ous way from fundamental axioms in a way comparable with Euclids treat- ment of geometry. He gives a rigorous definition of the conditional expecta- tion which later becomes fundamental for the definition of brownian motion stochastic integration, and Mathematics of Finance.(Kolmogorov's mono- graph is available in English translation as Foundations of Probability Theory, Chelsea, New York, 1950). And he was not finished. In 1938 he publishes the paper Analytic methods in probability theory which lay the foundation work for the Markov processes, and toward a more rigurous approach to the Markov chair Kolmogorov later extended his work to study the motion of the planets and the turbulent How of air from a jet engine. In 1941 he published two pa- pers on turbulence which are of fundamental importance. In 1953 and 1954 two papers by Kolmogorov, each of four pages in length, appeared. These are on the theory of dynamical systems with applications to Hamiltonian dynam- ics. These papers mark the beginning of KAM-theory, which is named after Kolmogorov arnold and moser. Kolmogorov addressed the international Congress of Mathematicians in Amsterdam in 1954 on this topic with his important talk General theory of dynamical systems and classical mechanics He thus demonstrated the vital role of probability theory in physics. His contribution in the topology theory is of outmost importance Kolmogorov had many interests outside mathematics, in particular he as interested in the form and structure of the poetry of Pushkin Like so many other branches of mathematics, the development of proba- bility theory has been stimulated by the variety of its applications. In its turn, each advance in the theory has enlarged the scope of its influence. Mathe- matical statistics is one important branch of applied probability; other appli cations occur in such widely different fields as genetics, biology, psychology economics, finance, engineering, mechanics, optics, thermodynamics, quan- tum mechanics, computer vision, etcetc. etc.. In fact I compel the reader to find one area in today's science where no applications of the probability theory can be found For its immense success and wide variety of applications the Theory of Probability can be arguably viewed as the most important area of Mathe matics 5ous way from fundamental axioms in a way comparable with Euclid’s treat￾ment of geometry. He gives a rigorous definition of the conditional expecta￾tion which later becomes fundamental for the definition of Brownian motion, stochastic integration, and Mathematics of Finance. (Kolmogorov’s mono￾graph is available in English translation as Foundations of Probability Theory, Chelsea, New York, 1950). And he was not finished. In 1938 he publishes the paper Analytic methods in probability theory which lay the foundation work for the Markov processes, and toward a more rigurous approach to the Markov Chains. Kolmogorov later extended his work to study the motion of the planets and the turbulent flow of air from a jet engine. In 1941 he published two pa￾pers on turbulence which are of fundamental importance. In 1953 and 1954 two papers by Kolmogorov, each of four pages in length, appeared. These are on the theory of dynamical systems with applications to Hamiltonian dynam￾ics. These papers mark the beginning of KAM-theory, which is named after Kolmogorov, Arnold and Moser. Kolmogorov addressed the International Congress of Mathematicians in Amsterdam in 1954 on this topic with his important talk General theory of dynamical systems and classical mechanics. He thus demonstrated the vital role of probability theory in physics. His contribution in the topology theory is of outmost importance. Kolmogorov had many interests outside mathematics, in particular he was interested in the form and structure of the poetry of Pushkin. Like so many other branches of mathematics, the development of proba￾bility theory has been stimulated by the variety of its applications. In its turn, each advance in the theory has enlarged the scope of its influence. Mathe￾matical statistics is one important branch of applied probability; other appli￾cations occur in such widely different fields as genetics, biology, psychology, economics, finance, engineering, mechanics, optics, thermodynamics, quan￾tum mechanics, computer vision, etc.etc.etc.. In fact I compel the reader to find one area in today’s science where no applications of the probability theory can be found. For its immense success and wide variety of applications the Theory of Probability can be arguably viewed as the most important area of Mathe￾matics. 5