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Andrey Nikolaevich Kolmogorov (Russian: Андре́й Никола́евич Колмого́ров) (25 April 1903 – 20 October 1987) was a Soviet Russian mathematician, preeminent in the 20th century, who advanced various scientific fields (among them probability theory, topology, intuitionistic logic, turbulence, classical mechanics and computational complexity). Kolmogorov was born at Tambov in 1903. His unwed mother died in childbirth and he was raised by his aunts in Tunoshna near Yaroslavl at the estate of his grandfather, a wealthy nobleman. His father, an agronomist by trade, was deported from Saint Petersburg for participation in the revolutionary movement. He disappeared and was presumed to have been killed in the Russian Civil War. Kolmogorov was educated in his aunt's village school, and his earliest literary efforts and mathematical papers were printed in the school newspaper. As an adolescent he designed perpetual motion machines, concealing their (necessary) defects so cleverly that his secondary school teachers could not discover them. In 1910, his aunt adopted him and then they moved to Moscow, where he went to a gymnasium, graduating from it in 1920. In 1920,
Kolmogorov began to study at the Moscow
State
University and
the Chemistry Technological Institute. Kolmogorov gained a reputation
for his wide ranging erudition. As an undergraduate, he participated in
the seminars of the Russian historian S.V. Bachrushin, and he published
his first research paper on the landholding practices in the Novgorod
Republic in the
fifteenth and sixteenth centuries. At the same time
(1921 – 1922), Kolmogorov derived and proved several results in set
theory and in the
theory of Fourier
series (trigonometrical
series). In 1922
Kolmogorov constructed a Fourier
series
that diverges almost
everywhere, gaining international recognition. Around this time he
decided to devote his life to mathematics.
In
1925 Kolmogorov graduated from Moscow
State
University, and began to study under the supervision of Nikolai
Luzin. He made lifelong friends with Pavel
Alexandrov who
involved Kolmogorov in 1936 in an ugly political persecution of their
common teacher, the so-called Luzin
case or Luzin
affair. Kolmogorov (together with A.
Khinchin) became interested in probability
theory. Also in 1925, he published his famous work in intuitionistic
logic — On the principle of the
excluded middle. In 1929 Kolmogorov earned his Doctor of Philosophy
degree, Ph.D.,
at
the Moscow
State
University. In 1930,
Kolmogorov went on his first long trip abroad, traveling to Göttingen and Munich,
Germany,
and then to Paris, France. His pioneering work About the Analytical
Methods of Probability Theory was
published
(in German) in 1931. Also in 1931, he became a professor at
Moscow University. In 1933, Kolmogorov published the book, Foundations of the
Theory of Probability, laying the modern axiomatic foundations
of
probability theory and
establishing
his reputation as the world's leading living expert in
this field. In 1935, Kolmogorov became the first chairman of
probability theory at the Moscow
State
University. In 1939, he was elected a full member (academician) of the USSR
Academy
of Sciences. In a 1938 paper, Kolmogorov "established the
basic theorems for smoothing and predicting stationary stochastic
processes" — a paper that would have major military applications
during the Cold
War to come. Around
the
same years (1936) Kolmogorov contributed to the field of ecology
and generalized the Lotka-Volterra model of predator-prey systems. In his
study of stochastic
processes (random
processes), especially Markov
processes, Kolmogorov and the British mathematician Sydney Chapman independently
developed
the pivotal set of equations in the field, the Chapman–Kolmogorov
equations. Later on,
Kolmogorov changed his research interests to the area of turbulence,
where
his publications beginning in 1941 had a significant influence on
the field. In classical
mechanics, he is best known for the Kolmogorov–Arnold–Moser
theorem (first
presented in 1954 at the International
Congress
of Mathematicians). In 1957 he solved Hilbert's
thirteenth
problem (a
joint work with his student V.I.
Arnold). He was a founder of algorithmic
complexity
theory, often referred to as Kolmogorov
complexity
theory, which he began to develop around this time. Kolmogorov
was
married to Anna Dmitrievna Egorova in 1942. He pursued a vigorous
teaching routine throughout his life, not only at the university level
but also with younger children, as he was actively involved in
developing a pedagogy for gifted children, in literature, and in music,
as well as in mathematics. At the Moscow State University, Kolmogorov
occupied different positions, including the heads of several
departments: probability, statistics,
and random
processes; mathematical
logic; and he also served as the Dean of the Moscow State
University Faculty of Mechanics and Mathematics. In 1971,
Kolmogorov joined an oceanographic expedition aboard the
research vessel Dmitri Mendeleev. He wrote a number of articles for the Great
Soviet
Encyclopedia. In
his
later years he devoted much of his effort to the mathematical and
philosophical relationship between probability
theory in abstract
and applied areas. Kolmogorov
died
in Moscow in 1987. A quotation, "Every mathematician believes he
is ahead over all others. The reason why they don't say this in public,
is because they are intelligent people" is attributed to him. |