# Kolmogorov, Andrei Nikolaievich

### probability theory foundations communication

[kol mo gorof] (1903–87) Russian mathematician: advanced the foundations of probability theory.

Kolmogorov graduated from Moscow in 1925 and in 1933 became director of the Institute of Mathematics. In 1933 his book *Foundations of the Theory of Probability* became the first rigorous treatment of the subject. The ‘additivity assumption’ basic to probability is set out (due originally to Jakob Bernoulli (1654–1705)): that if an event can occur in an infinite number of ways its probability is the sum of the probabilities of each of these ways. Kolmogorov then explored Markov processes–those where a probability of a variable depends on its previous value but not its values before that. He constructed such processes by analytic means.

Another of his interests was the theory of algorithms (or mathematical operations, such as division), and he showed its relationship to computing and with cybernetics, which is concerned with communication and control, and ‘feedback’. Kolmogorov produced a theory of programmed instructions and of how information is conveyed along communication channels.

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