Abel Prize winner Yakov Sinai: a lifetime of artful mathematics

While mathematics professor Yakov Sinai is known worldwide for his paramount contributions in dynamical systems, mathematical physics and probability theory, his students and friends say that he is, most strikingly, a gentleman.

A few of Sinai’s major developments in math include Kolmogorov-Sinai entropy, Sinai’s billiards, Sinai’s random walk, Sinai-Ruelle-Bowen measures and Pirogov-Sinai theory.

Sinai was recently awarded the prestigious Abel Prize in mathematics by the Norwegian Academy of Science and Letters for the cumulative impact of his research, adding to a long list of recognitions and accolades over the span of his 50-year career. The committee recognized Sinai for his groundbreaking results in the field and for establishing profound bridges between mathematics and physics.

“First I was surprised, then I was very glad,” Sinai said of his reaction to the award, adding that his best student, Grigory Margulis, was the first to congratulate him at six in the morning.

Many of his former advisees, however, said they were anything but surprised.

“I was very happy that he was elected now and that justice has been done, because in my mind he definitely belongs to this category,” University of Toronto professor Konstantin Khanin said.

“I was extremely happy and very proud that somebody whom I love, who was my supervisor, got this Abel Prize,” Tel Aviv University professor and Erdős Prize winner Leonid Polterovich said. “I was not very surprised because I always knew that he was on the top level.”

“I was waiting for this event already for some years,” Georgia Insitute of Technology professor Leonid Bunimovich said.

Sinai was also awarded $1 million in prize money from the Norwegian committee, which he plans on giving to his wife, Elena Vul.

“She will be 80 this year so that will be my present for her 80th birthday,” Sinai said.

Sinai is the author of several books and over 250 research papers, some of which he published with his wife, whom he met at Moscow State University and who is also a mathematician.

A family of academics

Sinai’s academic legacy reaches as far back as his grandfather, who was the head of the Department of Differential Geometry at Moscow State University, the institution from which Sinai obtained his undergraduate, master’s and doctorate degrees and eventually became a professor in 1971. He was named a senior researcher that same year at the Landau Institute for Theoretical Physics near Moscow.

Sinai’s parents were both microbiologists, and his stepbrother was a very successful mathematician, strongly influencing Sinai’s academic path.

“My father wanted me to be an engineer,” Sinai explained of his early career prospects. “He thought that engineering was easier to apply to a job.”

Instead, Sinai pursued dynamical systems and was advised by Andrey Kolmogorov, a famous mathematician and Wolf Prize winner. The two developed the Kolmogorov entropy theory together while Sinai was a graduate student.

Sinai joined one of Kolmogorov’s seminars as an undergraduate and was later invited to become one of his advisees. Undergraduate students who showed academic promise were automatically inaugurated into the graduate program, Sinai explained.

“I could not solve the problems which he gave to me and he was very unhappy with me, but then later the situation changed,” Sinai said of his advising experiences with Kolmogorov.

Teaching in the Soviet Union

Like all professors at Moscow State University, Sinai did not have a personal office, but shared a small room with about 10 other mathematicians, according to Polterovich. Polterovich, who would meet in Sinai’s office with Sinai and the rest of his advisees, noted that 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,” Polterovich said.

Khanin said that although it was harder to gain access to papers and research materials, the Moscow mathematics community always had a large number of visitors and was not isolated in the field. Sinai also travelled to Western countries during his professorship at Moscow State.

Technische Universität München professor Herbert Spohn said he met Sinai during a 1975 conference on statistical physics at which Sinai spoke. Spohn, a German mathematician and mathematical physicist working with topics including kinetic equations and disordered systems, noted that Sinai was already very famous in the field and added that such conferences were truly exciting scientific exchanges, enabling a key form of communication among scientists that was not facilitated at the time.

However, when Sinai was awarded the Boltzmann Medal in 1986 for his work in statistical physics, he was not allowed to go abroad to accept the prize because international travel was heavily restricted during the Communist regime, according to Bunimovich.

Despite ideological exchanges, the top mathematical institutions in Moscow in the late 1970s and ’80s had virtually no Jewish professionals due to the communist regime’s anti-Semitic policies, which prevented the acceptance of new Jewish professors, Polterovich explained. Therefore, many of Sinai’s seminar participants could not work in academia, but pursued engineering or researching.

“Sinai’s seminar served for us as a door into the scientific world,” Polterovich said. He also noted that although it was common for bosses at that time to be “rude, harsh and oppressive” towards subordinates, Sinai was uniquely friendly.

Challenging Seminars and Lectures

Sinai ran two influential seminars on dynamical systems and on statistical mechanics, Polterovich said. He added that Sinai often invited speakers and discussed problems for weekly two-hour sessions that often went overtime, and would spur discussion by asking the speaker questions.

“Participants learned actually from these questions often more than from the talk itself, but somehow Sinai did this in a very friendly and polite manner,” Polterovich explained.

The seminars always featured lively discussions among many bright people, Bunimovich recalled. Bunimovich, who later garnered acclaim for his work in dynamical systems, said that at the very beginning he was embarrassed and couldn’t understand a thing.

“A lot of problems were solved right there,” he explained. “It was the place where the most interesting parts of our lives happened.”

Sinai’s seminars had a uniquely pleasant atmosphere, Polterovich recalled, and Sinai’s charisma was a driving force towards this quality.

“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,” Polterovich said.

University of California at Irvine professor Svetlana Jitomirskaya said she recalls taking a probability and statistics class with Sinai, where all examinations were conducted orally. Jitomirskaya said she often opted to take her exams early, as she would be questioned by Sinai instead of a random examiner and knew she could study his favorite material to prepare.

During one of these exam sessions with Sinai, Jitomirskaya answered all of his questions on probability without difficulty. As he was about to inscribe “excellent” in her grade book, however, he remembered to ask her a basic question about statistics, since the class involved both topics. Jitomirskaya said she had not studied the material because she had previously noticed Sinai’s much stronger enthusiasm for probability.

“At that moment, perhaps of all the stress of almost succeeding, I somehow completely blanked, with the only thought rushing through my mind being ‘Here goes my A,’ ” she recalled.

Sinai lifted his pen again and wrote “excellent.”

“I am sure you will learn it very fast when you need it,” he said.

Jitomirskaya explained that this episode definitely played a role in her motivation to become Sinai’s student, as he showed her respect long before she deserved it.


Sinai advised over 50 Ph.D. students over the course of his career and was known for introducing them to insightful challenges.

“I spent half of my life working with each of my students because we were working on problems which were interesting for both of us,” Sinai explained.

Sinai was always surrounded by students, according to Khanin, who said that Sinai was not only well established at an early age but also had the charisma to attract students. Khanin explained that Sinai would provide enough guidance to ignite enthusiasm in his students, but also gave them the freedom to form their own original ideas.

“He naturally had this ability to inspire young people and to get them into research,” Khanin said. “He was caring but he was not over-caring.”

Polterovich said that Sinai was a very gifted supervisor, approaching students of varying levels with patience and flexibility.

“Some [students] were probably with less potential at the beginning but somehow he had the key to develop a person,” Polterovich said. He also said that Sinai only co-authored a paper with a student if he had written the majority of it.

“Sinai took care of students in various stages of their lives, which included, for instance, finding help with finding jobs,” Polterovich added, noting that finding jobs was a particularly difficult feat in Russia.

Jitomirskaya was one of Sinai’s advisees at Moscow University a few years before he moved to Princeton in 1993 and said that he advised an incredible number of students.

“Still, he managed to give quite a bit of attention to everyone and he managed to put his students on totally different roads,” Jitomirskaya explained.

Jitomirskaya also said that Sinai was an engaging professor and that he was always very polite to his students.

“He is a real gentleman. He always showed respect to his students even when they did not deserve it,” she said.

Although Sinai’s projects were very challenging, Jitomirskaya said, her initial struggles helped prepare her for the field’s inevitable obstacles and improved her resilience.

Sinai at Princeton

Sinai transitioned to teach mathematics at the University in 1993 following the dissolution of the Soviet Union. Sinai will be teaching MAT 385: Probability Theory next fall.

Sinai said that he visited several times before committing to a teaching position and that the University offered considerably better academic resources than other prospects.

“I had many friends here and the scientific climate here was very good,” Sinai said.

Alex Kontorovich ’02, an assistant professor of mathematics at Yale, who took Sinai’s probability class and later wrote both his spring junior paper and his senior thesis under Sinai’s guidance, said Sinai was a caring adviser with striking humility.

“If there’s something that you don’t understand then it’s my fault, not your fault,” Kontorovich recalls Sinai saying during his lectures. Kontorovich also said he wanted to work with Sinai because Sinai was a fantastic lecturer who made everything exciting and interesting.

Sinai remains a senior researcher at the Landau Institute for Theoretical Physics and won a number of prizes during his time at the University, including the Wolf Prize in Mathematics, the Nemmers Prize and the Leroy P. Steele Prize for Lifetime Achievement. Sinai also holds several honorary degrees and became a Moore Distinguished Scholar at the California Institute of Technology in 2005.

Sinai is a remarkable example of scientific longevity, Posterovich said, as he maintains a youthful curiosity, great technical skills and continues to produce superb mathematics.

According to the famous theoretical physicist and mathematician Freeman Dyson, there are two kinds of mathematicians: frogs and birds. While frogs reside in the mud and enjoy scoping out details, birds spend their time in the air, unifying different concepts under a mathematical umbrella. Bunimovich said Sinai is clearly a bird.

“He opens up so many new directions,” Bunimovich explained. “A new, interesting approach in mathematics is as important as fresh air.”

When asked about his advice to young students striving to make a difference in the world, Sinai’s answer was simple: “Always do what you like.”

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