Yakov Grigorevich Sinai

Quick Info

21 September 1935
Moscow, USSR (now Russia)

Yakov Grigorevich Sinai is a Russian mathematician known for his work on dynamical systems. In 2014 he was awarded the Abel Prize for his fundamental contributions to dynamical systems, ergodic theory, and mathematical physics.


Both of Yakov Grigorevich Sinai's parents, Grigory Sinai and Nadezda Veniaminovna Kagan, were microbiologists with research careers. Yakov's mother Nadezda died when he was three years old having been infected by viral encephalitis while working in her own laboratory on making a vaccine. The family had strong mathematical connections since Yakov Grigorevich's grandfather (Nadezda Kagan's father) was Benjamin Fedorovich Kagan, the Head of the Department of Differential Geometry at Moscow State University where he founded an important School of Differential Geometry. It is also worth recording that the family was Jewish, and Kagan had a long struggle against anti-Semitism. It was, however, a family which had, over several generations, taken a leading role in Russian scientific and cultural life. Kagan had a large influence on his grandson. 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. There is one other member of the family we should mention, namely Grigory Isaakovich Barenblatt (1927-2018). He was the son of Isaak Grigorievich Barenblatt and Nadezda Veniaminovna Kagan, so was Yakov Sinai's half brother. He studied under Boris Moiseevich Levitan (1914-2004) and Andrei Nikolaevich Kolmogorov in the Department of Mechanics and Mathematics of Moscow State University and graduated in 1950. Two years later he married Iraida Nikolaevna Kochina, one of the two daughters of Nikolai Evgrafovich Kochin and Pelageia Polubarinova Kochina.

Talking about his school years, Sinai said [17]:-
I participated in many olympiads in mathematics during my school years but never had any success and never won any awards. I say this to young people who have never won in olympiads; there may be compensation in the future. At this time, my grandfather was of a great age and he did not have the energy to push me into mathematics. And I also have a half-brother, G I Barrenblatt, who worked at Moscow State University and who was convinced that I should pursue a career in mathematics.
German armies invaded the Soviet Union in May 1941 and came close to Moscow by October of that year. By this time Yakov Grigorevich was six years old and had started school but an evacuation of Moscow began. It was 1943 before the Sinai family could return to Moscow. Sinai said [17]:-
I entered school in 1943 after my family returned from the evacuation of Moscow. At that time boys and girls studied separately; at the end of each year, we had about ten exams. Before the evacuation, life was different. It was forbidden to leave windows open in the apartments in Moscow because it had to be dark. In 1943 windows were allowed to be open again. In Moscow there were no clear signs of war, but life was hard because of the time of Stalin.
By the time he was sixteen years old, he was fortunate to have an excellent mathematics teacher when he was at high school in Moscow [18]:-
We had a very good teacher in mathematics at our high school. His name was Vasily Alekseevich Efremov and he was a great old-style schoolteacher. He always brought us his problems in accurate handwriting on a piece of paper which he distributed among the students. Because of the well-organised and inspiring work, mathematics was very popular among us. We discussed and tried to solve his problems. At this time I was not among the best in the class. There were definitely other students who were much better than I.
Getting into university was not easy for Sinai since he was Jewish. At this time certain Soviet universities had a deliberate discriminatory policy to prevent Jews entering. Since Sinai was Jewish, when he took the entrance examination to Moscow State University, he was failed. Only the intervention of his grandfather, Benjamin Fedorovich Kagan, and that of the President of Moscow State University, Ivan Georgievich Petrovsky, saw the decision reversed and Sinai was allowed to begin his university studies.

Sinai took an analysis course from Mikhail Alekseevich Lavrentev, a classical mechanics course from Nikolai Guryevich Chetaev, and an algebra course from Eugene Borisovich Dynkin. His first advisor at Moscow State University was 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. However, he changed advisors and began to work with Dynkin. 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 he began to undertake research for his Master's Degree (equivalent to a Ph.D.) working with Andrei Nikolaevich Kolmogorov. His entry into the graduate school was not straightforward, however, since again he had to take entrance examinations. He was required to take an examination on the History of the Communist Party and, being a topic in which he had no interest, he failed. Pavel Sergeevich Aleksandrov was head of mathematics and he, together with Kolmogorov, went to see the Head of the History of the Party Department and asked that Sinai be allowed to resit. He took another History of the Communist Party examination and passed with grade B. It was deemed marginally good enough to let him begin graduate studies.

He was awarded a Master's Degree in 1960 and, in the same year, was appointed as a Scientific Researcher at the Laboratory of Probabilistic and Statistical Methods at Moscow State University. He continued to work towards his doctorate (equivalent to the German habilitation) under Kolmogorov. Other members of staff had a major influence on him at this time, particularly Israil Moiseevic Gelfand and Vladimir Abramovich Rokhlin who led the seminar on the metric theory of dynamical systems. 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. The term 'Kolmogorov-Sinai entropy' was quickly established [20]:-
Sinai's work deals with measuring dynamical systems, or systems that change over time, such as weather, the motion of planets and economic systems. These systems can be accurately measured in the short term (short term being relative to the issue at hand); but when analysed in the long term, the systems are difficult to understand and predict. 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. Dynkin and Gelfand were both invited plenary speakers but did not attend. Kolmogorov did attend the Congress and read Dynkin's lecture. Sinai delivered the half-hour address Probabilistic ideas in ergodic theory on the invitation of the Organising Committee. He also read Dmitrii Viktorovich Anosov's Short Address, The roughness of geodesic currents in compact Riemannian manifolds of negative curvature.

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. Novikov had just been appointed as head of the Mathematics Division at the Institute. Sinai continued to teach at Moscow State University but he did not become a professor there until 1981. The authors of [12] explain the reasons:-
His signing (together with many other mathematicians) in 1968 of the well-known letter in defence of A S Esenin-Vol'pin was for a long time a barrier preventing his becoming a Professor (he became a Professor only in 1981, 17 years after submitting his Ph.D. thesis).
Alexander Sergeyevich Esenin-Volpin was both a poet and a mathematician who led a human rights movement in the Soviet Union. Beginning in 1949, Volpin spent many years in prison for anti-Soviet poetry or in exile as a socially dangerous person. Sinai suffered much for his support of Volpin. For example in 1970 he was invited to lecture at the International Congress of Mathematicians in Nice. However, he was not allowed to go to Nice by the Soviet authorities. Many others were also prevented from attending the Nice Congress including Dynkin, Gelfand, Linnik, Manin, Shafarevich and Sergei Novikov who should have received a Fields Medal at the Congress. Sinai, however, was able to accept the invitation to deliver one of the plenary lectures at the International Congress of Mathematicians in Kyoto in 1990; he spoke on Hyperbolic Billiards. Continuing with his contributions to the International Congress of Mathematicians, we note that in 2001 he was appointed Chairman of the Fields Medal Committee of International Mathematical Union which decided on the awards of the Fields Medals at the Congress in Beijing in the following year.

In 1993 he was appointed Professor in the Department of Mathematics at Princeton University. He continued with his appointment at the L D Landau Institute of Theoretical Physics but gave up his position at Moscow State University. During 1997-1998 he was Thomas Jones Professor of Princeton University and in 2005 he was Moore Distinguished Scholar at the California Institute of Technology at Pasadena, California. He continued to hold his professorship at Princeton University until 2023 when he became professor emeritus. He continues (in 2023) to hold a professorship at the L D Landau Institute of Theoretical Physics in Moscow.

We have already looked at the deep contribution which was made by Sinai early in his career. Perhaps the best summary of his achievements up to the start of the 1990s is given in [5]:-
Sinai has done foundational, deep and highly influential work in the fields of ergodic theory, dynamical systems and statistical mechanics. Already in the sixties he had a deep understanding of the principles of what is now called chaos, and was among the first to recognise the significance of this phenomenon for dynamics. He has also done fundamental work in statistical mechanics. Besides his many major contributions to these subjects, he has had a very wide influence through a number of well-known expository texts and through his many research students.

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. In this he has had some remarkable successes. In ergodic theory his work on hyperbolic systems, on billiards and the hard sphere gas has laid the foundation of many of the techniques presently used for proving that such systems are ergodic and for studying the finer statistical properties of their behaviour. He has influenced the general trend of ergodic theory away from the study of rather artificially constructed examples back to the problem which originally motivated the subject, namely the substantiation of Boltzmann's ergodic hypothesis.

The idea of applying the Kolmogorov theory of entropy to smooth dynamical systems was Sinai's. Previous work of the Russian school had studied entropy, as introduced by Kolmogorov, entirely in the context of probabilistic systems. His results in this direction were new and unexpected. He investigated the class of dynamical systems with transversal foliations, now known as stable and unstable manifolds, and proved that all systems in this class were ergodic, mixing and K. Subsequently he introduced the idea of Markov partitions and constructed such partitions for hyperbolic systems.

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. He has made many contributions to statistical mechanics, in particular to the theory of phase transition. His book on this topic is well known. In recent years, Sinai has made important contributions to KAM theory using renormalisation methods. He is currently developing some entirely new and very interesting ideas in quantum chaos.
It is remarkable, given the depth and originality of Sinai's papers that he has been so productive. In [29] there are 386 papers listed with Sinai as author or co-author. Yet Sinai finds writing papers the least interesting part of doing research. He considers it boring since he has already achieved his aim of solving the problem which he may have thought about for several years and spent periods in which everything else had to be put out of his mind.

Sinai has received many major awards, prizes and honours for his remarkable contributions. For example he has received the following medals and prizes: the Boltzmann Gold Medal from the Commission on Statistical Physics of the International Union of Pure and Applied Physics (1986); the Heineman Prize from the American Physical Society (1989); the Markov Prize from the USSR Academy of Sciences (1990); the Dirac Medal from the Abdus Salam International Centre for Theoretical Physics in Trieste (1992); the Wolf Prize in Mathematics (1997); the Brazilian Award of Merits in Sciences (2000); the Moser Prize from the Society for Industrial and Applied Mathematics (2001); the Frederic Esser Nemmers Prize in Mathematics (2002); the Kolmogorov Lecture and Medal, University of London (2007); the Lagrange Prize from the Institute for Scientific Interchange, Torino, Italy (2008); the Henri Poincaré Prize from the International Association of Mathematical Physics (2009); the Dobrushin International Prize from the Institute of Information Transmission of the USSR Academy of Sciences (2009), the Leroy P Steele Prize (2013), the Abel Prize (2014), and the Marcel GrossmannAward (2015).

Here are some extracts from the citations for these awards. The Wolf Prize (1997) [7]:-
Sinai received the prize for "his fundamental contributions to mathematically rigorous methods in statistical mechanics and the ergodic theory of dynamical systems and their applications in physics." Sinai brings to bear on the problems of mathematical physics the powerful tools of dynamical systems and probability theory, often developing new tools for this purpose. He is generally recognized as the world leader in the mathematics of statistical physics. Working in the tradition of the Kolmogorov school, he first formulated the rigorous definition of the invariant entropy for an arbitrary measure-preserving map. His subsequent work covers areas from the ergodicity of the motion of billiards to spectral properties of quasi-periodic Schrödinger operators. Statistical mechanics is one of the most active and rewarding areas of modern mathematics, and Yakov Sinai is its recognised leader today.
The 2002 Frederic Esser Nemmers Prize in Mathematics [20]:-
His work has revolutionised the study of dynamical systems and influenced statistical mechanics, probability theory and statistical physics.
The Henri Poincaré Prize (2009) was awarded to Sinai:-
... for his ground-breaking works concerning dynamical entropy, ergodic theory, chaotic dynamical systems, microscopic theory of phase transitions, and time evolution in statistical mechanics.
The Leroy P Steele Prize for Lifetime Achievement was presented to Sinai on Thursday, 10 January 2013, at the joint meeting of the American Mathematical Society and the Mathematical Association of America held in San Diego. The Prize was awarded to Sinai for [26]:-
... his pivotal role in shaping the theory of dynamical systems and for his ground-breaking contributions to ergodic theory, probability theory, statistical mechanics, and mathematical physics.
The Citation states:-
Sinai's research exhibits a unique combination of brilliant analytic technique, outstanding geometric intuition, and profound understanding of underlying physical phenomena. His work highlights deep and unexpected connections between dynamical systems and statistical mechanics. ... In the past fifteen years Sinai has brought novel tools and insights from dynamical systems and mathematical physics to statistical hydrodynamics, obtaining new results for the Navier-Stokes systems. Specifically, along with D Li, Sinai devised a new renormalisation scheme which allows the proof of existence of finite time singularities for complex solutions of the Navier-Stokes system in dimension three. Sinai's mathematical influence is overwhelming. During the past half-century he has written more than 250 research papers and a number of books. Sinai's famous monograph, 'Ergodic Theory' (with Cornfeld and Fomin), has been an introduction to the subject for several generations, and it remains a classic.
In 2014 Sinai was awarded, what many would say is the most prestigious mathematical prize of all, namely the Abel Prize for his [1]:-
... fundamental contributions to dynamical systems, ergodic theory, and mathematical physics.
The citation for the award ends with the words [28]:-
Sinai has trained and influenced a generation of leading specialists in his research fields. Much of his research has become a standard toolbox for mathematical physicists. His works had and continue to have a broad and profound impact on mathematics and physics, as well as on the ever-fruitful interaction of these two fields.
Stein Arne Nistad gives an interesting description of the award ceremony [32]:-
When Yakov Sinai entered the university Aula in Oslo to receive this year's Abel Prize, an award as rare and prestigious as a Nobel Prize in physics or medicine, the gathering of dignitaries and great minds was one of the smartest likely to attend an event in the Norwegian capital this year. On the walls, eleven monumental murals by Norwegian artist Edvard Munch illuminated the vast hall with images of northern light and the ages of man. The audience included academics from home and abroad, national and international press, and a broad selection of people all with an above-average interest in the field of mathematics. The musicians entered the scene and the youthful Crown Prince Haakon, representing his father, handed over the beautiful and weighty Abel prize almost deferentially to the slightly stooped, academic giant.
As part of the Abel Prize presentation, Arne B Sletsjøe wrote four elementary articles which illustrate ideas introduced by Yakov Sinai, which you can see at THIS LINK.

In 2015 Sinai received the Marcel Grossmann Award [10]:-
... for applying the mathematics of chaotic systems to physics and cosmology.
The Citation stresses his contributions relevant to the relativistic astrophysics community [10]:-
Particularly noteworthy for the general relativity community are his fundamental results on the stochastic nature of early cosmology obtained in his pioneering 1983 paper in collaboration with E M Lifshitz, I M Khalatnikov, K M Khanin, and L N Shchur. Landau had designated the problem of the initial cosmological singularity as one of the three fundamental problems of theoretical physics and the members of his school V Belinski, I Khalatnikov and E Lifshitz then found the general cosmological solution near a big bang or big crunch singularity in a series of papers from 1969 into the 1970s. This "BKL solution" gives rise to a chaotic dynamical system characterised by a positive Kolmogorov-Sinai entropy. The chaotic behaviour of the higher-dimensional analogues of the BKL solution has also been deciphered by T Damour, M Henneaux and H Nicolai. The results of the Kolmogorov-Sinai school have thus illuminated the stochastic nature of the BKL cosmological solution.
Lev Shchur, a leading computational physics researcher at the Landau Institute, explained Sinai's involvement in this 1983 paper came about [33]:-
Once we were working on a problem in the now fashionable field of cosmology, and in the process of solving it a strong suspicion arose that the answer could be obtained precisely, and not just a numerical approximation. We called Sinai and shared our guesses. He thought for two minutes and said: "if it can be solved, then only in this way." Two hours later the solution was ready. Among other things, this shows how well he can work in a team. When a young scientist approaches him at a seminar and talks about something, Sinai can easily answer: "Are you doing this? I have ideas here too, let's do it together."
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); the Royal Society of London (2009); American Mathematical Society, Fellow (2013); and the Norwegian Academy of Science and Letters (2014). He has received honorary degrees from: Warsaw University (1993); Budapest University of Science and Technology (2002); the Hebrew University in Jerusalem (2005); and Warwick University (2010).

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).

For his seventieth birthday in 2005 a special issue of the Moscow Mathematical Journal was dedicated to Sinai:-
Yakov Grigorievich Sinai is one of the greatest mathematician of our days. The list of international prizes awarded to him as a sign of recognition of his scientific contributions is extremely long, the list of his fundamental results being even longer. His permanent interest in mathematics and his exceptional scientific enthusiasm inspires several generations of scientists all over the world. His mere presence at a seminar or at a conference makes scientific life brighter and more exciting.
In 1956 Yakov Grigorievich Sinai married his fellow student Elena Bentsionovna Vul, daughter of the famous physicist Bentsion Moiseevich Vul (1903-1985) who made a major contribution to the physics of semiconductors and dielectrics. Elena is a mathematician and physicist who has written a number of joint papers with her husband; seven are listed in [29]. They have one son.

What are Sinai's interests outside mathematics? As a young boy, he was good at chess but preferred football and volleyball. Later he liked both downhill and cross-country skiing. He loved the outdoors and often went hiking and mountaineering.

Let us end with some quotes from those who know him best. David Gabai, the Hughes-Rogers Professor of Mathematics at Princeton University, said after Sinai was awarded the Abel Prize [8]:-
I believe Sinai is definitely one of the great mathematicians of the 20th and 21st centuries and certainly one of the most influential mathematicians. He's also been a tremendous influence to the young people who have worked underneath him. For 50 years he's been producing stellar students.
The Dean for Research at Princeton University, Pablo Debenedetti, said [8]:-
He's widely considered to be one of the most influential mathematicians of the 20th century and this prize is unquestionably one of the most prestigious in mathematics. It's a wonderful recognition of a wonderful career.
Tel Aviv University professor and Erdős Prize winner Leonid Polterovich said [31]:-
I was not very surprised [Sinai received the Abel Prize] because I always knew that he was on the top level. ... Like all professors at Moscow State University, Sinai did not have a personal office, but shared a small room with about ten other mathematicians. I would meet in Sinai's office with Sinai and the rest of his advisees; topics discussed by Sinai ranged from mathematical physics to geometry. Students got the opportunity to learn about each others' projects, which was pretty important because Sinai was a very broad scientist. ... Sinai's seminar served for us as a door into the scientific world. ... He was a handsome man in an excellent physical shape, so he was doing some sports, had impeccable manners and highly developed social skills. These features were combined with a kind, friendly and human approach to people.

References (show)

  1. 2014: Yakov G Sinai, The Abel Prize, The Norwegian Academy of Science and Letters (2014).
  2. D V Anosov, A M Vershik, R V Plykin, E A Sataev, N E Klinshpont, D A Kamaev, Yu I Ustinov and S O Starkov, Yakov Grigorevich Sinai (on the occasion of his seventieth birthday) (Russian), Uspekhi Mat. Nauk 60 (5)(365) (2005), 183-186.
  3. D V Anosov, A M Vershik, R V Plykin, E A Sataev, N E Klinshpont, D A Kamaev, Yu I Ustinov and S O Starkov, Yakov Grigorevich Sinai (on the occasion of his seventieth birthday), Russian Math. Surveys 60 (5) (2005), 995-998.
  4. L Barreira, 2014 Abel Prize: Yakov G Sinai (1935-), Societat Catalana de Matemàtiques Notícies 37 (2015), 55-59.
  5. Citation for Yakov Grigorievich Sinai, Bull. London Math. Soc. 25 (1993) 303-304.
  6. Yu S Ilyashenko, K M Khanin, S Shlosman and M A Tsfasman, Yakov G Sinai, Mosc. Math. J. 5 (3) (2005), 497-498.
  7. Keller and Sinai Receive 1997 Wolf Prize, Notices Amer. Math. Soc. 44 (3) (1997), 351-352.
  8. M Kelly, Sinai receives Abel Prize for lifelong influence on mathematics, Office of Communications, Princeton University (26 March 2014).
  9. K Khanin, Mathematical journey of Yakov Sinai, Journal of Statistical Physics 166 (3-4) (2017), 463-466.
  10. Marcel Grossmann Awards, Rome 2015, International Center for Relativistic Astrophysics (2015).
  11. S P Novikov, L A Bunimovich, A M Vershik, B M Gurevich, E I Dinaburg, G A Margulis, V I Oseledets, S A Pirogov, K M Khanin and N N Chentsova, Yakov Grigorevich Sinai (on the occasion of his sixtieth birthday) (Russian), Uspekhi Mat. Nauk 51 (4)(310) (1996), 179-191.
  12. S P Novikov, L A Bunimovich, A M Vershik, B M Gurevich, E I Dinaburg, G A Margulis, V I Oseledets, S A Pirogov, K M Khanin and N N Chentsova, Yakov Grigorevich Sinai (on the occasion of his sixtieth birthday), Russian Math. Surveys 51 (4) (1996), 765-778.
  13. On the awarding of the Wolf prize to Yakov Grigorevich Sinai (Russian), Teor. Veroyatnost. i Primenen. 42 (4) (1997), 850-854.
  14. On the awarding of the Wolf prize to Yakov Grigorevich Sinai, Theory Probab. Appl. 42 (4) (1997), 717-719.
  15. B Rabar and S Slijepcevic, Yakov G Sinai - dobitnik Abelove nagrade za 2014, Matematicko-fizicki list 55 (1) (2014-2015), 21-24.
  16. R Ramachandran, Mathematician Ya G Sinai is 2014 Abel Laureate, The Hindu (26 March 2014).
  17. M Raussen and C Skau, Interview with Yakov Sinai - Abel Laureate 2014, European Mathematical Society Newsletter 93 (2014), 12-19.
  18. M Raussen and C Skau, Interview with Yakov Sinai, Notices of the American Mathematical Society 62 (2) (2015), 152-160.
  19. Russia's Yakov Sinai wins Abel mathematics prize, Phys.Org (26 March 2014).
  20. Sinai Receives 2002 Nemmers Prize, Notices Amer. Math. Soc. 49 (7) (2002), 802.
  21. Sinai Awarded 2014 Abel Prize, Notices of the American Mathematical Society 61 (6) (2014), 628-629.
  22. A B Sletsjøe, Chaos: Yakov G Sinai, Abel Prize Laureate 2014, The Abel Prize, The Norwegian Academy of Science and Letters (2014).
  23. Arne B Sletsjøe, Dynamical billiard: Yakov G Sinai, Abel Prize Laureate 2014, The Abel Prize, The Norwegian Academy of Science and Letters (2014).
  24. A B Sletsjøe, Entropy of 0, 1-sequences: Yakov G Sinai, Abel Prize Laureate 2014, The Abel Prize, The Norwegian Academy of Science and Letters (2014).
  25. A B Sletsjøe, The entropy of a dynamical system: Yakov G Sinai, Abel Prize Laureate 2014, The Abel Prize, The Norwegian Academy of Science and Letters (2014).
  26. Yakov Sinai Receives 2013 AMS Steele Prize for Lifetime Achievement, Department of Mathematics, Princeton University (2013).
  27. Yakov G Sinai, Biography, The Abel Prize, The Norwegian Academy of Science and Letters (2014).
  28. Yakov G Sinai, Citation, The Abel Prize, The Norwegian Academy of Science and Letters (2014).
  29. Yakov G Sinai, Landau Institute of Theoretical Physics.
  30. P Yas'kov, Russian mathematician wins the 2014 Abel Prize, Theory of Probability and its Applications 59 (1) (2015).
  31. Daily Princetonian Staff and A Windemuth, Abel Prize winner Yakov Sinai: a lifetime of artful mathematics, The Daily Princetonian (9 April 2014).
  32. S A Nistad, Chaos vs Disorder, Reflection. PGS Magazine (2014 / 2), 14-17.
  33. Axiom of Generosity (Russian), Magazine "Ogonyok" (26 May 2014).

Additional Resources (show)

Other pages about Yakov Grigorevich Sinai:

  1. An elementary approach to concepts by Yakov G Sinai

Other websites about Yakov Grigorevich Sinai:

  1. Mathematical Genealogy Project
  2. MathSciNet Author profile
  3. zbMATH entry

Honours (show)

Cross-references (show)

Written by J J O'Connor and E F Robertson
Last Update December 2023