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Kolmogorov
was one of the broadest of this century's mathematicians. He laid the mathematical
foundations of probability theory and the algorithmic theory of randomness
and made crucial contributions to the foundations of statistical mechanics,
stochastic processes, information theory, fluid mechanics, and
nonlinear dynamics
.
All of these areas, and their interrelationships, underlie complex
systems, as they are studied today.
Kolmogorov graduated from Moscow State University in 1925 and then
became a professor there in 1931. In 1939 he was elected to the Soviet
Academy of Sciences, receiving the Lenin
Prize in 1965 and the Order of Lenin on seven separate occasions.
His work on reformulating probability started with a 1933 paper in
which he built up probability theory in a rigorous way from fundamental
axioms, similar to Euclid's treatment of geometry. Kolmogorov went on to
study the motion of the planets and turbulent fluid flows, later publishing
two papers in 1941 on turbulence that even today are of fundamental importance.
In 1954 he developed his work on dynamical systems in relation to planetary
motion, thus demonstrating the vital role of probability theory in physics
and re-opening the study of apparent randomness in deterministic systems,
much along the lines originally conceived by
Henri Poincare
.
In 1965 he introduced the algorithmic theory of randomness via a measure
of complexity, now referred to
Kolmogorov
Complexity
. According to Kolmogorov, the complexity of an object
is the length of the shortest computer program that can reproduce the object.
Random objects, in his view, were their own shortest description. Whereas,
periodic sequences have low Kolmogorov complexity, given by the length
of the smallest repeating "template" sequence they contain. Kolmogorov's
notion of complexity is a measure of randomness, one that is closely related
to
Claude Shannon
's entropy rate of an
information source.
Kolmogorov had many interests outside mathematics research, notable
examples being the quantitative analysis of structure in the poetry of
the Russian author Pushkin, studies of agrarian development in 16th and
17th century Novgorod, and mathematics education.
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