Transcript Biography of Andrei Nikolaevich Kolmogorov

Andrei Nikolaevich Kolmogorov, 1903-1987
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Andrei Nikolaevich Kolmogorov, 1903-1910
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Kolmogorov was born in Tambov, 25 April
His father Nikolai Kataev, the son of a priest,
was an agronomist. He died in fighting in
1919. Kolmogorov's mother Maria
Kolmogorova tragically died during his birth.
Her sister, Vera Yakovlevna, very
independent woman, brought Kolmogorov
up and he always had the deepest affection
for her.
Early Andrei’s childhood was passed in
Yaroslavl region, at her father's estate, his
grandfather, Yakov Kolmogorov, a former big
landowner.
I discovered the pleasure of mathematical
discoveries early, at the age five or six
years. I noticed the relations 1=12, 1+3=
22 , 1+3 +5=32 etc. (A.K.)
Kolmogorov's family
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Andrei Nikolaevich Kolmogorov, 1903-1910
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Together with his aunts, Andrei lived in
village Tutoshna near Yaroslavl. Aunts
organized a small school for around 10
children of different age. Education
followed modern for that time pedagogical
ideas.
Aunt’s pedagogical principles of raising
him with high social ideals were:
-responsibility
-independence of opinion
-intolerance toward idleness
-intolerance to poorly performed tasks
-desire to understand and not only to
remember
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Andrei Nikolaevich Kolmogorov, 1910-1920
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Kolmogorov moved in Moscow. He studied
at private Repman’s gymnasium organized
by two intelligent and progressive women
Evgeniya Repman and Vera Fedorova. It
was due to the family tradition and
friendly atmosphere Andrei obtained a
general principle to search for himself right
serious deed.
Worked for while as a conductor on the
railway.
1920, Graduated school.
Moscow, 1910
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Andrei Nikolaevich Kolmogorov, 1920-1925
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1920, Kolmogorov entered Moscow State
University. He also studied at the
Metallurgical Department of the ChemicalTechnological Institute. Besides
mathematics and metallurgy he studied
Russian history.
Machinery were then as something more
serious and necessary as pure science.
My first scholarly talk (which I gave at the
age 17 at Moscow University) was at the
seminar of professor Bakhrushin’s seminar
on landowners in ancient Novgorod. (A.K.)
Crossroad moment. Bakhrushin:” You offer
only one proof. For a historian that is not
enough. One needs at least five proofs”.
May be this moved Kolmogorov to prefer
mathematics where just one proof is
enough.
Moscow University, 1910
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Andrei Nikolaevich Kolmogorov, 1920-1925
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N. Luzin
Nikolai Luzin’s school.
The seminar of Vyacheslav Stepanov on
trigonometric series.
Teaching mathematics and physics in
Potyiliha secondary school.
1921, the first paper “Division
into squares”.
1922, Trigonometric series.The paper on
Almost everywhere diverging Fourier series.
Worldwide atention (19 years old).
1924, The first results in probability theory.
Three series theorem for convergence of a
series of random variables (joint with
A. Khinchin).
First paper on embedding classical logic into
intuitional logic on the law of the excluded
third.
V. Stepanov
D. Egorov
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The first page of the paper
An almost everywhere diverging
Fourier series (1922 )
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Andrei Nikolaevich Kolmogorov, 1926-1929
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1925, Kolmogorov graduated from
Moscow State University and became
Luzin's graduate student. Kolmogorov
published eight papers in 1925.
1928, LLN (strong Law of Large Numbers)
and LIL (Law of Iterated Logarithm) for
sums of random variables. Kolmogorov
inequality. Important methods and only
the results.
Friendship with Pavel Sergeevich
Aleksandrov. The boat trip down the Volga
then across the Caucasus mountains to
lake Sevan in Armenia. Kolmogorov
worked on Markov processes with
continuous states and continuous time.
1928, the paper The general theory of
measure and the calculus of probabilities.
The first sketch of the famous axioms.
A. Kolmogorov and P. Alexandrov
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Andrei Nikolaevich Kolmogorov, 1929-1933
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In 1929 Kolmogorov completed his doctorate. By
this time he had 18 publications
Researcher in Institute of Mathematics and
Mechanics of Moscow University.
06.1930-03.1931. The first abroad trip with P.
Aleksandrov. They visited Germany (Berlin,
Göttingen, Munich) and France (Paris). Kolmogorov
met with Hilbert, Caratheodory, Kurant, Landau,
Levi, Frechet, Lebesque, Borel, Weyl, and other
leading mathematicians
1931, Kolmogorov was appointed a professor at
Moscow University (28 years old). First PhD
students.
1933, Grundbegriffe der Wahrscheinlichkeitsrechnung. Foundation of Probability theory. A
rigorous definition of conditional expectation.
Probability Theory became a mathematical science.
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The theory of probability as mathematical discipline
can and should be developed from axioms in
exactly the same way as Geometry and Algebra.
(A.K.)
A. Kolmogorov and P. Alexandrov
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Andrei Nikolaevich Kolmogorov, 1934-1939
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1935, Full Doctor in Mathematics (without
defence)
1937, Head of the chair of Probability theory
Analytic methods in probability theory which
Kolmogorov published in 1938 was laying
the foundations of the theory of Markov
random processes. Theory of stationary
random processes as curves in Hilbert space.
Mathematical statistics. Empirical distribution
function test.
Topology. Norms in linear topological spaces.
Algebraic topology. Introduced the notion of
cohomology groups.
Approximation theory. Best approximation of
functions of a functional class.
Full member of the Academy of Sciences of
the USSR.
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Andrei Nikolaevich Kolmogorov, 1934-1939
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Aleksandrov and Kolmogorov bought a house
in Komarovka, a small village outside Moscow,
in 1935. Many famous mathematicians visited
Komarovka: Hadamard, Frechet, Banach, Hopf,
Kuratovski, and others.
Journal “Uspehi Matematicheskih Nauk” was
organized. Kolmogorov was Editor in 1946-55,
1982-87 and always a member of the board.
Kolmogorov was elected Academician of
Academy of Science of USSR, the SecretaryAcademician of the Physics-Mathematical
Sciences Section of the Academy of Sciences
(1939-42), . The Department of Probability
and Statistics was set up at the Institute of
Steklov and Kolmogorov was appointed as
Head of Department.
The house in Komarovka
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Andrei Nikolaevich Kolmogorov, 1940-1945
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1941, the Second World War became in USSR.
Kolmogorov was evacuated in Kazan. He returned in
Moscow in 1942. Kolmogorov worked and
essentially developed ballistics
Applied sciences. Kolmogorov worked on biological
problems, addressed problems in geology,
meteorology, statistical control and crystallography.
Mathematics. Stationary sequences: interpolation
and extrapolation. The classic work (joint with B.
Gnedenko) Limiting distributions for sums of
independent random variables. Foundation of
theory of branching processes.
USSR State Prize (together with A. Ya. Khinchin in
1941), the Chebychev Prize of the USSR Academy
of Sciences (together with B. V. Gnedenko in 1949).
1942, Kolmogorov married Anna Egorova. They
studied together in Repman’ gymnasium in Moscow,
1910-1918.
Kolmogorov and
Anna Egorova, (a late photo)
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Andrei Nikolaevich Kolmogorov, 1946-1949
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Turbulence theory. Law of two thirds: in a
turbulent flow the average of the square of the
difference of the speed of two points at a
distance r from each other (average size) is
proportional to r^{2/3}
Head of Turbulence Laboratory in the Institute
of Theoretical Geophysics.
My interest to studying turbulence flows and
gases arose in the end of 30th. For me it
became clear that the main mathematical
research technique has to become theory of
random functions of many variables (random
fields) which was just born this time. (A.K.)
Joint Meeting of Academy of Science. Review
of spectral theory of random processes.
All-Union Meeting of Mathematical Statistics,
1948. The main problems of Mathematical
statistics.
1945
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Andrei Nikolaevich Kolmogorov, 1950-1959
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The rise in creative energy. Again, as in his
younger days, the creation of important new
concepts is combined with the solution of long
standing and fundamental problems.
Classical mechanics. The three body problem
(traced back to Newton and Laplace). This
problem was solved in the general situation in
Kolmogorov's work for most initial conditions.
The methods of proof developed in this work
played a great role in classical analysis,
mechanics and other areas of natural science.
Later it was further developed in the work by V.
I. Arnold and J. Moser and became known
under the name KAM-theory (the theory of
Kolmogorov-Arnold-Moser).
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Andrei Nikolaevich Kolmogorov, 1950-1959
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Hilbert's 13th problem. Any continuous function on an
n-dimensional cube (any n) can be represented as a
superposition of continuous functions of three variables.
This reduces Hilbert's 13th problem to the concrete
problem of representing functions on universal trees in
three dimensional space. This last problem was solved
by V. I. Arnold (solved under the guidance of A. N. in
third year student work), thus refuting the hypothesis
of Hilbert.
Developing ergodic theory Kolmogorov introduced a
new metric invariant, the entropy of dynamical systems.
On the one hand, this solved the classic problem about
the non-isomorphism of Bernoulli automorphisms, and
on the other hand, a completely new field of research
was opened, later leading to chaos theory.
Information theory, theory of automata, theory of
algorithms. The first lectures on Cybernetics. Automata
and life.
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Andrei Nikolaevich Kolmogorov, 1960-1970
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Kolmogorov advanced the grandiose program
of the simultaneous study of complexity, the
stochastic properties of deterministic processes
and regular indeterminacy of random processes
and phenomena. The experience of practically
all his creative life is concentrated in this
program. In his articles of 1965 and 1969
published in 'Problemi Peredachi Informatzi'
(Problems of Information Transfer) Andrei
Nikolaevich laid the foundation of a new field of
knowledge,
the
algorithmic
theory
of
information, and gave a new approach to the
logical foundations of Probability Theory.
Statistical
linguistics
and
text
entropy.
Kolmogorov
organized
competitions
on
recognition
of
sentence
continuation.
Laboratory of mathematical statistics was
organized.
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Andrei Nikolaevich Kolmogorov, Teacher
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The 60th was the last ten year period when Andrei
Nikolaevich actively studied mathematics properly.
In this period he started to turn more often to
pedagogical problems
1963, A mathematical boarding school, No 18 at
the University of Moscow otherwise known as the
Kolmogorov school was organized. Kolmogorov
took a special interest in the project to provide
special education for gifted children from all over
the country.
To this school he devoted a major proportion of his
time over many years, planning syllabuses, writing
textbooks, spending a large number of teaching
hours with the children themselves, introducing
then to literature and music, joining in their
recreations and taking them on hikes, excursions,
and expeditions.
Kolmogorov intensively worked on a new secondary
Kolmogorov with pupils, 1963
school textbooks on mathematics.
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Andrei Nikolaevich Kolmogorov, Teacher
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Andrei Nikolaevich has influenced many scholars
Nearly seventy graduate students worked under
Kolmogorov's supervision. Many of them later
became leaders of various scholarly schools. The
spectra of these schools is tremendous.
Probability theory: Yu. Prohorov (acad. A.Sc.,
USSR), A. Borovkov (corr.member,A.Sc.,USSR),B.
Sevastyanov (corr. member A.Sc.), B.Gnedenko
(acad. Ukranian A.Sc.,), S. Sirazdinov (acad.
Uzbekistan A.Sc.), Professors P. Dobrushin, V.
Zolotarev, L. Meshalkin, Yu.Belyaev, Ya.Rozanov, A.
Shlryaev, etc.
Mathematical Statistics: L.Bolshev (corr.mem.
A.Sc.).
Dynamical Systems, Mechanics: V. Arnold (acad.
A.Sc.) Professors V. Alexseev, Ya. Sinai.
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Andrei Nikolaevich Kolmogorov
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Approximation theory: S.
Nikolski (acad. A.Sc.),
Professor V. Tihomirov, V. Erohin, etc.
Applied Physics, Mechanics: M. Millionchikov (acad.
A.Sc.).
Atmospheric Physics: A.Obukhov (acad. A.Sc.),
Professors M. Yaglom, G. Barenblatt.
Oceanology: A. C. Monin (corr. mem. A.Sc.).
Mathematical Logic: A. I. Mal’tsev (acad. A.Sc.),
Professor V. Uspenski.
Cybernetics: V, Mihalevich (acad. A.Sc.).
Information Theory: Professors M. Pinsker, L.
Bassaligo.
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A.N.Kolmogorov’s PhD students
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Abramov, Alekseev, Arato, Arnold, Asarin, Bavli, Barenblatt, Bassalygo,
Belyaev,
Bityutskov,Bolshev,Borovkov,Bulinskii,Verchenko,Vovk,Galperin,
Gelfand,Gnedenko,Gordeev,Dvoichenkov,Dmitriev,Dobrushin,
Dynkin,Erokhin,Zhurbenko,Zasukhin,Zolotarev,Ivashev-Musatov,
Kozlov V.V.,Kozlov M.V.,Levin,Leonov,Mal’tsev,Matveev,Martynov,
Martin-Löf,Medvedev,Meshalkin,Millionshchikov,Mikhalevich,Monin,
Nikol’skii,Obukhov,Ofman,Ochan,Penkov,Petrov,Pinsker,
ProkhorovA.V.,Prokhorov Yu.V.,Rozanov,Rozenblat-Rot,Sevast’yanov,
Sinai,Sirazhdinov,Skorokhod,Statulyavichus,Tikhomirov,Tulaikov,
Tyurin,Uspenskii,Fage,Fomin,Shen,Shilov,Shiryaev,Shmidov,Yunovich,
Yaglom
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Andrei Nikolaevich Kolmogorov
His usual working week:
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Three days in week were in Moscow
and the rest in Komarovka.
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2 hours , a compulsory undergraduate
course (usually appr. 200 students).
He developed courses Functional
Analysis (Analysis III), Mathematical
Logic etc.
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2 hours, a free-choice course
(measure theory, information theory,
random processes etc.)
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2-4 hours a research seminar for lastyears and graduate students, and
researchers.
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Andrei Nikolaevich Kolmogorov
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In the arts Kolmogorov was especially
knowledgeable on ancient Russian architecture, all
of Russian poetry, worldwide sculpture and
painting. He spent a lot of time systematically
listening music especially last years.
He liked to travel In the span of fifty years he
travelled annually, with friends and later with
many of his students. He was especially drawn to
the Russian North, the Volga, the Crimea and the
Caucasus. Nature endowed him with excellent
health, which gave him a chance to lead an active
sports life, drawing the young along with him.
He was an expert cross-country skier, he could
stand atop his skis for twelve hours while skiing
large distances. He also engaged in swimming and
downhill skiing and hiking.
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Andrei Nikolaevich Kolmogorov
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National Honours. In 1939 he was elected to the
Academy of Sciences of the USSR. He received one of
the first State Prizes in 1941, the Lenin Prize in 1965,
the Order of Lenin on seven separate occasions, and
the Lobachevsky Prize in 1987. He had the title of Hero
of Socialist Labour.
International Honours. He was also elected to the many
other academies and societies including the Romanian
Academy of Sciences (1956), the Royal Statistical
Society of London (1956), the Leopoldina Academy of
Germany (1959), the American Academy of Arts and
Sciences (1959), the London Mathematical Society
(1959), the American Philosophical Society (1961), The
Indian Statistical Institute (1962), the Netherlands
Academy of Sciences (1963), the Royal Society of
London (1964), the National Academy of the United
States (1967), the French Academy of Sciences (1968).
Kolmogorov received the Balzan International Prize in
1962 and Wolf prize in 1981. Many universities awarded
him an honorary degree including Paris, Stockholm, and
Warsaw.
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A.N.Kolmogorov as supervisor ( 1956-1960)
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Belyaev Yuri
Leonov Viktor
Matveev Rostislav
Meshalkin Lev
Rozanov Yuri
Shiryaev Albert
Sinai Yakov
Tikhomirov Vladimir
1956
1957
1956
1956
1957
1957
1957
1957
Two types of research problems:
Submitted for personal research and
all have been informed,
Problems open to be solved in
competition.
 Appointed times at Moscow
Kolmogorov’s flat after seminars
and in his house in Komarovka.
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Andrei Nikolaevich Kolmogorov, 1946-1949
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Usually in the middle of a week
Kolmogorov invited several of his
under-/postgraduate students in
Komarovka.
In a summer time, the long trip was
planned. During the trip Kolmogorov
discussed in turn with all students
progress and difficulties in their
research problems. By Academy’s car
with sandwiches from Komarovka all
drove out near 30 km from the
house and returned back by foot. In
winter time it was more short ski trip.
After such trip it was a joint dinner
with all student and P. Alexandrov.
The evening ended up by listening
classical music (Bach, Vivaldi, Mozart
etc.) performed by the best
musicians of the world.
Komarovka in winter
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Andrei Nikolaevich Kolmogorov
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1980-1987, Head of the chair of Mathematical
logic.
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Men are cruel but Man is kind (A.K.)
Andrei Nikolaevich Kolmogorov,
25 April, 1903- 20 October,1987
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