Interview with Prof. Alexander Bobylev

Interview Editorial Consultant: Tai-Ping Liu
Interviewer: Tai-Ping Liu(TPL)
Interviewee: Alexander Bobylev(AB)
Date: October 22-23, 2019
Venue: Institute of Mathematics, Academia Sinica

Prof. Alexander Bobylev was born in Moscow on February 27, 1947. He received his M.S. from Moscow Engineering Physics Institute (MIFI) in 1972 and earned his PhD in 1977 from the Keldysh Institute of Applied Mathematics (KIAM), which was called the Institute of Applied Mathematics, USSR Academy of Sciences before 1978. Between 1973 and 1999, he served at KIAM and then served at Karlstad University in Sweden from 2000 to 2014. Since 2014, he has been a Chief Scientist at KIAM. For his outstanding contributions in the fields of aerodynamics and mathematical physics, he won several awards, including USSR State Prize in Science and Technology.

TPL: Let’s get started. I would like to ask you just a question I have in mind now first. You had been in Russia all these years and then you came to the West. There’s clearly some differences, in general cultural and scientific environment, right? Would you like to make some comments on that?

AB: Oh, this is a complicated story. I lived in Soviet Union until its end. So I was 44 in 1991. And then we were not allowed, most of us have difficulties, to go abroad, say, before 1986. And when I started to work in Keldysh Institute, I published a few papers in 70s which caused some interest to my work. Then, more or less, regularly I started getting invitations to different conferences. But only once I was allowed to go. First time I was allowed to go was in 1982 to Oberwolfach. And it was, of course, interesting experience. It was one week in Oberwolfach. I was impressed by a level of comfortability for this institute and organization of conference, and how nice it was to stay here. And I have some people who are my friends since that moment, in particular, Mario Pulvirenti. I met him first there, and Herbert Spohn also. And then I started to travel much more frequently after Gorbachev Era, which started in 1985. But I would not say that the destruction of Soviet Union was what I wanted. Actually I never planned to emigrate. I just wanted, from the beginning, to spend more time abroad and to do some job there and more or less, this was the way to support my family. And I thought that a period like 3-6 months per year is enough. But then I understood that there is no way back. And the social interest to science in Russia was absolutely lost in the beginning of the 90s. So roughly speaking, they stop paying us salaries. We got salaries like students and this was the same situation with almost all people for professions like teacher. So this was a very difficult transition in Soviet Union, in Russia, whatever you call it, in 90s. And finally, I decided to apply the position in Sweden and I got it in 1999. Then I stayed 15 years in Sweden. Then I retired and came back to my institute in Moscow. A few words about differences in educational systems in the West and in Russia. I have been working at some universities on both sides and I could try to compare. That’s not only comparing, as I say, university job in Soviet Union and in the West, but also, it is generational question. You mentioned this yesterday that our generation looked completely different when we were students compared to today’s students. And in our generation, roughly, I related the difference in one sentence—in Soviet Union, teachers were bosses and students were slaves. In the West, sometimes it is vice versa. (laugh) But I think in the East, there is a difference. You respect, let’s say, people of certain age. But in some western countries, there’s not very much respect.

TPL: But, let me intercept, but I can see that in Karlstad, you were very much respected.

AB: Well, I would say yes. I don’t want to complain about everything. It was very nice in Karlstad, but, simply, in Sweden, it is very, say, rigidly, that after 67th birthday, now 69—but in my time, it was 5 years ago, it was still 67—you must apply immediately for retirement. Otherwise, you just wait until your administration does it themselves on your behalf just on the basis of your age and that’s it. There was a Swedish professor—at least, there was such a rumor—I heard that he tried to protest and went to a court, tried to appeal that this is, of course, discrimination by age. But he lost. Therefore, no one wants to do it again.

TPL: You mentioned that after Soviet Union dissolved during the Gorbachev era, general public has a different attitude toward science and education. Why is that?

AB: First, of course, also, I found that in the West the science is not very popular. If you are in United States, you will find just a few “white Americans” (I mean people who are not emigrants in the first generation) in many mathematical departments. I don’t say about very prestigious universities like Princeton or Harvard, but in a regular university. Somehow it’s clear that people don’t consider it as a very profitable work. But on the other hand, it was always so. I remember memories of Hardy, where he writes about it. Of course, the career of a university teacher is something when you don’t want to take too much, to have too much, but you want safety. And safety is something you can have at a university job. But why I mention it? Because in Soviet Union, it was a bit different. Maybe, let’s say, also, we were both also students in 60s. In 60s, science was extremely popular in Soviet Union. But I guess, also in the United States, especially when they started to compete.

TPL: With Russia.

AB: Yes. And so I was happy. I was very proud that I joined this Keldysh Institute at that time. It was not yet called Keldysh Institute because Keldysh was alive and its director. So the science was very much respected, it was an official point of view. There were people in government, in party who decide that science is important, but mostly because of military applications, of course, and the technological application. But then in all newspapers, scientists are described only from a positive side. And then, all this was, also, in the whole world, the total number of scientists was exponentially growing and it was clear that something must be changed. Otherwise, all, we now, would be physicists or mathematicians. Anyway, something really changed since that time, we see it. I think the governments expected that something like a new kind of thermonuclear weapon will be created. Therefore, they paid a lot for research of elementary particles, for example. This part of physics is not actually related to application and never showed itself useful for military application. But it costs more and more and more, these accelerators, huge accelerators and it was decided that, okay, now, things moved completely to biology, for example, and this is, I think, a general trend.

TPL: I see. So what happened after Soviet Union ended, in some sense, it is just go back to normal situation?

AB: Yes, on one hand. On the other hand, it was too dramatic. It was like a hurricane in 1992, actually, millions of people actually lost jobs though many of them formally didn’t lose the job. Simply, it was inflation like a thousand percent the first half of 90s. And so, you have the same salary, but it’s nothing and people understood that nobody need them. And so, this was a very dramatic situation for many. I was lucky because I had good connections with some universities in Europe. So, it was now, years from 1991, when I spent 3 and more months per year abroad, collaborating with my colleagues in Italy, Germany, France, Norway. This was a complicated period for most of Russians.

TPL: I see. Let’s go back to the Soviet Union time because that is as normal as others as you have explained it. In the early 1970s, I was a graduate student and my advisor told me that you should learn Russian. Before it was German, but now, Russia is the language for the sciences. Russians are excellent. So I tried to learn Russian. To learn the alphabets is already very difficult for me. At that time, it’s fair to say that Russia was on top in fields that I know, such as in mathematics. You have great people like Kolmogorov and so on. Now, that was also the time you started your career in the early 70s. So maybe, you could describe a little bit. It must be an exciting time. But at first, before you go to university doing research, there may be also a process starting in high school? I understood that, there, some people who are very talented are already put into selective high school before entering the university.

AB: Let me thank you very much for your kind words, of course, about Soviet Union and, in particular, Soviet science. But actually, I can speak only about my own experience. So, as I just said, in 60s—also, it was a big interest to science supported by government in Soviet Union, I don’t want to use expressions like totalitarian state or something like that, but at least, if it was decided in the government, that certain point of view was postulated, then you read in all newspapers only one opinion. And I remember that members of Academy of Sciences were extremely important, extremely respected. And also, what was interesting is the huge difference, I would say, with the situation now: There is one problem which is well known in Russia; yesterday, I read that 10 % of population now have 83% of everything. But no one respect these people because no one understands how they made it. In contrary, especially in my generation, in generation of people whose background is from even earlier times in Soviet Union, there were rich people, relatively, for example, all members of Academy were consider like that. They had summer houses, cars with the drivers, etc., but somehow, there was no protest because it was considered that they deserved it, and such logic is very important. For example, also, now, we understand that in normal situation, football player must get big money simply because there are tens of thousands, sometimes, hundreds thousands of viewers who come to the game or want to view them in TV. And if it is just a team of 11 players, probably, they deserve, also, some money. But not in Soviet Union. Sport was considered, actually, as not professional. Professional sport was forbidden. And therefore, people did not like that football players have, also, big money. But for scientists or for actors, not for famous artists, no. Sorry, I may be moved too far from the question.

TPL: Oh, no, no.

AB: And also, for example, as many boys, I wanted to be a sailor because I was growing up in Odessa—it is now Ukraine—on the Black Sea. I always had good grades in school. But then, also, I read newspapers and journals. I started to read more and more about physics and then I started thinking that maybe I must do physics and mathematics. So it was, shortly speaking, it was mostly influence of media maybe. My mother was a doctor, my father was a military officer and there was no people doing physics or mathematics in the family. On the other hand, it was very easy for me to do school mathematics and I remembered that, when it was time, in crucial time, to make a choice. We were supposed to study 11 years in school. And after first 8 years, you can choose some professional direction. By chance, I saw a new school with the announcement that there will be 2 mathematical classes there. To be accepted you need a sort of composition, not entrance exams, but at least some interviews. And this was how I started and I must say that in my class, it was about 30 people and all they were very good in mathematics. None of them became famous, but they all became decent professionals in education, science and engineering.

TPL: Yes.

AB: Just one more thing. I might be not quite stupid, but I was in doubt—am I able to do mathematics or physics—because I always see the science as an art. In any art, there are only a few people who really are good. The rest maybe also needed, but only to be in the background? Then I remember the article in general newspaper, not in scientific, but in central newspaper. It was an article by Kolmogorov, and he said that, now (in the beginning of 1960s!), mathematics needs a lot of new people and don’t be afraid that you are not good enough because we’ll find work for you! Note that it was a beginning era of computers and the working specialty, we studied in my school, was a programmer. So it’s very funny to think now about it because to be a programmer, at that time was a very difficult job. I remember a big computer with a magnetic band which was often broken. Programs must be written in digital codes and it was much more difficult work than now.

TPL: I remember when I was a graduate student, we had to stack up the cards to put inside the computer and if it happened to fall on the ground and then you have to put back into the right order.

AB: Yes, yes, yes, cards. Magnetic band was the worst because it was less reliable.

TPL: In carrying our research, you have a unique way. You try to find the exact solution in some sense, right? it seems that people doing mathematics in the physics community operate that way, is this so? They go to great length, to use special functions, for example, so that they can express the solution in the neat formula. If what I said makes sense, how did you get to that route doing research when you started?

AB: Okay, probably I must say a few words about difference between physics and mathematics. I also read books (not only newspapers!) before I entered university and I remember one book, which was a biography of Einstein. I also remember one point from the book. At that age, as we discussed yesterday, you automatically look for good sentences for citations. So the book says that Einstein once said that mathematics is beautiful, but the problem with mathematics is that you don’t know where to go. You don’t see the right direction. So the mathematics is too big in a sense. You don’t have a criteria—what is really needed and what is just exercise of your brain, which is completely senseless otherwise, or meaningless. And physics can tell you that this direction is definitely correct because we have nothing around us but nature. And whatever we do in physics, we try to clarify something related to nature.

TPL: The observations.

AB: Yes, yes, yes. And the criterion is the experiment, the observation. It was his sort of explanation why he chose to do theoretical physics. So somehow, I remembered it. And also, there was a second point. I still consider mathematics is a sort of pure art and I was very much in doubt if I’m good enough for it. Another thing that the choice of university in Soviet Union was narrow more or less. There were 3 appropriate institutes in Moscow for me (now they all are called universities): Moscow Physical Engineering Institute, Moscow Physical Technical Institute and Moscow State University. But then, when you decide where to go, you first try to solve all the problems that they give in entrance exams. And finally, I chose Moscow Engineering Physics Institute partly because I was afraid of difficult problems in exams. I mentioned only these three institutes, because they had entrance exams a month before others, so you have the second chance if you lost. And for men, it was extremely important because if you lose, you go to army and army was 3 years or even 4 in Navy. If you go to Navy, then you needed to spend there for 4 years of your life. Now these periods are shorter, than it was in 1965.

TPL: Okay. But you wanted to be a sailor.

AB: I wanted, yes, but I changed my mind completely. You said yesterday that after age 10, a person has no change. I can say there was a dramatic change for me. But absolutely, I wanted to.

TPL: I see.

AB: Going back to your question, let me say a few words about the university (known to Russians as MIFI) where I was a student. Now it is called National Research Nuclear University (MIFI). Roughly speaking, it is the main source of specialists in nuclear industry and nuclear research for Russia. And I wanted to be—you asked me about my relations to physics and mathematics—so I wanted to be in theoretical physics, but I did not pass the crucial exam. There was a strong composition after first 2 years among students, who wanted to study theoretical physics. I still remember the decisive question at the exam. I think professor was not correct. The exam was on the piece of theoretical physics that includes electrodynamics and special relativity in mechanics. And he asked me why it is impossible to move with the speed greater than the speed of light. In my view, it is a very philosophical question, which is impossible to answer, at least, today.

TPL: This is the way it is.

AB: Yes, because it’s postulated. Yeah. I started thinking and then after one minute, he became angry and said: “You don’t know, because momentum is infinite!”. And then, I lost one year as a result because I was not accepted. I tried to continue as experimentalist, but I found that my hands are not good enough and really wanted to do theory. Then I found, maybe half a year after, that we have a new department of Applied Mathematics and I asked to take me there with the loss of one year. So as a result, I graduated with a Masters degree in Applied Mathematics at the age of 25.

TPL: I see.

AB: Yeah, so it was not early. But then I became a PhD student of the Institute of Applied Mathematics, where I already did my master work. So I has a background of a physicist, and I found in our institute, where all people are related to applications, that sometimes pure mathematicians have more difficulties when they come and start doing some applied things than people who came from decent engineering institutes. Now almost all such institutes/universities have good departments of applied mathematics because the mathematical modeling became very important part of research in any area with the development of computers. I read in another book (by V. Arnold), that mathematics is not connected too much with the computations. It is more qualitative thing. And he said about Landau, that Landau understood mathematics as a continuation of arithmetic (meaning just evaluation of integrals, using special functions, etc.). Probably I am also from that school. Suppose that you are doing a certain job like I remember one of our professors. There was a story, at least a rumor, that he was working on some nuclear physics problem and he was asked to make calculations for defense, I mean, from nuclear, from radiation of some device. He did all these calculations and finally it was found that he made a mistake in order. And after that, he was fired. So really, we can see the role of calculations. Especially if you have in mind the comparison with experiment. Somehow, experiment is more important than your theory. And so, calculations are also very important.

TPL: Doing it correctly.

AB: Yes, you must do it correctly. Physicists like identities and the exact solutions. Therefore, somehow, in the ideal sense, I always wanted to get something like that. But in our problems, this is, of course, impossible.

TPL: Then sometimes you estimate.

AB: Yes, you move ahead, more or less, do exact calculations until you reach some point when you see that now, you cannot move farther with identities. You need to change to inequalities.

TPL: Could you describe Keldysh, the person, you have met him?

AB: Yes, of course, I met him. Keldysh was born in 1911. He became president of Academy of Science USSR, to my recollection, in 1961, at the age of 50, and I met him 10 years after, so he was, yeah, first time I saw him, maybe at 61, and at that time, he was always occupied in his office of president somewhere. I don’t know where it is. Yes, but once on Thursday, his big car, a big limousine, was in the yard of our institute and he came to institute to check something, more or less, to keep in course and this was his connection with the institute in this period. But at the age of 64, in the year of 1975, he retired, finally, from president position because his health was in very bad shape and he died 3 years after. So these 3 years, I saw him more closely. Still, he was our director. Probably I saw him closely only once, he shook my hand after the defense of my PhD dissertation. And the most important for the institute part of these 3 years was his regular, once in a week, seminar. So it was interesting to attend these seminars. Many colleagues did not listen too much what the speaker are saying. The most important was what Keldysh was going to say at the end. I remember, the talk of Gelfand on KdV-type equations. At that time, they were very popular. It was known that Keldysh liked and always supported Gelfand, maybe less in the very last years of his life. As always, Gelfand gave a very good talk. Another remarkable speaker, that I remember, was Zeldovich. Zeldovich and Gelfand both were directors of relatively small departments in the institute. This position looked a bit strange for Zel’dovich, who was one of a few highly decorated academicians. He had 3 Golden Stars, like Keldysh himself. The Golden Star was the highest award in USSR. But it was a surprise that Zeldovich wanted to do only astrophysics and did not want to be involved in applied problems, thinking that he did enough for applications. And he has a small department of approximately 10 people, but it was his choice to have 10 because he wanted to have a sort of elite, not to have just many people. Several people from his department became famous in astrophysics, for example, R.Syunyaev and I.Novikov. And I remember that Zeldovich gave a talk about black holes. It was in mid 70s. So Keldysh was very skeptical. It was clear that he is in general very skeptical about astrophysics, that he did not believe that experiments are sufficiently reliable there, and he perhaps did not believe much black hole existence. He said: ”But did they really prove existence of black holes?”. To finish with the seminar I can add that I also gave a talk there on Fourier Transform of the Boltzmann Equation and got very positive comments from another famous mathematician, A.N. Tikhonov, who was a vice-director at that time. The seminar was really very important for the institute. Unfortunately the “all institute” seminar existed only for a short time, until the death of Keldysh in 1978. Once I asked an older colleague of mine, who worked closely with Keldysh all these last 3 years, 1975-1978. I asked him after Keldysh’s death, you were close to the great man, what was your general opinion and your impression. And he said, you know, he was very ill, very sick. He was a strong smoker and he had problems with the blood vessels of legs. The government even invited famous American surgeon with his own laboratory and he operated Keldysh. But it only helped for 2 years like that. They did some bypass from heart. At that time, this was a big operation. Keldysh started from being pure mathematician and he was in Steklov Institute. It was the main academic institute in mathematics in the 40s. There was just one institute of mathematics in Soviet academy. And the director was Vinogradov. Maybe you know such name.

TPL: Yeah, the analytical number theorist.

AB: Yes, and Keldysh became a vice director and he was a head of Applied Mathematics division, which finally became independent and became our institute. And so what is interesting, maybe, that I have a friend, who told me this story. Vinogradov died like at age of 91 in 1983 and still, he was the director. It was such time that they don’t touch members of academy. If people want him to be director, then okay. By the way, he was very strong.

TPL: Physically strong.

AB: Physically strong, yes, yes, yes. But last years of his life, of course, he was mostly in hospital and scientists from Steklov Institute took care of him because he was not married. He was never married. And my friend told me that once he was sitting near a bed of Vinogradov and they were speaking about different things and about mathematicians. And Vinogradov said, but who’s the most beautiful mathematician? I think Keldysh.

TPL: Keldysh? I see.

AB: Yes. Especially when Keldysh was young. He was beautiful.

TPL: Oh, I see. (laugh) Not mathematical beauty. He is physically beautiful.

AB: Yes, yes. A view from absolutely different position. This is a story I like.

TPL: Vinogradov is very big in China and there is someone called Hua Luogeng, who maybe the most well-known mathematician in China. And he followed Vinogradov school. I understood that Vinogradov was the director from something like half a century.

AB: Yes, yes, yes. Like 40 (Wikipedia says 49). We can check that Vinogradov became a head of Steklov Institute in 1934.

TPL: While we were in Moscow, you took us to Moscow State University. Yeah, we know that there are so many great names during that period, Kolmogorov, Pontryagin and all these big names. That was really golden age of the Russian school. But of course, the Russian school in mathematics, it went all the way back to 19 century and beyond, right?

AB: Yes, yes, of course. In 19 century, I think only a few names like Chebyshev and then, who else?

TPL: Oh, there are some people in real analysis before Kolmogorov., for example.

AB: Perhaps you mean Luzin.

TPL: Yes, Luzin.

AB: Luzin was a head of a school in real analysis, but it was mostly 20s and 30s. (actually his first publications were in 1910s)

TPL: I see.

AB: But he also had a brilliant group of young people mostly in 30s. And so there was Kolmogorov, Aleksandrov. Pontryagin was near but not exactly in that group. It was in the group, by the way, a sister of Keldysh, the mother of S.P. Novikov (mathematician, Fields medalist), and some others. They made the seminars in the apartment of Luzin, he had a big apartment in Moscow. It is also, important for the history of mathematics in Russia, that our capital of science was originally in Saint Petersburg. Then, after revolution, the government moved to Moscow.

TPL: Only after revolution?

AB: Yes, because it was too close to the border and there was civil wars and intervention, as we call it. So it was all dangerous. Finland was not a friendly country at that time.

TPL: I remember Ilya Repin retired to a town that was part of Finland.

AB: Yes. Exactly. He wanted to escape the revolution. Therefore the government moved to Moscow in 1918, but the Academy of Sciences stayed in Leningrad until 1934. Institute of Mathematics was initially in Saint Petersburg, and then, also, they decided that better to move the Academy of Sciences to Moscow and it was done in 1934.

TPL: I see.

AB: But Luzin was always in Moscow. So more or less, this golden age is related to these 30s. And then, it was interesting, there was a conflict between Luzin and his pupils.

TPL: Kolmogorov?

AB: Many. 1930s were not a good time for Russia, for Soviet Union. There were repressions, ideological struggle. In particular, Luzin was accused that he published all his papers in Western journals. And so, somehow it was a time beginning of pressure on scientists from government of Soviet Union to move more closely to problems of the country, say, more applied problems. Also, until mid 30s, they traveled freely more or less. At least some of them, like the famous physicist P. Kapitsa. And he lived in Cambridge. Do you know such name? Kapitsa?

TPL: He is a physicist?

AB: Yeah, yeah. Physicist. He worked with Rutherford, and then he lived like 15 years in Cambridge, but visited his mother in Moscow every year and there was no problem. And the year 1934, he was not allowed to go back. The government asked him to be a head of institute, whatever you like. So it was, and he was very close to Rutherford. He was already a member of Royal Society in England, because he was a very good experimentalist. Finally he got Nobel Prize much later. And so, this was not a simple situation for scientists.

TPL: Just a little bit digression. I learned of his story, he was with Rutherford, then moved back. I learned this story from the Aeroflot Airline magazine on the way to Moscow, my first trip.

AB: Story about Kapitsa?

TPL: Yeah, right. Right. It was on the airplane magazine.

AB: Yes.

TPL: That is surprising. Yeah, the airplane magazine has some serious article.

AB: Yes, I know. For example, I remember that once in airplane, the British Airways flight, not in magazine, but I could listen a book of Villani there.

TPL: Oh, okay.

AB: Yes, you can listen to it. There are some books you can take and listen. And there was a book about how he proved the theorem with Mouhot, but I didn’t listen. It was not very interesting to me. But what was interesting was it was in British Airways, the flight from London to Austin Texas.

TPL: Let’s go back to your story. You said in the 1930s, there’s a lot of ideological things.

AB: Yeah, yes, yes. And there was also some fights. Some well-known mathematicians died. In particular, Egorov, the teacher of Luzin, died in exile in Kazan in 1931. It was a dangerous time. This is a very controversial story about the motion of former students of Luzin against him. Actually, they wrote sort of complaint against him that he is far from applications. I don’t remember exactly who signed, but Kolmogorov had a conflict with Luzin later. Aleksandrov signed, and some others. Now you can read this story in detail in the paper by Lorentz, for example. It looks like they did a very bad thing to their teacher, because it was very dangerous for him. He simply can be taken to prison and there was just a historical “good luck” for Luzin that at some point, government decided that, no, they don’t like this new public conflict, discussion what is Marxists understanding for mathematics, something like that. But they could decide...

TPL: Otherwise.

AB: Otherwise, yes. Yes, yes. And Egorov died in 1931, I think there is an Egorov theorem in the theory of functions of real variable. He was a member of Academy and a head of Moscow Mathematical Society for some years. But Luzin just lost his position in Moscow State University and have been working in Technical University and published textbooks in mathematics for engineers. He died in 1950.

TPL: In real analysis, we always start with Luzin properties.

AB: To my very rough understanding, the main thing for this group was the set theory and its part called “Descriptive theory of sets”, that is all I know, but perhaps you know much better?

TPL: So Luzin’s group had done something more fundamental. The one that I learned was about something more superficial, what he has done in real analysis. Yeah, I see.

AB: A former Soviet mathematician from Leningrad, Lorentz, who emigrated to US somewhere in 60s or 70s published a good paper in 2000s. He wrote a very nice paper about this golden age of Soviet mathematics, I will try to find it (it is done now). So you were right that exactly 30s should be called the golden age of Soviet mathematics, though not everything was very smooth in that period.

TPL: I now see.

AB: Yeah, we discussed about 60s, but still, 60s, just a few names maybe, newcomers. Like, I don’t know, Sinai, Arnold, a few others. But from 30s, there are Pontryagin, Kolmogorov, Aleksandrov, Vinogradov.... So without speaking about years of our generation, it is too difficult to be objective. The history will show …

TPL: Before 1990s, there was not much communication between East and West, and there’s the situation where the Russians’ results, Russian school were not known to the west. So I have this question—what is the research situation on kinetic theory in Russia before 1990s?

AB: Let me try to explain what I’m thinking. I’m thinking that before 90s, 1990s, I would say, maybe 80s, there were just a few mathematicians working in nonlinear kinetic theory, relatively few.

TPL: All over the world.

AB: Yes, all over the world, yeah. Like up to 10-15 serious people in some countries, like, for example, in Germany, it was H.Neunzert. He has famous work on Vlasov equation. In late 1970s he organized (together with his colleagues) the first Oberwolfach conference called like “Mathematical Problems in Kinetic Theory”. And more or less, from that conference, everything started. At least, it was a place and a conference, where mathematicians who were doing kinetic theory met. Before, there were T.Carleman and later H.Grad in the West. And it was N.Bogolyubov in USSR. These are 3 big names of people who have published their main papers before 1950s. Then, new people like M. Kogan in Russia, and C. Cercignani in Italy came. The Rarefied Gas Dynamics (RGD) Symposium, which became a regular (once every 2 years beginning in late 50s) meeting of scientists, working in that area. Usually a small group of scientists from USSR was allowed to participate in these meetings. This was the way to make more close contacts with the West. It is remarkable that the first Soviet satellite (“Sputnik”, 1957) became a symbol of the Symposium. Let me also mention another example of exchange of ideas. In the West, the famous physicist G. Uhlenbeck was interested in 1950s in more theoretical physics type development of kinetic theory, to write kinetic equations for dense gases, etc. And he found a book of Bogolyubov and he liked it very much, advertised it and organized its translation to English. You remember, Uhlenbeck was very famous because of his discovery (jointly with S. Goudsmit) of spin of electron. Yes. But he never got Nobel Prize for this great discovery.

TPL: Uhlenbeck was in University of Michigan, right?

AB: Yes, this is true. But he was originally from Holland. He started in Europe, then emigrated to US. Another name of Soviet mathematician, who worked in kinetic theory is A. Povzner. He proposed in 1961 a sort of generalized Boltzmann equation, assuming that each collision happens not in one point, but in some small domain of positive measure. For this modified equation he proved theorems of existence and uniqueness. He also derived important inequalities for moments, which are called “Povzner inequalities”. His theorem is valid also for classical spatially homogeneous Boltzmann equation. Two more Russian names from younger generation are A. Arsen’ev and N. Maslova.

TPL: She was in Saint Petersburg, no?

AB: Yes. N. Maslova was from Leningrad University at that time. A. Arsen’ev was in Moscow State University. In 60s he was a PhD student and decided to write his thesis about the linearized Boltzmann equation. It was after he had read maybe a couple of papers by H. Grad on this topic I guess that he immediately realized how to construct the solution of the Cauchy problem and expansion in orders of Knudsen number very accurately and mathematically rigorous on the basis of Kato results in perturbation theory for linear operators. And then, he published in Russian a remarkable paper in 1965 called “The Cauchy problem for linearized Boltzmann equation”. Unfortunately this paper was never translated to English and remains almost unknown in the West. A big part of his results was independently obtained in mid. 70s by other authors (in particular, by S. Ukai and also Ellis and Pinsky). N.Maslova, on the other hand, knew her results very well and used them for the proof of global existence of solution to the Cauchy problem for the nonlinear Boltzmann equation near absolute Maxwellian. This theorem was published in Russian in 1974-1975, i.e. approximately at the same time as the famous paper of S. Ukai, devoted to the same problem. I know that roughly in 1990 Maslova published a book in English. So, her main results must be well known in the West after that. I have to apologize that my absolutely incomplete list of names does not include many other important names. For example, there were great schools in linear transport theory in Soviet Union and in US (also in France). Concerning results obtained in 60s-70s in nonlinear kinetic equations we should mention such names as J.P. Guiraud and J.Darrozes (both from France), actively working in that period, C. Cercignani (Italy) and Y. Sone (Japan), and others. Both Kogan and Cercignani published their books on Boltzmann equation in late 60s and both books were immediately translated to “opposite” languages. By the way, Sone was in Courant Institute for some period, right?

TPL: In the 60s.

AB: Yes, yes, yes, in 60s. Right. But he was also very active participant of RGD-Symposiums because his department was directly connected with aeronautics and aerodynamics, right? Therefore, he was supposed to be in this area, as a scientist and professor from engineering department related to rarefied gas. But he and Aoki, Takata are, of course, very close to mathematics, they do understand mathematics and know a lot. Let us now discuss the next period of 80s and later. Indeed a big change happened in late 80s, when French mathematicians started doing this. There was a huge crowd simultaneously, a huge crowd (in our scale) like 10 people, 10 young people, very active. Half of them are students of C.Bardos, including B. Perthame and P. Degond, who probably were not his students, but they were very close.

TPL: So that’s the modern era.

AB: Yes. And then I want to stress that Oberwolfach meeting was actually the first regular (once in 2-3 years) meeting of mathematicians devoted to kinetic equations. And still in 1982 half of its participants were from linear theory. And C. Cercignani, who became the main organizer of that meeting, did some work in order to get rid of this linear theory and to concentrate on nonlinear kinetic equations. He also made a great contribution in making kinetic theory popular in Italy. Another great impact came from the Fields medalist P.L. Lions, who obtained the award for the famous joint work with DiPerna. And then, if you go in 90s, then you see a lot of small conferences. But in number of participants, they have the same order as Oberwolfach, so in France and Italy, especially. So the number of good mathematicians involved in kinetic theory had a great increase. And this is very good.

TPL: Yeah, I see. I’d like to go back to Keldysh because when I went to this library in your institute. It’s like a shrine and where he wrote to the central government to propose: Let’s go to the space. How did Keldysh manage to do that? This is a big undertaking. I understand that at that time people like Landau, who is highly respected scientist in Russia all over, he did not think that is such an important thing because going to space is Newtonian physics. It doesn’t break new frontier in physics. So therefore, how did Keldysh managed to get the government to support this major undertaking, which turned out to really change the world. So he must be very persuasive.

AB: I will try to answer maybe in a very strange way. It is possible, in principle, to compare Landau and Keldysh. The Second World War was a very important factor. We both are from the same generation, of course, from completely different countries and conditions, but anyway… At that time, after the war, people in Russia thought that everything is not too bad. The main condition of life was to avoid another war. You understand what I mean because I think it was similar feeling everywhere. Perhaps the different background played certain role. Landau’s father was engineer in oil industry. The father and both grandfathers of Keldysh were military generals (though his father was also an important military engineer related, to my recollection, to construction of bridges). Landau worked closely with the West from the very beginning in 30s. He visited Nils Bohr in Copenhagen and they worked together. He became famous in the West when he was very young. So Landau was actually not involved in work related to military applications (except for a short period in early 50s). On the other hand, when Keldsyh started, he even wanted to become engineer. His father was a military engineer in construction industry, and also one of the authors of concrete in Russian military because this is all important for military constructions. He was a member of Academy of Architecture. A sister of Keldysh was a student of Luzin, who was in pure mathematics. And so, finally, he changed to mathematics, maybe it was also her influence. But then his first job was, by the way, the same institute where Kogan worked all his life. It was called the Central Aero- and Hydrodynamical Institute and it was known for applications to aviation and (later) rocket industry. And his first famous contribution was, to my understanding, a mathematical model of certain type of instability of the plane. He made some proposals based on that model on how to avoid this dangerous instability. He did other important contributions to aviation techniques. To tell the truth, I do not know details. And besides this, he has many publications, but not so many in pure mathematics, in the theory of non-self-adjoint linear operators, for example, in some questions of analytic functions. Because analytic functions are used a lot in hydrodynamics, right? For plane problems. What is also known is that he became the full member of Academy in 1946, when he was 35. By the way, Landau was elected in Academy in the same year, when he was 38. After the war Keldysh was working on problems related to military applications. In the Cold War period people were afraid to get another war and considered it normal work for defense.

TPL: To prevent war.

AB: Yes. People believed that the only way to prevent war is to reach certain equilibrium. When the Cold War started, the space research was not that important. What was important is to have rockets to be able to send the big bomb far enough, because United States always had this possibility. They have a lot of military bases in Europe. But Russia, vice versa. Therefore, it was crucial question for government, first, to make the big bomb, and second, to make means of transportation of that bomb. By the way, the work of Landau in that period (the beginning of 1950s) was also related to thermonuclear weapon, but this is another story. Keldysh also had some diplomatic and administrative skills. Probably, he had an extremely good ability to formulate things and to speak with the people from government. Vinogradov wrote that there was some meeting of people from government with people from Academy and Keldysh was young and present, but not a central figure. And some respected man, I don’t remember who, was asked to explain the situation with the solution of some important applied problem. He started to answer and then it was clear that they don’t understand him. Then finally, Keldysh was asked to help him and he made a very nice and clear report. After that, Vinogradov said: I understood that soon he will be taken from us. (laugh). Yes, he was taken and since then he always had several important positions: he became a director of our institute, but also he was a head of another institute, which is now called Keldsyh Center. He also had other positions. In Soviet Union, there was not much competition in industry, and it was not good. Of course, it has positive sides, but also negative sides. But in military industry, they always have this sort of competition. Several big groups were trying to solve, more or less, the same problem. So they have great success with military things. But as a result, different responsible persons (rocket designers, for example) sometimes can become almost enemies. Keldsyh was probably an ideal mediator in such situation. Everybody respected him and he was, very often, appointed a head of various government committees. He was very close to the counsel of these rocket designers. I read memoirs of one of them (B. E. Chertok), and he wrote that they liked very much to have meetings in the room of Keldysh, I think in the same room you were.

TPL: I see.

AB: And in that room, in the year 1954, they decided that, of course, the most important problems that are military problems. We have already a good rocket, that, in principle, can be able to put a small satellite (“sputnik” is just Russian word for satellite) to the orbit around the Earth. Why don’t we do it, at least, for sort of advertising of Soviet Union?

TPL: I see.

AB: But also, they feel that, in principle, they can solve now such problems like, to get to the Moon, though it is not easy. Therefore, it is a sort of military problem to reach some given points and to prove that they can do it far away. So they wrote a letter to Soviet government asking to begin the project, which finally led to the first flight of Soviet satellite/sputnik in October 1957. At that time they could not imagine how important it will be for international reputation of Soviet Union. It will be. At that time, it was far from evident. Because everybody was skeptical that, okay, what is the point? You put something in the orbit... (laugh)

TPL: I remember when I was in elementary school, when Soviet has put this in orbit, it was such an event all over western world, that even in the small rural elementary school, the principal of the school gathered all the students to tell us that Russia had put a satellite up there. Now we need to improve our scientific education and so on. I’m sure that Taiwan got that message from US and in the US, as we know, John F. Kennedy make this famous speech. So the ripple effect was heard even in my small elementary school in village. It’s very difficult to predict human’s psychology.

AB: Yes, yes, of course. Yes, like it was very hard to predict what will be use of this and future satellites. Now we can see that communications changed completely due to satellites. But at that time people mostly speak about traveling to other planets in the future. We (or our children) will see…

TPL: Life in another planet.

AB: Yes, yes.

TPL: Oh, that’s a great story.

TPL: I always have this impression that in culture, scientific culture in particular, doesn’t come up suddenly. It doesn’t go away suddenly. And it must be something about the Russian culture that’s values all things artistic, musical and scientific. I understand that Russia now is not in its best period historically, but this culture is there and it would be okay. It will be revived.

AB: Hopefully. Thank you, we hope so, but it depends on many things and in particular, we have some problems like the one with Ukraine, some problems which make us worried. I hope that one way or another, this will be solved. This was a huge event, the destruction of Soviet Union. I mean that if you take a big state and change it in one day into 16 states, then you have a very long tail of consequences.

TPL: Well, I have such a superficial understanding of Russian culture. As you know, I tried to read things about Russian literature, art and so on. But while we were in Moscow and we went to Tretyakov Gallery, and I can see that it’s completely full, with people of all age, particularly young people. You must have noticed that, right? And they are very eager, very lively, yeah.

AB: But what you say about Metropolitan Museum, for example, in New York, this is...

TPL: Yeah, Metropolitan Museum in New York, they try to argue to the city government that we create other financial benefit to the city of New York because people come to Metropolitan Museum, they will have to eat in the restaurant, they have to stay in the hotel and the city benefits financially. Okay, now who go to Metropolitan Museum? A lot of visitors go to New York City. But Tretyakov Gallery is a little bit different. It seems to me that most of them are actually Russian and maybe most of them are people from neighborhood of Moscow. It seems to me.

AB: It is difficult to say because Moscow is not the whole Russia. I mean, like French people, sometimes they say that Paris is not France at all. Then Moscow, you can say that is not Russia. There is a big difference in the level of life, salary in Moscow and in another place. Therefore, Moscow is a tourist attraction.

TPL: Yeah, I understand.

AB: There are more tourists from Russia.

TPL: Oh, from Russia.

AB: Yes. Also, for example, some schools, they make special excursions in Moscow. And first point to where they go is Tretyakov Gallery. In Italy, you can find similar things. Of course, you can say that they are, by definition, very cultural people. Yes, yes, definitely. But still, there are many Italians in Uffizi. Most of them are Italians actually. Yes, in gallery of Uffizi in Florence and...

TPL: Sistine Chapel.

AB: Yes. So I just think maybe you did not expect the cultural level is good enough in Russia.

TPL: Of course, cultural level is very high. But I am thinking that they go to a museum which is really, it’s only for Russian arts.

AB: Oh, yes, yes. I just had it in mind only one point. For most of Russian people, the first 2 museums in Moscow are Tretyakov Gallery and Pushkin Museum. So simply, they are known to everybody and people like to go there. But maybe it is not that simple, I never thought about Tretyakov Gallery. I must think more about your very interesting comments, thank you.

TPL: Yeah, it’s very Russian.

AB: Yes, Russian.

TPL: Okay, so perhaps we stop here. It’s always nice to have you around. It is so nice to talk to you, you are very straightforward.

AB: I am sorry. I do not understand enough English to understand clearly, is straight-forward good or bad?

TPL: Straight-forward good or bad? For me, it is not good, not bad; the more interesting thing is whether one’s different, and you are different from other people. That’s more important.

AB: Good.

TPL: Look forward to seeing you again. Thank you very much.

  • Tai-Ping Liu is a faculty member at the Institute of Mathematics, Academia Sinica.