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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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