Interview with Yakov Sinai Martin Raussen and Christian Skau Yakov Sinai is the recipient of the 2014 Abel Prize of the Norwegian Academy of Science and Letters. This interview was conducted by Martin Raussen and Christian Skau in Oslo on May 19, 2014, in conjunction with the Abel Prize celebration. This article originally appeared in the September 2014 issue of the Newsletter of the European Mathemati- cal Society and is reprinted here with permission of the EMS. Professor Sinai: Yes. That happened on March 26. Youth Raussen and Skau: You were born in Moscow in 1935 into a family of scientists. Your parents were both biologists, and your grandfather was well known in mathematics. We suppose this had important consequences for the development of your interests? Professor Sinai: Definitely, yes. How could I say no to this question? Everything was about math- © John Jameson/Princeton University ematics and mathematical events. But, at that time, Professor Yakov Sinai I preferred to play volleyball. The Prize The influence of mathematics was not as direct Raussen and Skau: Professor Sinai, first of all we as you may think. I participated in many olympiads would like to express our congratulations. You have in mathematics during my school years but never been selected as the twelfth winner of the Abel Prize had any success and never won any awards. I say and you will receive the prize tomorrow. We are this to young people who have never won in olym- curious; did you have any expectations beforehand? piads; there may be compensation in the future. How did you receive the information? At this time, my grandfather was of a great age Professor Sinai: In early March this year I got and he did not have the energy to push me into to know that the Abel Committee was interested mathematics. And I also have a half-brother, G. I. in taking my photograph. A friend of mine told Barrenblatt, who worked at Moscow State Univer- me this, and I thought this must mean something sity and who was convinced that I should pursue because this had never happened before. And then a career in mathematics. there was a telephone call from the Norwegian Raussen and Skau: Do you remember when Academy of Science and Letters informing me you found out that you had an exceptional talent about the prize. for mathematics? Raussen and Skau: And this was on the same Professor Sinai: If at all, it happened very late. day that the prize was announced here in Oslo? I was a graduate student when I brought my paper on entropy to my advisor, A. N. Kolmogorov and Martin Raussen is associate professor of mathematics he said, “At last you can compete with my other at Aalborg University, Denmark. His email address is students.” But I am not sure that he was right and [email protected]. that I have an exceptional talent for mathematics. Christian Skau is professor of mathematics at the Norwe- Raussen and Skau: You must have entered gian University of Science and Technology, Trondheim, Norway. His email address is [email protected]. school at about the same time that Nazi Germany invaded Russia. How did the war influence your DOI: http://dx.doi.org/10.1090/noti1210 first years at school? 152 NOTICES OF THE AMS VOLUME 62, NUMBER 2 Professor Sinai: I entered school in 1943 after the enthusiastic students. Among such students in my family returned from the evacuation of Mos- my year I could particularly mention I. Girsanov, cow. At that time boys and girls studied separately; who became a famous probabilist, and L. Seregin. at the end of each year, we had about ten exams. Raussen and Skau: Was it Dynkin who inspired Before the evacuation, life was different. It was your first paper in mathematics? forbidden to leave windows open in the apart- Professor Sinai: Yes. I was a student of Dynkin ments in Moscow because it had to be dark. In during the second and third years and I wrote 1943 windows were allowed to be open again. In the first paper under his supervision. I solved a Moscow there were no clear signs of war, but life problem that he formulated for me; this became was hard because of the time of Stalin. People had my first published paper when I was a student in to behave in a special way. the third year. I loved the work I did and still do. Raussen and Skau: And that also influenced Dynkin wanted me to work on problems on life at school? Markov processes in the style of Feller. The papers Professor Sinai: It was everywhere; you could by Feller became very popular in Moscow at that be expelled from school or even sent to prison for time, and Dynkin suggested that I should continue being controversial. along this line. However, I was not very excited and Raussen and Skau: Were there teachers with a interested in it. lot of influence on you, in particular in mathemat- Raussen and Skau: To what extent were mathe- ics? matics and mechanics integrated in the curriculum? Professor Sinai: We had a very good teacher Professor Sinai: These were independent parts in mathematics at our high school. His name was of the curriculum. Everybody could attend lectures Vasily Alekseevich Efremov and he was a great within each branch. I was attending lectures in old-style schoolteacher. He always brought us his mathematics and mechanics but also, to a minor problems in accurate handwriting on a piece of degree, some lectures in physics. But on the whole paper which he distributed among the students. it was mainly in the mathematics department. Because of the well-organized and inspiring work, Raussen and Skau: We imagine that besides mathematics was very popular among us. We Dynkin, Kolmogorov and Gelfand must have been discussed and tried to solve his problems. At this very important figures for you? time I was not among the best in the class. There Professor Sinai: Kolmogorov had many stu- were definitely other students who were much dents, and I became one of them. His students better than I. had complete freedom to work on any problem. Raussen and Skau: What was your age at this Kolmogorov loved to discuss their results. There point? were several cases when Kolmogorov wrote their Professor Sinai: This was still in high school just papers in order to teach them how to write math- before I entered university. Thus, I was probably ematical texts. sixteen or seventeen years old. Kolmogorov organized a seminar, which was initially a seminar on random processes and later Student at MSU-Mech-Mat became a seminar on dynamical systems and Raussen and Skau: You entered the Faculty of ergodic theory. I began to attend, together with Mechanics and Mathematics at Moscow State Uni- other mathematicians like Arnold, Alekseev, Tik- versity in 1952 still a teenager. How was it to study homirov, and others. Later I became a student of at this famous institution as such a young student? Kolmogorov. At that time he was also interested Professor Sinai: We had a number of very good in problems of entropy in different compact and professors there. For example, the lecture course functional spaces. Questions of this type were very in analysis was given by M. A. Lavrentiev, who was much discussed at that time. a very famous scientist at the time. He was also Raussen and Skau: But Gelfand tried to recruit involved in administration but was a great teacher you as a graduate student as well? and his lectures were very interesting. We also Professor Sinai: Yes. Gelfand organized his had a very good lecturer in classical mechanics, famous seminar, which was attended by many Chetaev. I was his student in the second year. More- mathematicians of different generations. I took over, we had lectures in geometry given by Bach- part in it for many years. It happened, if I remem- valov, who was famous in Russia but not so much ber it correctly, in 1955 when Gelfand was writing known in the West. There is a story about him: a famous volume in his series of books on distribu- when we entered the university on 1 September, tions. Gelfand was interested in probability theory he came into the room and said, “Let’s continue.” and he wanted me to become his student. We had And that was the beginning of his lecture course. some discussions about it, and I told him that I In algebra we had lectures by Dynkin, who was wanted very much to work on problems related an excellent teacher for those who had started to to probability theory but I had already written a study. These were lectures at a very high level. paper under the supervision of Dynkin. He asked Dynkin used to hand out interesting problems for me, “Do you want to have probability theory as an FEBRUARY 2015 NOTICES OF THE AMS 153 appetizer or as a dessert?” I answered, “I want it this limit. The existence of the limit actually fol- as a main course.” That was the end of the story.… lows from some hypothesis about the equations of This did not mean that our contact came to motion. This gives the existence of the distribution, an end; we met many times, especially when he which determines the value of all kinds of averages worked on problems in representation theory, (or, it is better to say, the existence of the averages which were connected with problems in ergodic and also finding their values).