傳播數學知識．促進數學教育

Interview with Prof. Junkichi Satsuma

**Interview Editorial Consultant:** Tai-Ping Liu

**Interviewers:** Tai-Ping Liu (TPL), Fon-Che Liu (FCL)

**Interviewee:** Junkichi Satsuma (JS)

**Date:** November 7th, 2004

Professor Junkichi Satsuma was born in 1946. In 1964 he graduated from Nara High School and entered the Graduate School of Engineering of Kyoto University. He graduated in 1968 and finished his Kyoto University PhD courses in 1973. He was a research assistant in Kyoto University from 1975 to 1981, and then held a position in the University of Miyazaki from 1981 to 1985. In 1985 summer, he was offered a professorship by the University of Tokyo, first as a professor in the Graduate School of Engineering and then in the Graduate School of Mathematical Sciences.
After his retirement from the University of Tokyo in the spring of 2005, he has been holding a professorship at the Graduate School of Science and Engineering in Aoyama Gakuin University.

Professor Satsuma has made important contributions in the fields of integrable systems, nonlinear waves, and difference equations. He has also devoted his efforts to enhance mathematics research such as organizing research groups in Tokyo and serving as a reviewer of Kyoto Prize.

TPL: We usually start with the beginning, how you got into Mathematics?

JS: It may take more than one hour to talk about it (Ha,…,Ha). When I was in the undergraduate study, no even in the graduate study, I was at the Faculty of Engineering. Professor Mimura and Professor Nishida came also from the same department, i.e. the Department of Applied Mathematics and Physics of the Faculty of Engineering. My first hope was to work on Operations Research or something like that, but unfortunately I did not like lectures by Professor (Every one laughs…), oh you may cut this off….

TPL: No…, this is good, we just had a spontaneous reaction!

JS: The professor I liked at that time was a physicist, so I chose the laboratory of Fluid Dynamics. My graduation thesis was on "Solving boundary layer equation by Oleinik difference scheme". That was my first, I mean, exercise. In the graduate school, in the first two years, I had been working on turbulent diffusion, but all the job was done by computer. Then, in the Doctor course I was still interested in turbulence, tried to find something and read several papers, but it is so hard subject. At that time there were many results, analysis by renormalization groups, Kraichnan theory, Taylor's work and so on. I still keep one box full of papers of that kind. Actually I could not do anything. The associate professor in our laboratory was worried about my situation. He was working on nonlinear waves, actually he was a plasma physics. Unfortunately he died very early at the age of 58. He became my real supervisor.

TPL: What was his name?

JS: Yajima.

TPL: At Kyoto University?

JS: Yes. He later moved to Kyushu University and became the director of an institute. In Kyushu he worked so hard. At one time, on his way to Ministry of education, he wanted to meet his two children in Tokyo. He wanted to meet in front of a bookstore in Tokyo … There he fell down and died a week later. It was really a pity.

FCL: Was he a student of Tomonaga?

JS: No, he was a student of Fushimi at Osaka University.

Anyhow he was worrying about my study, because I did not do anything… Ha… Ha.

He suggested to me to work on something in nonlinear waves. Actually I like
calculation very much, but turbulence is not a kind of theory on which we
can work on calculation. New direction on nonlinear wave theory just appeared
at that time. Discovery of soliton by Zabusky and Kruskal was in 1964.
Around 1970 when I was a student, many results came out …. I first worked on
the nonlinear Schroedinger equation and tried to solve it by using the inverse
scattering transform under the very heavy guidance of Professor Yajima.
Our paper was published in 1976 …, that means, since I was born in 1946,
at the age of thirty. At 27 when I finished the Doctor course, I had not
written any paper at all, but in two years I wrote eight papers. A paper
on KP equation was something I did myself after Prof. Yajima moved to Kyushu.
I got some exact solutions of the equation by using the bilinear method
on which not so many people were working at that time.

TPL: And because well-known.

JS: Yes, but I have been lucky. For example, seven years after we published the paper on the nonlinear Schrodinger equation, people at Bell lab. did some experiment and they got nonlinear pulses. They cited our paper because the pulses was in our paper. I just handwrote the graph of soliton solutions, which were found in their experiment. But for me it was just an exercise. I just solved the nonlinear Schroedinger equation. Since it is nonlinear, to solve was not easy, but still it was a kind of exercise. Anyhow by the picture I wrote done, I become very famous in that field …ha …

TPL: Sorry to interrupt you, you say it was an exercise, but of course it was clearly not just an exercise, because you found it and nobody else found it. Can you tell us how you did do that, you just worked hard, how did you get about it?

JS: The reason I say it was an exercise is that the method to solve it had already been given by two Russians, Zhakharov and Shabat. They claim that by using the inverse scattering transform we could solve the initial problem of the nonlinear Schroedinger equation and just gave some particular solutions. But they did not care so much about the concrete initial value problem. We worked on that. We solved for various initial values and studied asymptotics of the solutions. In that sense our work was an exercise.

TPL: So it was an exercise in that sense, but really it was not just an exercise, your input was really relevant.

JS: But if I found the method of solving it, it would be really a big thing.

TPL: I guess the point might be that you saw it an important topic and need to be done.

JS: Yes, but of course at that time people just started to work on nonlinear staff and people never thought to solve exactly. But we knew something. Actually Yajima knew something about it and we just started to play with that kind of nonlinear dispersive wave theory.

TPL: But you were then in Kyoto, you graduated from Kyoto; when you solved the nonlinear Schroedinger equation, where were you?

JS: Kyoto, and the work on KP equation also started there. After finishing my Doctor's course, I do not mean I got my Doctor's degree, but at age of 27, I was still staying in Kyoto university. At the same time I had been working at a preparatory school. I already had a child at that time. Any way I worked very hard on KP equation and some others.

TPL: Not an exercise of course!

JS: No, not really an exercise, but it's a kind of extension. KP equation is now very famous and very important. I just did a work in very early stage. I could be called one of the pioneers.

TPL: Sorry to interrupt you again, so you found particular solutions of KP equation involving wave interaction. How did you find that?

JS: … Ah …. Why I said it was maybe an exercise. In the one-dimensional case of the KdV equation, The particular solutions were given by Hiroda-sensei. But in the two dimensional case, although it's in some sense in the same direction, we have to think of something more. And I just tryed and got them. I was lucky and was successful. I am telling to students that research is gambling. Is this right? In Tokyo University students are very good, but they usually do not want to do some thing new. They are so smart, understand very easily and they can write many papers, but to do quite new thing is very hard for them, because they do not like such a gambling. Of course after beeing given a result, people can say "Oh, this is simple, this is quite easy". But to do first is important, yes? So I always shout to students. Do gambling! Research is gambling, but of course life is also gambling. (Everybody laughs...)

FCL: Probably the young people want to secure their career first, so that they do not want to go into gambling, is that the reason?

JS: Yes, but smart people can get job easily, they can write so many papers, but if you fail in gambling, you have to wait. So after I say research is gambling, I also tell to the students that if you are smart enough , even if you fail in gambling you get very good experience and you could learn many other things, so do gambling. As I have said, in Tokyo University, there are many good students. So I can say this kind of things to them. I should not say such things at some other place, because it could be very bad to some of them sometimes.

FCL: You had been in some other places before you settled down at Tokyo University. Can you tell us some of your experience? Is it a good experience for you?

JS: Yes, very good experience. At the age of thirty, one of the research assistants at our department of Kyoto University was killed by a traffic accident. At that time Ukai-san was also a research assistant there. It was very unfortunate for the killed assistant, but fortunate for me. I could get the position left by him. It was at the age of 30, a little late. And at age of 35 I thought it was a good idea to go somewhere else. Oh … but the five year as research assistant at Kyoto University was very good for me. It was a very good position. I could do any thing I liked. Acutually I stayed three years in U.S during this period. First I was invited to visit for one year. Then I did several works and my boss there told me to come and stay as long as I like the next time.

TPL: Who was the boss?

JS: Mark Albowitz, he is one of the famous person in our field, he has been the head of the school of Applied Mathematics of the University of Colorado at Boulder, he just retired this year at the age of 60, but he is still working as a professor. Anyhow I stayed 8 months the first time, then returned for more than two years the next time, totally three years. I learnt many things, but I had something the Japanese style research and they had the inverse scattering kind of American group, so somehow we complemented each other, it was real fun because I could say something from my point of view and they could say something from other point of view. So at the age of 35 I wanted to move somewhere, and there was an open position at Medical School of Miyazaki University in Kyushu Island, it's very far. I was actually chosen as an associate professor and the Chairman of the Department of Mathematics of the Medical School, but the Department consisted only of one professor (Everybody laughs!). I enjoyed the life at Miyazaki very much, but unfortunately the people were very bad somehow, no, no, not all people, but some people were very bad, and I …, I stayed there four and half years; I decided to leave after three years. If the people were very good, I might want to stay there the whole life, I mean it's a very nice place, it's a resort area, and I will do some calculation, teaching and drink shochiu, of course also enjoy having sashimi.

FCL: I noticed that you wrote a book on statistics and probability at that time, right?

JS: Yes, at Miyazaki, because to students of Medical School, statistics, yes, statistics not probability, is very important. I still remember the funny story. It's almost a joke. One of the Doctor came to me and asked me how to treat a certain kind of problem, it's a problem about a disease, diarrhea, he had three patients. If we want to write a paper, we have to give a statistical treatment, since we had three samples we could do it, because for two samples we have average, but that's not enough, but for three samples we have deviation, then we can say anything, right? So just from three samples, on paper we could say anything ha… ha.. I enjoy that kind of thing.

TPL: Not unique conclusion!

JS: But still we could say anything, not difficult at all, you can say anything. At that time I worked on some ecological problem. Tokihiro-san mentioned some epideictic problem. I am this kind of person so one of the professors working on that area and we easily become good friends and I wanted to work on that direction. But there were lots of stress because of human relations and I am that kind of person who can't be too gentle. After four years, my professor told me that there was an open position at Tokyo University and they looked for someone good at nonlinear dynamics and said: "Why don't you apply for it?" So I applied and I was lucky to get the position at Department of Applied Physics in the Faculty of Engineering of Tokyo University. Their teaching was very interesting, they were teaching mathematics to all students of Faculty of Engineering, there was an Applied Mathematics Department, but they did not teach any mathematics, no, some ... , but anyway I had to teach mathematics to the students of Engineering.

TPL: They are good students, the engineering students?

JS: Yes, not all, but many are good. Tokihiro-san also graduated from there,
and I mentioned Takahashi-san and Matsukidaira-san… They were all my
students, Takahashi-san was really not my student, he was my research
associate, I was just asked why not having him as a research associate
from a professor and I say O.K. My students are all very good. Not a few
people say why you have so good students. It was just by luck. We did several
works on solitons. Later on we were also involved with some discrete systems.
I stayed there for six and half years until I was at age of 45 when the
Graduate School of Mathematical sciences just opened and they wanted to have
some people a little bit on the side of mathematics … yea … yea that's kind of their
intention. Mathematicians there thought recent mathematics were so narrow.
They should have a widegroup. That's the reason they named the department
the Graduate School of Mathematical Sciences, not of Mathematics. I thought
I could have been a member of Mathematical Sciences, so I moved to the School
of Mathematical Sciences.

Let me talk about my research. When I was still at the Faculty of Engineering,
I gave a talk at my laboratory about cellular Automata. Mark Ablowitz did some
work on cellular automata showing soliton behaviour. I gave a talk about his
model since the kind of cellular automata or pure discrete system should be
very important in the age of computer. His model is not quite so good. So I
asked students to find a nicer model. Just a few weeks later Takahashi-san
found a rules for soliton cellular automaton. The solutions of the model only
consists of solitons. It is a quite beautiful model. We have been working on
the model for many years. Tokihiro-san was also involved. We discussed very
often and in 1996 we found a process to directly relate the cellular automaton
and differential equations which we call ultradiscretization. I just want to
say a comment. I am a physicist in the sense that I do not care about types
of equations, but just want to have a system that describes the phenomenon
very well. Navier-Stokes equation is of course very important, that I know,
but from my experience it is very hard to handle. Numerical computations in
computer is the same as just solving cellular automata. That is why the kind
of cellular automata are important. Do you understand what I mean?

TPL: Yes, they are all discretized, computers only know discrete numbers.

JS: Yes, they don't know real numbers at all! So by extending our method I want to obtain a model equation, … a cellular automata equation for describing fluid dynamics. … It is very nice at Math. Department… I like mathematics people very much … but unfortunately mathematics people somehow do not know to have some kind of group work, so it is very hard to operate some kind of laboratory. That's why Mimura-san went back to Hiroshima, he was invited to join Tokyo University, but he stayed only for two or three years - because he could not form a group. In our work, we need to do very heavy computation. We need to have a group. But unfortunately it is not a case. You are real mathematicians (everybody laughs!) I should also say that there are mathematics in that kind of experimental works.

FCL: You said that you are fortunate to have a group, is it because you started from Engineering School so that you succeeded in forming a group?

JS: Yes, if I started from Mathematics Department, it would not be possible, because we could not have research associates. All the professors in Mathematics Department are alone. They have only students. But computation is a continuous work, something might just happen suddenly and people have to learn from others. People can't just work alone. But mathematics, any one can do alone if the one is smart enough, right? (Every one laughs!)

TPL: Yes, because mathematics is self-generating, the rules are clear and what to do is also clear.

JS: Yes, in algebra very young people could do a big thing, right? (Every one laughs!)

TPL: In Japan there are many outstanding people in discrete integrable systems, you have mentioned Toda, Hirota.

JS: And Sato.

TPL: Do you know them personally? Maybe you can describe them to us a little?

JS: Sato-sensei, I should call him sensei, I should call all of them, Toda, Sato, Hirota, sensei, I like them very much. Toda is the oldest of them, he is now 89. He is a physicist and his hobby is toy, he collects all kinds of toys and even has a factory to make toys himself, especially the tops. He is always interested in how tops are spinning and what kind of shape is important, this is also an important problem for mathematicians. And actually Euler and Lagrange gave analytic expressions for some tops, I also learnt many from Toda-sensei's book. He mentioned Kowalewskaya, I knew her name, because she did some estimation of the diffusion equation, a condition called Cauchy-Kowalewskaya condition, something like that, do you know that? It's an important estimation for the equation. It was mathematically elegant. At the same time she gave an example of top which she solved analytically. It is called Kowalewskaya top. But that equation has a very special structure that the removable singularity is only the poles. I don't know how she put that kind of condition, but that is a very important condition and Panleve and the group started to work on that. She is the first person who pointed it out. I read her paper, there are two big ideas followed by very heavy calculations; she died very young, probably because she worked so hard on that… Yes, I learnt this kind of thing from Toda-sensei's book. Toda-sensei is also very interested is special functions from the physical point of view, … but I have to say that kind of physics should also be mathematics.

TPL: Mathematics should include those.

JS: Yes, actually Euler or Gauss are mathematicians and at the same time
physicists in some sense. I learnt this kind of thing when discussing with
Toda-sensei. What we are doing? We are doing mathematics, yes? Now mathematics
and physics are separated. It may not be so good. By the way, Toda lattice
is Toda-sensei's invention, I always say he did not discover it,
he invented it. It is sophisticated, not realistic, so the system has very good
mathematical structure.

Now I will talk about Sato-sensei, he is about 80, he just got Wolfe's
prize lest year, and he is famous for Sato hyperfunction. When I was at
Kyoto University, he was organizing a seminar, Jimbo, Miwa, Kashiwara, Kawai
were in the seminar. You may know some of these names, they are big names now,
Jimbo-san is now at Tokyo University,… Sato-sensei was then in some sense
the boss of those good students. Sato-sensei himself has a very interesting
career. He graduated from Tokyo University. He was a student in mathematics.
For graduate school he went to Tokyo University of Education, where he was a
student of Tomonaga-sensei. After finishing graduate school he could not get
a research position, so he began to teach at an evening high school.
He had to work on several things. So for several years he just did research
by himself after his main job. After some years he visited Professor Kosaku
Yosida and showed what he had done, and got a position of research assistant
at Tokyo University. Then he became a lecturer at Tokyo University of Education.
I think at that time he had already finished his work on the theory of Sato
hyperfunction. Then he became a young professor at Osaka University. He then
visited Columbia University. But at that time nobody cared so much of what he
did, so he was very depressed and just disappeared for one year, ha… ha,
It's an interesting story and has been written in a popular journal by his
classmate. After one year, he appeared at the annual meeting of the
mathematics Society at Okayama. The main invited talk of the meeting was on
Sato hyperfunction, The classmate asked Sato-sensei what you have been doing.
Then he simply said "Lumpen".

FCL: What does Lumper mean?

JS: Lumpen means a person wondering around like a beggar. He had been in U.S. and, I think, saved enough money so he just walked around for one year. After then he got a job at Tokyo University in Komaba campus. There he gave strong impression on the students like Kashiwara, Kawaii, Jimbo, Miwa …, but he is so strange a professor. When he started the class at five o'clock, he did not stop until somebody stopped him, at eight or nine o'clock, but some students enjoyed very much.

TPL: So he is physically strong?

JS: Yes, mentally strong… physically strong, I don't know. Anyway, the place
is not suitable for him. He was already famous, and some one suggested him to
move to RIMS at Kyoto University. It is a better place, because no teaching
duty there. After he moved to RIMS, he started many new works on solitons.
He did very heavy calculation. To get a simple result he used a pocket
calculator. In his talk he said that he required 15 hundred hours to get a
result. In the case of computer you may just leave calculation to the computer,
but using a pocket calculator you have to use your finger all the time, so you
have to concentrate on that for 15 hundred hours, that is about 60 days.
He enjoyed that kind of calculation. He was interested in the number of
conserved quantities of K-dV equation by bilinear form, he just counted and
counted, then he related them to algebraic representations or something like
that and he obtained the big result which we call Sato Theory. He is like
Japan's Euler, he always says "Go back to Euler!" He often cites Euler's
words.; Mathematicians should be like experimentalists. Do the calculation first
and guess some theorem, then try to move the theorem. The first we have to do
is calculation. Later I will talk something about pecuriality of these three
sensei.

Now Hirota-sensei, he was originally from Kyushu University, physics
Department, he was very good at Japanese chess, the Shogi. When he was a
student, he liked to make some puzzles, some questions for Shogi. Oh, this is
an interesting story, he failed to pass the first year Analysis exam. When he
was a student, Analysis is a so hard a subject for first year student… ha… ha;
in my case, I am a kind of optimistic person so I did not care so much, but he
cared so much and failed to pass… ha…ha.

TPL: He tried hard and did not pass!

JS: After he finished master course, he went to U.S. to study, because at that time it was almost impossible to get a job at university or research institutes. There was a story, he cheated somehow! His grades were not so good, so he invented grades like Yu, Riou, Ka for himself, those are like A, B, C in America, but who decides them? Anyway, he went to Northwestern University near Chicago. There he did a good job, but at that time it was so hard to get a job for the person who got Ph.D. in the foreign country. He could not get a academic position in Japan. Now it is changing. I learnt you have a postdoctor from Japan in this institute. It may have been hard for him to get a job in Japan. But he is enjoying postdoctoral job here… until when, that I do not know.

TPL: But now I have a former student from Stanford, and he got a job at Tokyo Institute of technology.

JS: Oh! That is nice. Oh… Oh that is really nice. But anyhow in Hirota-sensei's case, he could not get any job, so he was working for the RCA, the tele-electric company and engaged in fundamental research. At that time it was a good company, they had a Tokyo Institute of Fundamental Research or something like that. And he had been working on something, he was actually interested in making circuits, the nonlinear circuits which were related to Toda equation. But he also enjoys calculation, I worked with him several years and I noticed that he did very heavy calculations. He made thirty papers calculations every day. But of course he writes in big characters… ha…ha. While he was working for the electric company, he started his work on that bilinear staff. And he always gave the result only from the calculation, in that sense he is not a mathematician. I want to point out that all big senseis just enjoy calculation, even Sato-sensei, Toda-sensei also. Japan had some tradition to do calculation…. In Japan traditionally temple is the place to learn calculation and writing. I do not know whether this is the case in Taiwan or China. There was a famous Japanese 'Seki Kowa' who found determinant before Leibnitz. People in say several centuries ago just enjoyed calculation very much. In Japan in many shrines there are a kind of boards on which mathematical questions are written. I like calculation very much. Of course calculation only may not give good results but we need calculation and for nonlinear stuff still we need big calculation, otherwise we can not get anything.

TPL: The truth is rather hidden!

JS: Yes…Yes… still many things we have to learn by heavy computation, by computer or by hand on paper. And also there is a similarity among these three senseis. All of them are very Kenkyo (modest in a sense).… I still remember Sato sensei often says in his talk "I do not know so much about this, but probably this might be O.K.'' and when he gave a simple example, he also say: "I don't knows any thing about geometry…" He actually knows everything, but he believes that he doesn't know.

TPL: And that's good for the students, because it gives them the impression that there are lots still to the discovered.

JS: Yes… I think he really thinks so, "Since I don't know … so I am still working." He is never being proud of…

TPL: Are these three people still alive?

JS: Yes, we celebrated Toda-sensei's eighty eight years birthday last year. Sato-sensei is more than eighty. Hirota-sensei is the youngest, he is 73 or 74…. But what is remarkable is that they are still working.

TPL: Life is so good! You talked about Toda-sensei, Sato-sensei and Hirota-sensei. But I noticed that you also deal with young people in a very positive way, you always say something nice and encouraging to them.

JS: That I don't know… It actually depends on people ha…ha… some people are just waste… but are O.K. But at least I have learnt that we should always remain honest about research. Yes, I always remind my students that one should be honest about research, should not behave like… well you know… and great people are always like that… I never saw great people behave like playing great… ha…ha… that might be just a belief. So I am very lucky, I have contacts with them and work with them. I wrote a paper once with Toda-sensei, three or four papers with Hirota-sensei, although I never wrote any paper with Sato-sensei, but joined his seminars… I like him because he is interested in my work, because some mathematicians never find any value in my work… ha…ha.

TPL: You have mentioned several times that you are lucky… I interpret this as to mean that you take risk…but as we all know if you are lucky for once that could be lucky, twice… maybe, three times it's not lucky.

JS: I know that,… but I have been lucky… hope also in the future…

FCL: But that could mean also that you are Kenkyo.

JS: Yes… to be lucky of course the necessary condition is to work hard, without working hard and without Kenkyo you will never be lucky. But even if you work hard and with Kenkyo, you may still be not lucky.

TPL: I also like to relate to what you said earlier, alse indicate that you take risk, you gamble, if you gamble you find surprise of discovery or invention and then you feel lucky.

JS: To get something new, of course we have to do many gambling… even for us we tried and tried, maybe just one is good, then we are lucky. To have one lucky thing we have 99 unlucky things…

TPL: Since you are going to visit the Palace Museum which definitely deserve your attention, probably we should stop here. It has been very nice to talk to you, it's really inspiring. Thank you!

- Tai-Ping Liu and Fon-Che Liu are faculty members at the Institute of Mathematics, Academia Sinica.