**Yakov Grigorevich Sinai **is a Russian mathematician known for his work on dynamical systems.

- He retired from his chair at Moscow State University in 1952, the year in which his grandson Yakov Grigorevich entered the Faculty of Mechanics and Mathematics.
- Sinai's first advisor at Moscow State University was Nikolai Guryevich Chetaev who was an expert on analytical mechanics, particularly on stability of motion.
- Sinai quickly became interested in the dynamical systems on which Chetaev worked.
- The problem which Dynkin suggested that Sinai work on, led to his first paper On the distribution of the first positive sum for a sequence of independent random variables (Russian) (1957).
- In 1957 Sinai was awarded his first degree from Moscow State University and began to undertake research for his Master's Degree (equivalent to a Ph.D.) working with Andrei Nikolaevich Kolmogorov.
- Sinai's papers published around the time he was working for his Master's Degree include: On the concept of entropy for a dynamic system (Russian) (1959); Flows with finite entropy (1959) (Russian); The central limit theorem for geodesic flows on manifolds of constant negative curvature (1960) (Russian); and Dynamical systems and stationary Markov processes (1960) (Russian).
- Already, in the first of these 1959 papers, Sinai gives theorems which make it possible to calculate the entropy for a large variety of dynamical systems.
- Sinai was the first to come up with a mathematical foundation for determining the number that defines the complexity of a given dynamical system.
- His mathematical system is called Kolmogorov-Sinai entropy.
- The high quality and importance of Sinai's papers led to him being invited to lecture at the International Congress of Mathematicians in Stockholm in 1962.
- In 1971, following Sergei Petrovich Novikov's advice, Sinai accepted a position as Senior Researcher at the L D Landau Institute of Theoretical Physics of the USSR Academy of Sciences.
- Sinai continued to teach at Moscow State University but he did not become a professor there until 1981.
- Sinai suffered much for his support of Volpin.
- Sinai was able to accept the invitation, however, to deliver one of the plenary lectures at the International Congress of Mathematicians in Kyoto in 1990; he spoke on Hyperbolic Billiards.
- We have already looked the deep contribution made by which Sinai early in his career.
- Sinai's work centres round the grand aim of deriving the basic physical laws which describe the behaviour of many particle systems as a direct consequence of simple rules governing the interaction of individual particles.
- The idea of applying the Kolmogorov theory of entropy to smooth dynamical systems was Sinai's.
- Sinai laid the foundations of the theory of billiards, for which he has more recently also constructed Markov partitions, and of the motion of a hard sphere gas.
- In recent years, Sinai has made important contributions to KAM theory using renormalisation methods.
- Sinai has received many major awards, prizes and honours for his remarkable contributions.
- Statistical mechanics is one of the most active and rewarding areas of modern mathematics, and Yakov Sinai is its recognized leader today.
- Many mathematical societies and academies have elected Sinai to membership or honorary membership: the American Academy of Arts and Sciences (1983); the USSR Academy of Sciences (1991); the London Mathematical Society (1992); the Hungarian Academy of Sciences (1993); the United States National Academy of Sciences (1999); the Brazilian Academy of Sciences (2000); the Academia Europaea (2008); and the Royal Society of London (2009).
- Sinai has also been invited to give many prestigious lectures or lecture courses including: Loeb Lecturer, Harvard University (1978); Plenary Speaker at the International Congress on Mathematical Physics in Berlin (1981); Plenary Speaker at the International Congress on Mathematical Physics in Marseilles (1986); Distinguished Lecturer, Israel (1989); Solomon Lefschetz Lectures, Mexico (1990); Plenary Speaker at the International Congress of Mathematicians, Kyoto (1990); Landau Lectures, Hebrew University of Jerusalem (1993); Plenary Speaker at the First Latin American Congress in Mathematics (2000); Plenary Speaker at the American Mathematical Society Meeting "Challenges in Mathematics" (2000); Andreevski Lectures, Berlin, Germany (2001); Bowen Lectures, University of California at Berkeley (2001); Leonidas Alaoglu Memorial Lecture, California Institute of Technology (2002); Joseph Fels Ritt Lectures, Columbia University (2004); Leonardo da Vinci Lecture, Milan, Italy (2006); Galileo Chair, Pisa, Italy (2006); John T Lewis Lecture Series, Dublin Institute for Advanced Studies and the Hamilton Mathematics Institute, Trinity College, Dublin, Ireland (2007); and Milton Brockett Porter Lecture Series, Rice University, Houston, Texas (2007).

Born 21 September 1935, Moscow, Russia.

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Prize Abel, Origin Russia, Prize Wolf

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive