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.[1] He has also worked on mathematical physics and probability
theory.[2] His efforts have provided the groundwork for advances in
the physical sciences.[1]
Sinai has won several awards, including the Nemmers Prize, the Wolf
Prize in
**Mathematics**

Mathematics and the Abel Prize.

Contents

1 Biography
2 Selected works
3 References
4 External links

Biography[edit]
Yakov Grigorevich Sinai was born into a
**Russian Jewish**

Russian Jewish academic family
on September 21, 1935, in Moscow,
**Soviet Union**

Soviet Union (now Russia).[3][4] His
parents, Nadezda Kagan and Gregory Sinai, were both microbiologists.
His grandfather, Veniamin Kagan, headed the Department of Differential
Geometry at
**Moscow State University**

Moscow State University and was a major influence on
Sinai's life.[3]
Sinai received his bachelor's and master's degrees from Moscow State
University.[2] 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
of entropy.[1]
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.[1]
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
day.[5]
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
1968.[6]
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.[3]
In 2002, Sinai won the Nemmers Prize for his "revolutionizing" work on
dynamical systems, statistical mechanics, probability theory, and
statistical physics.[2] In 2005, the Moscow Mathematical Journal
dedicated an issue to Sinai writing "
**Yakov Sinai**

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."[3]
In 2013, Sinai received the
**Leroy P. Steele Prize** for Lifetime
Achievement.[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.[7] Presenting the
award,
**Jordan Ellenberg**

Jordan Ellenberg said Sinai had solved real world physical
problems "with the soul of a mathematician".[1] 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,[1] equivalent at the time to $US 1 million or
£600,000. He was also inducted into the Norwegian Academy of Science
and Letters.[8]
Other awards won by Sinai include the
**Boltzmann Medal** (1986), the
**Dannie Heineman Prize for Mathematical Physics** (1990), the Dirac Prize
(1992), the
**Wolf Prize in Mathematics**

Wolf Prize in Mathematics (1997), the Lagrange Prize
(2008) and the
**Henri Poincaré Prize** (2009).[2][3] He is a member of
the United States National Academy of Sciences, the Russian Academy of
Sciences, and the Hungarian Academy of Sciences.[2] 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.[2][9] 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.[3]
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.[3] He has spoken at the
**International Congress of Mathematicians**

International Congress of Mathematicians four times.[2] In 2000, he
was a plenary speaker at the First Latin American Congress in
Mathematics.[3]
Sinai is married to mathematician and physicist Elena B. Vul. The
couple have written several joint papers.[3]
Selected works[edit]

Introduction to
**Ergodic** Theory. Princeton 1976.[10]
Topics in
**Ergodic** Theory. Princeton 1977, 1994.[11]
Probability Theory – an Introductory Course. Springer, 1992.[11]
Theory of probability and Random Processes (with Koralov). 2nd
edition, Springer, 2007.[11]
Theory of Phase Transitions – Rigorous Results. Pergamon, Oxford
1982.[11]
**Ergodic** Theory (with Isaac Kornfeld and Sergei Fomin). Springer,
Grundlehren der mathematischen Wissenschaften 1982.[11]
"What is a Billiard?", Notices AMS 2004.[11]
"Mathematicians and physicists = Cats and Dogs?" in Bulletin of the
AMS. 2006, vol. 4.[11]
"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.[11]

References[edit]

^ 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
**Mathematics**

Mathematics Prize
Recipient". Northwestern University. Retrieved March 30, 2014.
^ a b c d e f g h i j "Yakov G. Sinai". Abel Prize. Retrieved March
30, 2013.
^ "Legendary Russian academic
**Yakov Sinai**

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
2017-06-28.
^ "The
**Abel Prize**

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.
doi:10.1090/s0002-9904-1978-14515-7.
^ a b c d e f g h "Yakov Bibliography" (PDF). Princeton University.
Retrieved March 30, 2014.

External links[edit]

Wikimedia Commons has media related to Yakov Grigorevich Sinai.

Sinai on scholarpedia
O'Connor, John J.; Robertson, Edmund F., "Yakov Sinai", MacTutor
History of
**Mathematics**

Mathematics archive, University of St Andrews .
**Yakov Sinai**

Yakov Sinai at the
**Mathematics**

Mathematics Genealogy Project
List of publications on the website of the Landau Institute for
Theoretical Physics

v
t
e

Laureates of the Wolf Prize in Mathematics

1970s

**Israel Gelfand**

Israel Gelfand / Carl L. Siegel (1978)
**Jean Leray**

Jean Leray /
**André Weil**

André Weil (1979)

1980s

**Henri Cartan**

Henri Cartan /
**Andrey Kolmogorov**

Andrey Kolmogorov (1980)
**Lars Ahlfors**

Lars Ahlfors /
**Oscar Zariski**

Oscar Zariski (1981)
**Hassler Whitney**

Hassler Whitney /
**Mark Krein**

Mark Krein (1982)
**Shiing-Shen Chern**

Shiing-Shen Chern /
**Paul Erdős**

Paul Erdős (1983/84)
**Kunihiko Kodaira**

Kunihiko Kodaira /
**Hans Lewy**

Hans Lewy (1984/85)
**Samuel Eilenberg**

Samuel Eilenberg /
**Atle Selberg**

Atle Selberg (1986)
**Kiyosi Itô**

Kiyosi Itô /
**Peter Lax**

Peter Lax (1987)
**Friedrich Hirzebruch**

Friedrich Hirzebruch /
**Lars Hörmander**

Lars Hörmander (1988)
**Alberto Calderón**

Alberto Calderón /
**John Milnor**

John Milnor (1989)

1990s

**Ennio de Giorgi** /
**Ilya Piatetski-Shapiro** (1990)
**Lennart Carleson**

Lennart Carleson /
**John G. Thompson**

John G. Thompson (1992)
Mikhail Gromov /
**Jacques Tits**

Jacques Tits (1993)
**Jürgen Moser**

Jürgen Moser (1994/95)
**Robert Langlands**

Robert Langlands /
**Andrew Wiles**

Andrew Wiles (1995/96)
**Joseph Keller** / Yakov G. Sinai (1996/97)
**László Lovász**

László Lovász /
**Elias M. Stein**

Elias M. Stein (1999)

2000s

**Raoul Bott**

Raoul Bott /
**Jean-Pierre Serre**

Jean-Pierre Serre (2000)
**Vladimir Arnold**

Vladimir Arnold /
**Saharon Shelah**

Saharon Shelah (2001)
**Mikio Sato** /
**John Tate**

John Tate (2002/03)
**Grigory Margulis**

Grigory Margulis / Sergei Novikov (2005)
**Stephen Smale**

Stephen Smale /
**Hillel Furstenberg** (2006/07)
**Pierre Deligne**

Pierre Deligne / Phillip A. Griffiths / David B. Mumford (2008)

2010s

**Dennis Sullivan**

Dennis Sullivan /
**Shing-Tung Yau**

Shing-Tung Yau (2010)
**Michael Aschbacher** /
**Luis Caffarelli** (2012)
**George Mostow** /
**Michael Artin**

Michael Artin (2013)
**Peter Sarnak**

Peter Sarnak (2014)
James G. Arthur (2015)
**Richard Schoen**

Richard Schoen /
**Charles Fefferman**

Charles Fefferman (2017)
**Alexander Beilinson**

Alexander Beilinson /
**Vladimir Drinfeld** (2018)

Agriculture
Arts
Chemistry
Mathematics
Medicine
Physics

v
t
e

**Abel Prize**

Abel Prize laureates

**Jean-Pierre Serre**

Jean-Pierre Serre (2003)
**Michael Atiyah**

Michael Atiyah /
**Isadore Singer**

Isadore Singer (2004)
**Peter Lax**

Peter Lax (2005)
**Lennart Carleson**

Lennart Carleson (2006)
**S. R. Srinivasa Varadhan**

S. R. Srinivasa Varadhan (2007)
**John G. Thompson**

John G. Thompson /
**Jacques Tits**

Jacques Tits (2008)
Mikhail Gromov (2009)
**John Tate**

John Tate (2010)
**John Milnor**

John Milnor (2011)
**Endre Szemerédi**

Endre Szemerédi (2012)
**Pierre Deligne**

Pierre Deligne (2013)
**Yakov Sinai**

Yakov Sinai (2014)
**John Forbes Nash Jr.**

John Forbes Nash Jr. /
**Louis Nirenberg**

Louis Nirenberg (2015)
**Andrew Wiles**

Andrew Wiles (2016)
**Yves Meyer**

Yves Meyer (2017)
**Robert Langlands**

Robert Langlands (2018)

v
t
e

Fellows of the
**Royal Society**

Royal Society elected in 2009

Fellows

Robert Ainsworth
Ross J. Anderson
Michael Ashfold
Michael Batty
Martin Buck
Peter Buneman
Michel Chrétien
Jenny Clack
Michael Duff
Richard Ellis
Jeff Ellis
James Gimzewski
David Glover
Chris Goodnow
Wendy Hall
Nicholas Harberd
John Hardy
Brian Hemmings
Christine Holt
Christopher Hunter
Graham Hutchings
Peter Isaacson
Jonathan Keating
Dimitris Kioussis
Stephen Larter
David Leigh
David MacKay
Arthur B. McDonald
Angela McLean
David Owen
Richard Passingham
Guy Richardson
Wolfram Schultz
Keith Shine
Henning Sirringhaus
Maurice Skolnick
Karen Steel
Malcolm Stevens
Jesper Svejstrup
Jonathan Tennyson
John Todd
Burt Totaro
John Vederas
John Wood

Foreign

John Holdren
H. Robert Horvitz
Thomas Kailath
Roger D. Kornberg
Yakov Sinai
Joseph Stiglitz
Rashid Sunyaev
Steven D. Tanksley

Royal

Prince William, Duke of Cambridge

Authority control

WorldCat Identities
VIAF: 34589101
LCCN: no2008147720
ISNI: 0000 0001 0963 856X
GND: 124663079
SUDOC: 031926576
BNF: cb129423333 (data)
MGP: 1