealing with information theory and the theory of algorithms. Comments on these papers are included.
Translated into Russian by A. N. Kolmogorov and with introduction by A. N. Kolmogorov
Kolmogorov Pathways from Integrability to Chaos and Beyond 3
From Regular to Chaotic Motions through the Work of Kolmogorov 33
Dynamics at the Border of Chaos and Order 61
Kolmogorov's Legacy about Entropy, Chaos, and Complexity 85
Complexity and Intelligence 109
Information Complexity and Biology 123
Fully Developed Turbulence 149
Turbulence and Stochastic Processes 173
ReactionDiffusion Systems: Front Propagation and Spatial Structures 187
SelfSimilar Random Fields: From Kolmogorov to Renormalization Group 213
Financial Time Series: From Batchelier's Random Walks to Multifractal 'Cascades' 229
Préface Yakov G. Sinai
Introduction Roberto Livi et Angelo Vulpiani
This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The stateoftheart is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A.N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such "fully developed turbulence" is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. First, a qualitative introduction is given to bring out the need for a probabilistic description of what is in essence a deterministic system. Kolmogorov's 1941 theory is presented in a novel fashion with emphasis on symmetries (including scaling transformations) which are broken by the mechanisms producing the turbulence and restored by the chaotic character of the cascade to small scales. Considerable material is devoted to intermittency, the clumpiness of smallscale activity, which has led to the development of fractal and multifractal models. Such models, pioneered by B. Mandelbrot, have applications in numerous fields besides turbulence (diffusion limited aggregation, solidearth geophysics, attractors of dynamical systems, etc). The final chapter contains an introduction to analytic theories of the sort pioneered by R. Kraichnan, to the modern theory of eddy transport and renormalization and to recent developments in the statistical theory of twodimensional turbulence. The book concludes with a guide to further reading. The intended readership for the book ranges from firstyear graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers.
K41 A. N. Kolmogorov. Dokl. Akad. Nauk SSSR, 30;4:3201, 1941.
An English translation of this paper was recently republished (Translation by V. Levin):
A. N. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Proc. R. Soc. Lond. A, 434:913, 1991
in the book Turbulence and Stochastic Processes: Kolmogorov's Ideas 50 Years On (1991)
and in the book
Selected Papers on Adaptive Optics and Speckle Imaging (1994)
Mathematical Problems (in English)
(Lecture delivered before the International Congress of Mathematicians at Paris in 1900)
by Professor David Hilbert
Hilbert's Problems (in Russian) edited and with introduction by
P. S. Aleksandrov
See also Millenium Prize Problems by Clay Mathematics Institute
The Millenium Problems: The Seven Greatest Unsolved Mathematical Puzzles of Our Time
by Keith J. Devlin
Published October 2002 by Basic Books
In the 20th century, many mathematicians in Russia made great contributions to the field of mathematics. This invaluable book, which presents the main achievements of Russian mathematicians in that century, is the first most comprehensive book on Russian mathematicians. It has been produced as a gesture of respect and appreciation for those mathematicians and it will serve as a good reference and an inspiration for future mathematicians. It presents differences in mathematical styles and focuses on Soviet mathematicians who often discussed "what to do" rather than "how to do it". Thus, the book will be valued beyond historical documentation.
The editor, Professor Yakov Sinai, a distinguished Russian mathematician, has taken pains to select leading Russian mathematicians — such as Lyapunov, Luzin, Egorov, Kolmogorov, Pontryagin, Vinogradov, Sobolev, Petrovski and Krein — and their most important works. One can, for example, find works of Lyapunov, which parallel those of Poincaré; and works of Luzin, whose analysis plays a very important role in the history of Russian mathematics; Kolmogorov has established the foundations of probability based on analysis. The editor has tried to provide some parity and, at the same time, included papers that are of interest even today.
The original works of the great mathematicians will prove to be enjoyable to readers and useful to the many researchers who are preserving the interest in how mathematics was done in the former Soviet Union.
This volume contains articles on Soviet mathematical history, many of which are personal accounts by mathematicians who witnessed and contributed to the turbulent years of Moscow mathematics. In today's climate of glasnost, the stories can be told with a candor uncharacteristic of the "historical" accounts published under the Soviet regime. An important case in point is the article on Luzin and his school, based in part on documents only recently released. The articles focus on mathematical developments in that era, the personal lives of Russian mathematicians, and political events that shaped the course of scientific work in the Soviet Union. Another important feature is the inclusion of two articles on Kolmogorov, perhaps the greatest Russian mathematician of the twentieth century. The volume concludes with an annotated English bibliography and a Russian bibliography for further reading. This book appeals to mathematicians, historians, and anyone else interested in Soviet mathematical history.
Full texts of many issues of 'Kvant' is currently avalable from the Russian web site of MCCME, Moscow Center for Continuous Mathematical Education.
See also "Math in Moscow"  a program in English for undergraduates and graduate students at the Independent University of Moscow.
Portraits of A. N. Kolmogorov by his former student Dima Gordeev (click to enlarge)
Internat #18 alumni web site, alumni club, and questionnaire.
Kolmogorov Specialized Physics & Mathematics School  Internat #18 at Moscow State University
School was founded by A. N. Kolmogorov in 1964. A. N. Kolmogorov was lifelong Chairman of the Board of Trustees.
The School was named after A. N. Kolmogorov in 1988.
Lomonosov Moscow State University
A. N. Kolmogorov was student (19201925), graduate student (19251929),
researcher (19291931), and professor (19311987) at the University.
MechMath  Faculty of Mechanics and Mathematics
A. N. Kolmogorov was Dean of the MechMath Faculty (19541958) and
Head of the Mathematics Division (19541956 and 1978till his death in 1987).
From 1931 A. N. Kolmogorov was Head of graduate school of MechMath Faculty 
Director of the Institute of Mathematics and Mechanics.
In 1951 he was once again appointed Director of the Institute of Mathematics.
Department of Probability Theory
A. N. Kolmogorov was Founder (1935) and first Head of the Department (19351966).
From 1966 to 1995 head of the chair was his student B. V. Gnedenko.
From 1996 another student of A. N. Kolmogorov professor A. N. Shiryaev became head of the chair.
Department of Mathematical Logic and Theory of Algorithms
A. N. Kolmogorov was second Head of the Department of Mathematical Logic (19801987) after first Head A. A. Markov (19591979).
From 1988 to 1993 head of the chair was V. A. Mel'nikov.
Head of the Department since January 1995 is professor V.A.Uspensky who is Kolmogorov's student.
Russian Academy of Sciences
A. N. Kolmogorov was elected Full Member (Academician) of the Division of Mathematical and Natural Sciences since 29.01.1939.
He was elected Member of the Presidium of Academy and Head (AcademicianSecretary) of the
Division of Physical and Mathematical Sciences.
Steklov Mathematical Institute of the Russian Academy of Sciences
Department of Probability and Mathematical Statistics of the Steklov Mathematical Institute
Founded by A. N. Kolmogorov in 1938 who was Head of Department until 1958 (excluding 19461948 when A. Ya. Khinchin occupied this position).
After 1960 it is headed by
Yu. V. Prokhorov who is Kolmogorov's student.
A. N. Kolmogorov was Head of the Turbulence Laboratory (19461949) at the O. Yu. Shmidt Institute of Theoretical Geophysics of the Russian Academy of Sciences. His student A. M Obukhov became Head of the Turbulence Laboratory in 1949 and later Founding and lifelong Director of the Institute of Atmospheric Physics of the Russian Academy of Sciences. His other student A. S. Monin became Director of the Institute of Oceanology of the Russian Academy of Sciences.
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.
Small Hall of the Conservatory of
Moscow Academic Philarmonia
P. S. Aleksandrov and A. N. Kolmogorov were the lifelong
Season Tickets holders...
Johann Sebastian Bach: Concerto for 2 violins & strings in D minor ("Double"), BWV 1043 (P. S. Aleksandrov's and A. N. Kolmogorov's favorite)
Wolfgang Amadeus Mozart: Symphony No.40 in G minor, K.550 (P. S. Aleksandrov's and A. N. Kolmogorov's favorite)
Johann Sebastian Bach: St. Matthew Passion
Christoph Willibald Gluck: Orfeo ed Euridice
1. Gift of 59 books from the Class of 1976, 1 September 2002.
2. Gift of 9 books from the Class of 1976, 7 March 2003.
3. Gift of ~80 books from the Class of 1976, 11 June 2003.
4. Gift of ~35 books from the Class of 1976, 6 December 2003.
Some recent additions  Gifts to the Kolmogorov Library.
5,
6,
7, ... Thanks for your support.
Support Kolmogorov.com