Yakov Grigorevich Sinai (Russian: Я́ков Григо́рьевич
Сина́й; born September 21, 1935) is a mathematician known for
his work on dynamical systems. He contributed to the modern metric
theory of dynamical systems and connected the world of deterministic
(dynamical) systems with the world of probabilistic (stochastic)
systems. He has also worked on mathematical physics and probability
theory. His efforts have provided the groundwork for advances in
the physical sciences.
Sinai has won several awards, including the Nemmers Prize, the Wolf
Mathematics and the Abel Prize.
2 Selected works
4 External links
Yakov Grigorevich Sinai was born into a
Russian Jewish academic family
on September 21, 1935, in Moscow,
Soviet Union (now Russia). His
parents, Nadezda Kagan and Gregory Sinai, were both microbiologists.
His grandfather, Veniamin Kagan, headed the Department of Differential
Moscow State University
Moscow State University and was a major influence on
Sinai received his bachelor's and master's degrees from Moscow State
University. In 1960, he earned his Ph.D., also from Moscow State;
his adviser was Andrey Kolmogorov. Together with Kolmogorov, he showed
that even for "unpredictable" dynamic systems, the level of
unpredictability of motion can be described mathematically. In their
idea, which became known as Kolmogorov–Sinai entropy, a system with
zero entropy is entirely predictable, while a system with non-zero
entropy has an unpredictability factor directly related to the amount
In 1963, Sinai introduced the idea of dynamical billiards, also known
as "Sinai Billiards". In this idealized system, a particle bounces
around inside a square boundary without loss of energy. Inside the
square is a circular wall, of which the particle also bounces off. He
then proved that for most initial trajectories of the ball, this
system is ergodic, that is, after a long time, the amount of that time
the ball will have spent in any given region on the surface of the
table is approximately proportional to the area of that region. It was
the first time anyone proved a dynamic system was ergodic.
Also in 1963, Sinai announced a proof of the ergodic hypothesis for a
gas consisting of n hard spheres confined to a box. The complete
proof, however, was never published, and in 1987 Sinai declared that
the announcement was premature. The problem remains open to this
From 1960 to 1971, Sinai was a researcher in the Laboratory of
Probabilistic and Statistical Methods at Moscow State University. 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
Since 1993, Sinai has been a professor of mathematics at Princeton
University, while maintaining his position at the Landau Institute.
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.
In 2002, Sinai won the Nemmers Prize for his "revolutionizing" work on
dynamical systems, statistical mechanics, probability theory, and
statistical physics. In 2005, the Moscow Mathematical Journal
dedicated an issue to Sinai writing "
Yakov Sinai is one of the
greatest mathematicians of our time ... his exceptional
scientific enthusiasm inspire[d] several generations of scientists all
over the world."
In 2013, Sinai received the
Leroy P. Steele Prize for Lifetime
Achievement. 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. Presenting the
Jordan Ellenberg said Sinai had solved real world physical
problems "with the soul of a mathematician". He praised the tools
developed by Sinai which demonstrate how systems that look different
may in fact have fundamental similarities. The prize comes with 6
million Norwegian krone, equivalent at the time to $US 1 million or
£600,000. He was also inducted into the Norwegian Academy of Science
Other awards won by Sinai include the
Boltzmann Medal (1986), the
Dannie Heineman Prize for Mathematical Physics (1990), the Dirac Prize
Wolf Prize in Mathematics
Wolf Prize in Mathematics (1997), the Lagrange Prize
(2008) and the
Henri Poincaré Prize (2009). He is a member of
the United States National Academy of Sciences, the Russian Academy of
Sciences, and the Hungarian Academy of Sciences. He is an honorary
member of the
London Mathematical Society
London Mathematical Society and, in 2012, he became a
fellow of the American Mathematical Society. Sinai has been
selected an honorary member of the Brazilian Academy of Sciences, the
Academia Europaea, the Polish Academy of Sciences, and the Royal
Society of London. He holds honorary degrees from the Budapest
University of Technology and Economics, the Hebrew University of
Jerusalem, Warwick University, and Warsaw University.
Sinai has authored more than 250 papers and books. Concepts in
mathematics named after him include Sinai's random walk,
Sinai–Ruelle–Bowen measures, and Pirogov–Sinai theory. Sinai has
overseen more than 50 Ph.D. candidates. He has spoken at the
International Congress of Mathematicians
International Congress of Mathematicians four times. In 2000, he
was a plenary speaker at the First Latin American Congress in
Sinai is married to mathematician and physicist Elena B. Vul. The
couple have written several joint papers.
Ergodic Theory. Princeton 1976.
Ergodic Theory. Princeton 1977, 1994.
Probability Theory – an Introductory Course. Springer, 1992.
Theory of probability and Random Processes (with Koralov). 2nd
edition, Springer, 2007.
Theory of Phase Transitions – Rigorous Results. Pergamon, Oxford
Ergodic Theory (with Isaac Kornfeld and Sergei Fomin). Springer,
Grundlehren der mathematischen Wissenschaften 1982.
"What is a Billiard?", Notices AMS 2004.
"Mathematicians and physicists = Cats and Dogs?" in Bulletin of the
AMS. 2006, vol. 4.
"How mathematicians and physicists found each other in the theory of
dynamical systems and in statistical mechanics", in Mathematical
Events of the Twentieth Century (editors: Bolibruch, Osipov, &
Sinai). Springer 2006, p. 399.
^ a b c d e f Ball, Philip (March 26, 2014). "Chaos-theory pioneer
nabs Abel Prize". Nature. Retrieved March 29, 2014.
^ a b c d e f g "2002 Frederic Esser Nemmers
Recipient". Northwestern University. Retrieved March 30, 2014.
^ a b c d e f g h i j "Yakov G. Sinai". Abel Prize. Retrieved March
^ "Legendary Russian academic
Yakov Sinai awarded 'math Nobel'". RT.
March 27, 2014. Retrieved 31 March 2014.
^ Uffink, Jos (2006). Compendium of the foundations of classical
statistical physics (PDF). p. 91.
^ "Sinai biography". www-history.mcs.st-andrews.ac.uk. Retrieved
Abel Prize Laureate 2014". Norwegian Academy of Science and
Letters. Retrieved 26 March 2014.
^ "Gruppe 1: Matematiske fag" (in Norwegian). Norwegian Academy of
Science and Letters. Retrieved 30 March 2016.
^ "List of Fellows of the American Mathematical Society". Retrieved
July 20, 2013.
^ Chacon, R. V. (1978). "Review: Introduction to ergodic theory, by
Ya. G. Sinai" (PDF). Bull. Amer. Math. Soc. 84 (4): 656–660.
^ a b c d e f g h "Yakov Bibliography" (PDF). Princeton University.
Retrieved March 30, 2014.
Wikimedia Commons has media related to Yakov Grigorevich Sinai.
Sinai on scholarpedia
O'Connor, John J.; Robertson, Edmund F., "Yakov Sinai", MacTutor
Mathematics archive, University of St Andrews .
Yakov Sinai at the
Mathematics Genealogy Project
List of publications on the website of the Landau Institute for
Laureates of the Wolf Prize in Mathematics
Israel Gelfand / Carl L. Siegel (1978)
Jean Leray /
André Weil (1979)
Henri Cartan /
Andrey Kolmogorov (1980)
Lars Ahlfors /
Oscar Zariski (1981)
Hassler Whitney /
Mark Krein (1982)
Shiing-Shen Chern /
Paul Erdős (1983/84)
Kunihiko Kodaira /
Hans Lewy (1984/85)
Samuel Eilenberg /
Atle Selberg (1986)
Kiyosi Itô /
Peter Lax (1987)
Friedrich Hirzebruch /
Lars Hörmander (1988)
Alberto Calderón /
John Milnor (1989)
Ennio de Giorgi /
Ilya Piatetski-Shapiro (1990)
Lennart Carleson /
John G. Thompson
John G. Thompson (1992)
Mikhail Gromov /
Jacques Tits (1993)
Jürgen Moser (1994/95)
Robert Langlands /
Andrew Wiles (1995/96)
Joseph Keller / Yakov G. Sinai (1996/97)
László Lovász /
Elias M. Stein
Elias M. Stein (1999)
Raoul Bott /
Jean-Pierre Serre (2000)
Vladimir Arnold /
Saharon Shelah (2001)
Mikio Sato /
John Tate (2002/03)
Grigory Margulis / Sergei Novikov (2005)
Stephen Smale /
Hillel Furstenberg (2006/07)
Pierre Deligne / Phillip A. Griffiths / David B. Mumford (2008)
Dennis Sullivan /
Shing-Tung Yau (2010)
Michael Aschbacher /
Luis Caffarelli (2012)
George Mostow /
Michael Artin (2013)
Peter Sarnak (2014)
James G. Arthur (2015)
Richard Schoen /
Charles Fefferman (2017)
Alexander Beilinson /
Vladimir Drinfeld (2018)
Abel Prize laureates
Jean-Pierre Serre (2003)
Michael Atiyah /
Isadore Singer (2004)
Peter Lax (2005)
Lennart Carleson (2006)
S. R. Srinivasa Varadhan
S. R. Srinivasa Varadhan (2007)
John G. Thompson
John G. Thompson /
Jacques Tits (2008)
Mikhail Gromov (2009)
John Tate (2010)
John Milnor (2011)
Endre Szemerédi (2012)
Pierre Deligne (2013)
Yakov Sinai (2014)
John Forbes Nash Jr.
John Forbes Nash Jr. /
Louis Nirenberg (2015)
Andrew Wiles (2016)
Yves Meyer (2017)
Robert Langlands (2018)
Fellows of the
Royal Society elected in 2009
Ross J. Anderson
Arthur B. McDonald
H. Robert Horvitz
Roger D. Kornberg
Steven D. Tanksley
Prince William, Duke of Cambridge
ISNI: 0000 0001 0963 856X
BNF: cb129423333 (data)