He serves as the professor of mathematics at Princeton University since 1993 and holds the position of Senior Researcher at the Landau Institute for Theoretical Physics in Moscow, Russia.

Yakov Grigorevich Sinai was born into a Russian Jewish academic family on September 21, 1935, in Moscow, Soviet Union (now Russia).

His grandfather, Veniamin Kagan, headed the Department of Differential Geometry at Moscow State University and was a major influence on Sinai's life.

[4] Other contributions in mathematics and mathematical physics include the rigorous foundations of Kenneth Wilson's renormalization group-method, which led to Wilson's Nobel Prize for Physics in 1982, Gibbs measures in ergodic theory, hyperbolic Markov partitions, proof of the existence of Hamiltonian dynamics for infinite particle systems by the idea of "cluster dynamics", description of the discrete Schrödinger operators by the localization of eigenfunctions, Markov partitions for billiards and Lorenz map (with Bunimovich and Chernov), a rigorous treatment of subdiffusions in dynamics, verification of asymptotic Poisson distribution of energy level gaps for a class of integrable dynamical systems, and his version of the Navier–Stokes equations together with Khanin, Mattingly and Li.

In 1971 he accepted a position as senior researcher at the Landau Institute for Theoretical Physics in Russia, while continuing to teach at Moscow State.

He had to wait until 1981 to become a professor at Moscow State, likely because he had supported the dissident poet, mathematician and human rights activist Alexander Esenin-Volpin in 1968.

For the 1997–98 academic year, he was the Thomas Jones Professor at Princeton, and in 2005, the Moore Distinguished Scholar at the California Institute of Technology.

[3] In 2014, the Norwegian Academy of Science and Letters awarded him the Abel Prize, for his contributions to dynamical systems, ergodic theory, and mathematical physics.

[6] Presenting the award, Jordan Ellenberg said Sinai had solved real world physical problems "with the soul of a mathematician".