傳播數學知識．促進數學教育

Interview with Prof. Masayasu Mimura

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

**Interviewers:** Tai-Ping Liu (TPLiu), Fon-Che Liu (FCLiu), Jong-Shenq Guo (JSG), Nai-Heng Chang (NHC)

**Interviewee:** Masayasu Mimura (MM)

**Date:** November 6th, 2004

**Venue:** Institute of Mathematics, Academia Sinica

Prof. Masayasu Mimura (October 11, 1941 - April 8, 2021) was born in Takamatsu, Japan. He received his bachelor degree of Mathematics and Physics in 1965 and PhD degree in 1973 from Kyoto University. Since 1970, he had been a faculty in Konan University, and Hiroshima University. Between 1993 and 1998, he was a faculty at the University of Tokyo. In 1998, he went back to Hiroshima University, and later moved to Meiji University. Professor Mimura has been a leading figure in reaction diffusion equations. He has organized mathematics and life sciences centers in Hiroshima University, Tokyo University and Meiji University.

TPLiu: Usually we ask you about your background, where you were born and how you got into this field etc…

MM: Ok, First, I am an applied mathematician. Also in the future, I want to be a mathematical scientist. It is my academic dream in my life. I was born in Takamatsu(a largest city in Shikoku Island) which is faced to the Inland Sea of Japan. It took only 5 minutes from my house to the seashore. One day when I was a junior high school student (about 14 years old), I saw some spotty area of the sea which was surprisingly changed to be red or pink from blue color. (I could find later that it was called the red tide). Next day, I asked the teacher, who was teaching biology in my class, “Why such a red colored pattern appeared in the blue sea”. He answered to me that density of plankton in this region becomes enormously high so that the color of the sea changed into red. In order to have such high density, planktons aggregate in some region. However, there occurs a problem that planktons usually swim randomly and then they spread in a homogeneous way. This is a totally different behavior from aggregation. Unfortunately, my teacher could not clearly explain this problem. Instead, what he said to me is that biological systems are generally mysterious. This was the first experience on biological behavior which I had in junior high school ages. After I entered the high school, my main interesting subject was mathematics, though I was interested in biology too. Because, for the entrance examination to most universities in Japan, mathematics is one of the important subjects so that I studied it very hard. When I was 18 years old, I entered into Kyoto University and luckily met Professor Masaya Yamaguti who was a most influential researcher in the field of applied mathematics in our country. Since I was a graduate student, he was my adviser. One day, he asked me: ”why don’t you study mathematical biology?” Of course, I was interested in biology but I did not know what mathematical biology was. He also said ”If you would start to study mathematical biology now, you probably would become a top researcher in this field, because this is a new field in applied mathematics in Japan. However, one problem was that there was no guarantee for you to surely succeed. There would be somewhat risk.” Finally he advised “You should do that!”. This is the reason why one of my research fields is mathematical biology. At that time, Yamaguti’s laboratory was very active. One of members is Takaaki Nishida (a best friend of Professor Tai-Ping Liu). As he was studying nonlinear hyperbolic equations related fluid dynamics. I thought I should find a different field from him, to avoid academic competition with him. The first study which I chosen was numerical analysis of and qualitative analysis of nonlinear PDEs describing real phenomena in nature. When I was PhD student, I could know a very interesting story on certain equations of nonlinear PDEs which was studied by my supervisor.

TPLiu: Who was your supervisor of PhD?

MM: It was still Prof. Yamaguti. Let me tell you this story. One professor of University of Tokyo sent a nonlinear PDEs which were proposed as a model in neurophysiology and ask for him to analyze this system of equations mathematically. Prof. Yamaguti and his friend, Prof. Shigeru Mizohata (He was a well known mathematician in the field of linear hyperbolic equations) were studying this system and succeeded in proving the existence and uniqueness of solutions of this system. They were so happy to do it. However, one year later, the professor of University of Tokyo sent a mail to them, in which “It was so sorry that the equations was wrong and I has to change it. Please forget the previous equations and study this new one.”(laugh) This was a true but sad story for mathematicians. The new equations was nowadays called ”FitzHugh-Nagumo equations”.

TPLiu: A famous equation.

MM: This story gave me the following lesson. That is, It seems to me that the attitude of my supervisor was as if it were a sort of “slavery”.

FCLiu: Slavery?

MM: Yes, it means that he analyzed the equations without thinking about the background of the equations and someone who brought the equations was as if he were a master. Understand? (laugh) Then I took this story to heart and then I always studied the background of equations, if I decided to study it. Otherwise I might be a slave. Then I decided that the study of biology from the mathematical viewpoints is one my research fields., In order to do, of course, I need to study biology.

FCLiu: When was that? When you were in the college?

MM: No, I had not enough time to study biology during my PhD student. Because the field of my PhD was numerical analysis of nonlinear PDEs, guided by. Prof. Yamaguti Therefore, I spent most of time to do numerical analysis. After taking PhD, I went to Mathematical Institute at Oxford University to study mathematical biology. The host professor was Professor Jim, Murray (now, he is in University of Washington), who was one of the very outstanding mathematical biologists in the world. I studied a lot of biology from him, especially how to model biological phenomena. I stayed there only one year and came back to Japan. My academic career until now is the following: at first I was a numerical analyst, and then I was doing some analysis, on real biological systems for 3 or 4 years and then coming back to mathematical analysis. And probably you know my career since then. I came back to Japan and got a position in Hiroshima University, department of mathematics. I stayed there for almost eleven years. After ten years, it was so hard to continue to study there, because the atmosphere in the department was too rigorously mathematical and instead, I wanted to study more applied mathematical stuffs. Then I decided to move to University of Tokyo, department of mathematical sciences. I like the sound of “mathematical sciences” rather than “mathematics”. After 5 years when I stayed, I knew that Hiroshima University had a plan to built a new and unique department in faculty of science; which was called “Mathematical and Life Sciences”. This department was built by combining of two groups. One is applied mathematics(theoretical group) and the other is life science(experimental group). Then I decided to move back to Hiroshima University again. You can understand from my career how I gradually moved from mathematics to, mathematical sciences, and to mathematical and life sciences, and why I said in the beginning that I wanted to be a mathematical scientist. Instead of either a mathematician or an applied mathematician, but of course my language and tool are based on mathematics. The main target is to mathematically understand real phenomena. That was my background. Ah, I forgot to tell you the story about red tide; I wrote some papers “How to generate red tide in sea”.

JSG: Before the day you saw the red tide, did you see it?

MM: No, Now I know it really depends on the weather and the environment. But it appears very suddenly, I don’t know why.

JSG: Did it disappear after some time?

MM: Yes, it disappears in a week, which really depends on the environment.

JSG: Did you see it again?

MM: Yes, very easy. But when I was a kid, I never had such experience. Then I solved this problem in a mathematical way when I was 36 years old.

TPLiu: And it was during the first period when you were in Hiroshima University?

MM: Yes.

TPLiu: Although you classify this as a mathematical period, you think pretty much about the phenomenon.

MM: Yeah, this was an exception. In Japan, probably here as well, if you are a mathematician, and someone asks you if you are an applied mathematician? Usually they do not like to be called as an applied mathematician.

TPLiu: They think it is a lower level to be called that way.

MM: Yeah. However, personally, I wanted to be called me an applied mathematician. But now I really want to be called a mathematical scientist. Please call me a mathematical scientist. (laugh)

MM: In Japan, young people do not like to study mathematics, physics or basic theoretical sciences nowadays. As a tendency, they are more interested in computer science or economics, etc.. How about the situation in Taiwan?

FCLiu: I think it is practically the same in Taiwan. But we still get very good students interested in mathematics and theoretical sciences.

MM: Quite few or?

FCLiu: We always get some very good ones.

TPLiu: I want to sidetrack a little bit. You know Prof. Yamaguti very well, maybe you can tell us his personality or stories you remember about him.

MM: Ok. Usually in Japan, if you want to be a good mathematician, then you have to do quite deep mathematics for a long time, maybe for 20 or 30 years. But Prof. Yamaguti changes his fields every four years. In those four years, he emphasized on one topic to his students. For instance, he emphasized on the importance of Fluid dynamics to Nishida in the first stage. In the second stage, he emphasized on biology to me. Something like this. He always changes his field. The interesting point is the following, every four years, he thought that he could understand essential part in these fields. It is true. (laugh) However, most conservative mathematicians did not like his attitude. But he did not care about that.

TPLiu: Once he told me that if he had not studied chaos, he would consider his career incomplete. (laugh) He has a nice and charming personality to outside people.

MM: One day we went to zoo and saw very beautiful carps in pond.

TPLiu: The Japanese like to have it in the garden.

MM: Yeah, usually carp has very nice and their skins show colorful patterns, sometimes they posses golden color. Suddenly he said: “Mimura, why don’t you make a model for this pattern and coloring? If you could succeed to model and analyzed them, then you would be rich, because no body knows how such patterns appear. Therefore, one very colorful carp is incredible expensive, its cost is about one million yen for one carp. Do you believe it?”

MM: So he said that if you could study pattern formation of skins in living systems, then you would be rich. (laugh)

TPLiu: He is quick to relate surroundings and think about the new things right there.

MM: Not only for me, but also for other students. Now he specializes in chaos. And I had a story from his student Ushiki, who is in Kyoto University now. The story is as follows: Prof. Yamaguti pointed out to clouds in the sky and said “you should do mathematics for the dynamics of the clouds!” (laugh) That was sort of chaos.

MM: Do you know some mathematical scientist like me in Taiwan? The main purpose to understand phenomena, however, should be established by using mathematical methods. In that sense, sometimes I am a mathematician, sometimes I am a numerical analyst, and sometimes I am a mathematical scientist. This is how to describe me. Also I emphasize on the importance of interdisciplinary culture in high schools and universities.

FCLiu: I have been to your talk several times and noticed that you all choose the right problems to start.

MM: It’s my pleasure.

FCLiu: I would like to know how you can do that. It would be beneficial for young people to learn.

MM: When I found that this problem is very interesting, I concentrate on doing mathematics for a moment and involved in this problem mathematically. A little bit later, I recognized that I was a mathematician and I had to say something mathematical. However at the first stage, I am always interested in and love phenomena, as if I were a baby.

TPLiu: If the phenomenon is interesting, almost surely interesting mathematics will come later.

MM: That is my confidence. If the background of the problem is interesting, then there is good mathematics behind the problem. Agree?

TPLiu: Yeah. Also there is another quality which Fon-Che put very well which is necessary for the things you do; namely, you need to be able to get along with people, you need to have a personality to communicate well with people. And you communicate well with people.

MM: Yeah. I have to have communications with many people in different fields. Basically, I like human beings, no, I like living species, dogs, cows…etc. It is better for me to communicate with people and it will help me to understand phenomena. Let me switch to the modeling part, a mathematical model. So this is sort of phenomenon. But when I was young, maybe a graduate student, I thought one phenomenon corresponds to one model, that is, the model is unique for one phenomenon. But it is totally incorrect. It means that there are so many models from different aspects, it depends on what you are interested in. For instance, we have an elephant here, if someone is interested in the nose, then he just needs to know how to make such long nose. And someone else may be interested in formation of skin. It depends on what you are interested in. There are different models. If you are interested in the dynamics of an object, and there are several models from microscopic, mesoscopic and macroscopic levels. If we are interested in the dynamics, at first, we recognize only the boundary, after that we recognize what is inside and outside. If this object is in 3D and you are only interested in the boundary, it becomes 2D. It is a reduction of information. In such reduction is possible, we may succeed in understanding in a mathematical (rigorous) way. At first, I derive the mathematical model from that original model; and then in order to analyze it, we propose a mathematical thinking model from the original model by using a rigorous reductive method. Furthermore, if we want have more deep understanding of the phenomenon in a rigorous way. I try to derive a new model from that model, this is my way, Understand? Mathematical modeling and doing mathematics are very closely related. For instance, there are mathematical tools, and there are so many tools. That is the mathematical model. Then it is impossible to do anything with the model. If you move the model like this, then we can do mathematics for the model. This is my job, ok? For instance, you know the Boltzmann equation, which describes the interaction of particles and is very hard. But in some way, you can derive macroscopic equation, Navier-stokes equation. Or you may have a new mathematical model from this one.

TPLiu: There are many equations one can derive from the Boltzmann equation.

MM: This is the mathematical power, modeling power and you can change like this and catch it.

TPLiu: One needs friends to do science, one good source to have friends to have good students, not every good scientist is a good teacher. And you are clearly a good teacher.

MM: No, coming back to my supervisor. He was very good for me. Even if I didn’t get very good results and I showed to him, please. Then Prof. Yamaguti said “very nice!” (laugh) It was very important, it encouraged me. Then I thought I should try again.

TPLiu: And you are a great teacher.

MM: I try to have the same attitude.

TPLiu: To make them feel smart. What would you say to young female mathematicians?

MM: In Japan, most mathematicians are men. It is very bad for the young female students because they really want to know their future. If there are several good female mathematicians, they can just ask. In Japan, the number of female mathematicians is decreasing.

NHC: Yesterday, Mayumi Shoji of Japan Women’s University told me about that and asked whether the situation is the same in Taiwan. And I told her it was not. In fact, I think it is increasing in here.

FCLiu: It is increasing quite rapidly.

JSG: There are always some female professors in most mathematics departments in Taiwan.

MM: why? In my university, there is one female professor. In the previous university, there is none in Tokyo university.

TPLiu: How many students have you had?

MM: I just moved to the Meiji University (private university in Tokyo), so now I don’t have any student. In the previous one, I has ten.

TPLiu: How many phd students have you had so far?

MM: Not so many, maybe 15 or 20.

TPLiu: But I already know several very good ones.

MM: I was very happy about it.

TPLiu: Fon-Che and I were talking about 1989, you, Evans and Bardo came. We went to Hualian together and had good memories.

MM: You remember the story in Hualian. We just walked, and Tai-Ping was a guide but we lost our way.

TPLiu: Yes, and there was water and we went swimming.

MM: Naked. (laugh)

TPLiu: It was very cold.

NHC: Where is it in Hualian?

TPLiu: Bai-Yang Waterfall (白楊瀑布)

TPLiu: You propose collaboration between Taiwan and Japan, and then we had a conference. This thing was really initiated with you. That was very nice of you and thank you very much.

MM: Now young people also communicate with each other. We are the first generation, and the 2nd and 3rd generations have to inherit our attitude. I am very proud of it.

TPLiu: You are still very active now and many more years in front of you, I think maybe some years down the road, we will interview you again. It is so much for today, thank you very much.

- Tai-Ping Liu and Fon-Che Liu are faculty members at the Institute of Mathematics, Academia Sinica.
- Jong-Shenq Guo is a faculty member at the National Taiwan Normal University and the Tamkang University.
- Nai-Heng Chang was a faculty member at the National University of Kaohsiung, and a faculty member of National Taitung University since 2005.