Interview with Prof. Shigefumi Mori

Interview Editorial Consultant: Tai-Ping Liu
Interviewers: Tai-Ping Liu(TPL), Jung-Kai Chen(JKC)
Interviewee: Shigefumi Mori(SM)
Date: July 15th, 2009
Venue: Institute of Mathematics, Academia Sinica

Prof. Shigefumi Mori was born on February 23, 1951 at Nagoya. After obtaining his PhD in 1978 from Kyoto University, he held a teaching position at Nagoya University. Since 1990, he has been a professor at Research Institute for Mathematical Sciences (RIMS) at Kyoto. For his fundamental contributions to algebraic geometry, Prof. Mori was awarded the Fields Medal in 1990. He is a member of Japan Academy and was President of International Mathematical Union during 2014-2018.

TPL: Thank you for coming. These few days you have been working hard.

SM: Oh no. It my honor and pleasure to be here.

TPL: So we usually start with a very routine question. Do you always like mathematics since you were a child?

SM: It depends on what you mean by “like”.

TPL: You excelled in mathematics, for example.

SM: No. I did not

TPL: No? (laughs)

SM: When I was in grammar school, my parents were both working. So they sent me to an after-school learning center, which was in a sense like a nursery. So I was sent to the place and they taught me something. But I did not really work hard. In those days, they used to list the top ten or so students in each exam and I was never in the list.

TPL: I see. (laughs)

SM: Sometimes they gave us some problems. If some of the students did very well in solving the problems, they gave them cakes as a reward. One day there was only one cake which could cut to be shared by the students who got the problem right. Only at that time, my curiosity was aroused.

TPL: I see. So encouragement was important.

SM: Oh well, maybe, appetite.

TPL: Appetite! (laughs)

SM: It was a simple problem like; given number of cranes and turtles, with given number of legs we were expected to find out the number of cranes and turtles.

JKC: How old were you then?

SM: Ten or eleven.

TPL: So it’s a normal time. I see.

SM: Normal, completely normal. I was not the best at all. So you see, it’s nothing really difficult. I don’t remember the method. But there were only several cranes and turtles. So if you were determined, you could just do it.

TPL: I see. By the method of exhaustion.

SM: Yes, so it was nothing really difficult. But it turned out I was the only one who could solve it.

TPL: Ah I see.

SM: So they gave me the whole cake.

TPL: Not to share with many, just one person got it.

SM: Yes. I was surprised though. They worried that if I went home alone by myself with a cake and if my parents were away. So they came home with me, my parents were surprised and asked what happened, and my parents were really glad.

TPL: What do your parents do?

SM: They trade textiles, towels and those things.

TPL: I see. So they were doing well in their business.

SM: Well, just enough to make a living. So they were really glad.

TPL: So they got to share the cake with you.

SM: Yes. But that was the only thing I could be proud of in my grammar school days. After this event, I did not really do anything special. It was just that one occasion. But somehow, I felt that I could do mathematics, but not explicitly. I think I gained something.

TPL: Some confidence.

SM: Not so explicitly.

TPL: Oh yes, we also have the same problem, probably handed down from Japanese time. The problem was not called turtle and crane.

JKC: We have the chicken and rabbits.

SM: Chicken and rabbits, that’s interesting.

JKC: Chicken and rabbits in the same cage.

SM: I see.

TPL: So when did you decide to be a researcher in science, to major in mathematics?

SM: To major. Let’s see. So in my high school days, there was a magazine listing sort of unique problems. That’s intended for entrance exam. But somehow, these problems in that magazine were not easy to solve by sort of standard method. I did pretty well in that. So, it’s from that time I wanted to study more, but nothing really advanced. I didn’t start anything advanced.

TPL: You picked up the magazine and decided to do those questions?

SM: It just happened that way, when I was in the first year of the senior high school. I solved the problems and sent back the answer. They graded it and sent back the results. They listed the names of students who got it.

TPL: Can you remember one of the problems?

SM: Ah.. one of the problems… there were several. But when I was in second or third grade, I saw this problem. Let $N$ and $M$ be positive integers. Suppose there are $N$ white and $M$ black stones, like Go(圍棋). From them you pick up stones one by one and put them, say, from left to right, in such a way that there are always more white stones than black ones. You decide how many ways to do it.

TPL: I see.

SM: But the problem was given with specific numbers $N$ and $M$ which I do not remember. It was not an exam problem. It was not something you could do in just one hour. I spent a couple of days before I realized it could be solved.

TPL: That happened when you were in second or third grade of senior high school?

SM: Yes.

TPL: You spent days on that.

SM: I don’t remember how long it took me to solve the problem, but it was very interesting.

TPL: Wow.

SM: Shall I show you the answer?

TPL: Yes, please.

SM: So this is the number. $\left [ \begin{array}{c} M \\ N \end{array} \right ]$。It satisfies a recursive relation, $$ \left [ \begin{array}{c} M \\ N \end{array} \right ] = \left [ \begin{array}{c} M \\ N - 1 \end{array} \right ] + \left [ \begin{array}{c} M - 1 \\ N \end{array} \right ]. $$

TPL: M cross N ways.

SM: Yes, you see that. Then you get some sort of Pascal numbers. So each number is the same of the upper left and upper right. So left side is N, right side is M. So since there shall be more white, If M and N are equal, that would just be zero, since is no way. This right side is null. So you can only go by the left side. So usually we stuck here. I spent some time on this, and then I realized that there is a symmetry. If you put minus one here, that would be the usual Pascal triangle. So if you start n-1 and n+1 at this row. That would be the answer.

Professor Sen's manuscript.

$$\hskip -10pt \begin{array}{ccccccccccccc} &&&&&&0&&&&&&\\[7pt] &&&&&1&&0&&&&&\\[7pt] &&&&1&&0&&0&&&&\\[7pt] &&&1&&1&&0&&0&&&\\[7pt] &&1&&2&&0&&0&&0&&\\[7pt] &1&&3&&2&&0&&0&&0&\\[7pt] 1&&4&&5&&0&&0&&0&&0 \end{array}\leftrightarrow \begin{array}{ccccccccccc} &&&&&0&&&&&\\ &&&&1&&0&&&&\\ &&&1&&0&&0&&&\\ &&1&&\hbox{$\Big[\!\begin{array}{c} 2\\[-5pt] 1\end{array}\!\Big]$}&&0&&0&&\\ &1&&\hbox{$\Big[\!\begin{array}{c} 3\\[-5pt] 1\end{array}\!\Big]$}&&0&&0&&0&\\ 1&&\hbox{$\Big[\!\begin{array}{c} 4\\[-5pt] 1\end{array}\!\Big]$}&&\hbox{$\Big[\!\begin{array}{c} 3\\[-5pt] 2\end{array}\!\Big]$}&&0&&0&&0\\ &&&&&\vdots&&&&&\\ \end{array} $$
Figure 2 The additional explanation.
$$\begin{array}{ccccccccccccc} &&&&&&0&&&&&&\\[4pt] &&&&&1&&\hbox{-1}&&&&&\\[4pt] &&&&1&&0&&\hbox{-1}&&&&\\[4pt] &&&1&&1&&\hbox{-1}&&\hbox{-1}&&&\\[4pt] &&1&&2&&0&&\hbox{-2}&&\hbox{-1}&&\\[4pt] &1&&3&&2&&\hbox{-2}&&\hbox{-3}&&\hbox{-1}&\\[4pt] 1&&4&&5&&0&&\hbox{-5}&&\hbox{-4}&&\hbox{-1} \end{array}$$
Figure 3 The additional explanation.

JKC: That’s quite smart.

TPL: You need a symmetry. I need that triangle to begin with.

SM: So given any place, you just count the number of blacks to reach here time 1 plus the number of whites to reach here then minus 1 it would give you the answer. So that, I was excited just to see this. Just if you have noticed, it’s so simple. Then after that, I entered the university. In the graduate school, I realized that number is the degree of a specific Grassmanian, I don’t remember exactly. Say Grassmanian $(n,1)$ or something, in the Plücker embedding. So I could compute the degree.

JKC: So you did that when you were in high school.

SM: I solved the problem in high school but I did not realize then that it was related to higher mathematics. It was just a coincidence.

JKC: So when did you decide to become a mathematician?

SM: Well, it’s a hard question. So when I entered the university, I just want to study mathematics, not to become a professional in mathematics. I don’t know. I decided that I would continue to be a mathematician at around 30 years of age.

JKC: 30?

SM: I just did not have any confidence.

JKC: At that time, you already had some important works.

SM: Yes, so that’s why I could have continued. Maybe it’s not exactly the answer to your question.

JKC: At that time, you have already got your Ph.D. and you had been working in Nagoya.

SM: So when I went to US. Just before I went to US, I wondered, because it was a big decision to make. I thought that if I could not do math, I would just become a high school teacher or something. Maybe it’s an insult to high school teachers, but just to convince myself at that time I would do it.

TPL: But were you interested in teaching, when you said high school teacher?

SM: So you see, it’s not a very practical way of thinking.

TPL: I see.

SM: Just to convince myself. I understand that high school teacher isn’t easy. Because in the first place, I originally wanted to do mathematics was just because I thought by doing so I did not have to talk to people. But after becoming a mathematician, I have to talk to people. So the plan did not really work out well.

TPL: I see.

SM: But decisions are like that.

TPL: But are you enjoying the love of mathematics like a zen master type of existence? From time to time, say I want to meditate by myself. Is this one of the things you enjoying?

SM: I don’t know. I just want to think. When doing those problems, I was taught to really think over and over.

TPL: By yourself?

SM: Yes.

TPL: I see. That’s one thing you enjoy.

SM: Yes. Especially, when I notice something easy, or some seemingly difficult problems turn into easy ones, that’s very exciting. Once you have that experience, it becomes an addiction, a life time addiction.

TPL: You have this experience rather early on, right? In high school.

SM: I don’t know if it’s in high schools. Some people get excelled extremely early, but I am just usual.

TPL: I see. So you don’t force yourself in schools? You don’t try to shine or work hard to impress other people. You just let things happen naturally.

SM: Yes, in high school, I really enjoyed mathematics. I mean not higher mathematics, but high school mathematics.

TPL: Is it true that from what you have said, it was not any particular teacher who inspired you? You just like mathematics.

SM: Well, I said earlier that I wanted to do mathematics just to avoid talking to people. But through mathematics I could talk to teachers. So I liked the teacher and he taught me well. He encouraged me. He knew how to encourage me, I suppose.

TPL: So was this when you were in elementary school?

SM: No, it was when I was in high school.

TPL: So that was a good teacher. Where did you go to school?

SM: In Nagoya.

TPL: Recently, people heard the news that in Nagoya people are educated very well. You have a Nobel Prize and so on.

SM: Kobayashi, Masukawa and Shimomura. (physics/chem) Makoto Kobayashi , Toshihide Masukawa 和 Osamu Shimomura 。

TPL: So is Nagoya a particular place for good education? People value education or something? Anything special about Nagoya?

SM: Nagoya is nowadays known to be a place for passing by, though it was known as a place where Japanese classic art was appreciated.

TPL: Between Tokyo and Kyoto.

SM: Yeh, so they don’t stop at Nagoya. I mean, Nagoya is called the big countryside.

TPL: Big countryside?

SM: Yah, it’s a fairly big city with a fairly big population, but still, the way people live in old style. Of course it’s changing though it’s not like Tokyo or Osaka. It’s easier to live.

TPL: So maybe, children there have the environment to develop at their own pace.

SM: I think so. Nagoya is rather a conservative place. Things are abundant. So they don’t have to be innovative. Many people from Nagoya area, the greater Nagoya area, go outside and do very well. Like, Sony, one of the founders was from that area. Nowadays, Toyota is the big company based near Nagoya.

TPL: I see.

SM: Iyeyasu Tokugawa (德川家康) is from Nagoya area. He is actually from Okazaki not exactly Nagoya but a nearby city. Nobugawa Oda and Hideyoshi Toyotomi are also from the greater Nagoya area. In this sense, Nagoya is a very special place.

TPL: Oh yah. But mathematicians I know, the number of mathematicians from Nagoya, wasn’t the Shimura (of Shimura-Taniyama)?

SM: Oh no, not Shimura 志村. His mother or grandmother was from Nagoya. He told me that.

TPL: Okay. How about Kiyoshi Ito? He was also passing by there, or he was in Osaka.

SM: Yes, he had a position at Nagoya University. Quite a few good mathematicians are from Nagoya University.

TPL: Kosaku Yoshida, you know?

SM: Yes, he was at Nagoya University, I think. And Masatake Kuranishi.

JKC: So how did you choose to work on the threefolds when you were age 30?

SM: Threefolds, oh well. When I was a senior, my adviser, Nagata, gave me a problem to construct an interesting rational variety which is a threefolds. I did come up with something. But it turns out to be a linear-space section of a Grassmanian. It wasn’t the kind of answer that Nagata wanted. In that sense, I failed. But later, I realized this is a Fano threefold among the list of Iskovskikh. That’s why I was interested in birational geometry of threefolds. So I had an interest in that, but it does not mean I was working on it. That was at the bottom of my curiosity. I was working on Hartshorne Conjecture; I was influenced by my teacher, Sumihiro. He had been working on that problem. We worked together to settle one special case. Then I went to Harvard when I was 26. I solved Hartshorne Conjecture there. I found the solution after I made a wrong proof of a weaker intermediate problem. Furthermore I found the extremal ray. I felt that it could be useful for something. Then my memory and curiosity came back, and I started working on threefolds with Shigeru Mukai .

JKC: At that time, did you know the notion of terminal singularities is going to be that critical in minimal model program?

SM: That’s a delicate question. So around the time I found extremal rays. Miles Reid came up with canonical threefolds paper. Then I realized that terminal singularities shall come into play. Soon Miles Reid published the terminal singularity paper. (25:01)

TPL: So it seems to me that Japan in the field of algebraic geometry has a long tradition, is that so?

SM: well, The tradition was in Tokyo. I was not part of the tradition.

JKC: So you mean the tradition is the tradition from Kodaira. (小平邦彥)

SM: Yes, Kodaira school.

JKC: Kodaira and Litaka. (飯高 茂)

SM: You are right.

TPL: So in some sense, you have an advantage in that.

SM: I don’t know. I never thought that I am an expert in classification because of this. I have a curiosity and the curiosity of extremal rays, a new variant to classify Fano threefolds.

TPL: So the period of this very intense concentration is from what age to what age?

SM: Let’s see. I found the extremal rays around 1980 or 1981, I don’t remember. It depends on how you count. Then I solve the existence of flips at 87 or 88. So maybe 7 years, depending on how you count. I started from computation.

JKC: But at that time, you travelled in the United States a lot. You stayed in Harvard.

SM: That was an interesting time. Because in Japan, how to express that in English, I…So it’s like recharging my battery in Japan. I get half a year in the US.

TPL: To tell people know what you are doing.

SM: No no, just to do research and so on.

TPL: So Japan is a good place to contemplate.

SM: In those days, people didn’t ask too much about what you were doing. But nowadays, the government is asking the results all the time. So it’s getting harder and harder. Especially the young people feel obliged to create papers.

TPL: If it’s bad in Japan, I think that elsewhere in Asia it’s worse. That’s true, research is a slow business.

SM: Yes, I mean, you should not expect success, right?! It’s so hard, the government expects success.

TPL: Sometimes, the failure is more valuable.

SM: Yes, that’s right. I mean, my solution to Hartshorne Conjecture was started from a failure. I wanted to solve Frenkel Conjecture, the differential-geometry version of the Hartshorne Conjecture. I wanted to solve a partial result. I thought that I solved it, then I realized a gap in the argument. I examined the result carefully. The reason why there was a gap was that I created a rational curve. So the rational map is not a morphism. That’s how the rational came out.(29:51)

TPL: It’s a very important by-product.

SM: It’s like that. So those were the time I really got excited. By changing the viewpoints, the aspect changes completely.

JKC: So those attempts made you become a mathematician.

SM: I don’t know… I mean to continue to be a mathematician.

TPL: So am I right to say that whatever you decide, whatever you do, you try to follow your love in mathematics. At one point, you said that doing high school mathematics maybe good, because you can concentrate on mathematics, and pursue the love of mathematics.

SM: little by little.

TPL: So the thing you treasure is the love of mathematics, right? So when we asked you if you wanted to be a research mathematician that is not as important as whether you can pursue the love of mathematics.

SM: I think so, yes. I mean, I suppose every mathematician has a fear of tomorrow without new papers. (32:13)

TPL: One of my academic hero is James Glimm. I was 30 at the time when I first talked to him, and he was 40. Right now, when I looked back, 40 is young. But at that time, I thought that he was so famous and so senior, hence I asked him one question ‘so you have no worries about papers.’ ‘Oh yes, I am still and always thinking about what would be my next project.’ I was surprised, but he was actually only 40 years old then. Japan is unique among Asian countries, in particular, in mathematics, don’t you think so?

SM: Because of the people?

TPL: Well, for one thing, Japanese mathematics is so much better than rest of Asia. What was the reason…

SM: I don’t know much about histories, but one thing I have heard is that in Edo Era, Japanese had developed the Japanese mathematics. Because of this, we could easily absorb European or American culture in mathematics. We had that basis. Quite a few Japanese mathematicians are interested in studying histories, but I don’t know so well

TPL: Actually my question perhaps should be that when you meet people in Asia, do you feel a difference in culture and their attitude towards research? Inevitably, there would be a difference, right?

SM: Yes, I mean, everybody is different, even among Japanese. I know quite a few Japanese who started learning advanced mathematics at an early age. Quite different.

TPL: You were not one of those.

SM: No, totally different.

TPL: This would be encouraging to a lot of people!

SM: In the sense it was started because of my appetite, the cake.

TPL: So your parents were very happy at that occasion.

SM: Yes, and it made me very happy too.

TPL: Your parents still live with you now?

SM: No, my father passed away a few years ago, and my mother is with us. She is very old.

JKC: It seems that Japanese is quite flexible about your stay of long periods in the US around the age of 30 and 40. How did you manage it?

SM: I don’t exactly know how things are now, but in those days, assistant professors could go to US for 2 years, how do you call this?

TPL: A business trip or a leave. In any case, you keep the position?

SM: Yes, so altogether I stayed there for 3 years. But now I think it’s getting difficult. So after that, I went back of course. So I stayed in US for 2 years and went back to Japan for 2 years. Then I went to US for another year, something like that. So in Nagoya University, they encourage people to go out. So they did not pay too much attention to teaching. It depends on the place.

JKC: But they were encouraging people to go out.

SM: Yes. Now it’s getting harder.

TPL: So how long have you been in RIMS?

SM: I came to RIMS at 1990s, so 20 years by now.

TPL: So it was at the time when you got Fields Medal.

SM: Yes.

TPL: I read a report in the US at that time, that at the Kyoto Station, was it the old station or the new station at then?

SM: Maybe the old station.

TPL: So they had these big photographs at the station, one of the photographs was a baseball player, two other photographs which I do not remember and then another photograph was of yours. Big photo in Kyoto station. So the American said that, ‘Wow, Japan is a very nice country. They put a big photograph of a mathematician at the train station.’ It’s like a rock star. So how does RIMS operate? Can you say something?

SM: One aspect of RIMS is a research institute, and the other is a meeting place like MSRI, where mathematicians all over Japan can hold meetings.

TPL: I have just attended one meeting there last week.

SM: Ah, I see. Recently they started this sort of international version, but that cannot be held too often, only from time to time. So, RIMS has those functions. In Japan RIMS is still the only institute which covers the whole of mathematical sciences. There are new one covers some part of it, but not all.

TPL: Also RIMS is the only permanent one. The others are not.

SM: That’s right.

JKC: So when did RIMS founded?

SM: About forty years ago.

JKC: I see, about forty years ago.

TPL: Who was the first director?

SM: Masuo Fukuhada.

TPL: I see. Recently I heard this story. I don’t know if you have heard it or not. When Sato became the director of RIMS and disappeared immediately for more than 20 days, because he had this important research to work on.

SM: After he became the director?

TPL: At the beginning when he was appointed.

SM: Hahaha. I don’t know. I mean it’s possible, but I don’t know about this story.

TPL: But you know him, right?

SM: Yes …. But at that time I was not at Kyoto. I suppose once he got excited, he just pursued on.

TPL: This is a very nice story. Is there a general saying or discussions in RIMS on what are the future research directions that are exciting? Any discussions like that? So the hiring at RIMS turns toward a certain direction? Is there such a discussion at RIMS?

SM: That’s difficult. We do discuss something of this kind when we decide whom to make an offer. But I do not think RIMS should decide one direction is better than another. I don’t know whether it makes sense to decide a direction

TPL: Yes, it’s difficult to predict the future.

SM: Quite often it’s just nonsense. Rarely things turn out to be expected. A development often come out from unexpected areas and unexpected directions. Things go in their own ways. So this sort of prediction is paradoxical. I agree though that planning has to be done. But you should be prepared for unexpected outcomes Of course, we would like to think if some fields are missing, but we have to take good people. So excellence is the first priority. Then of course you have to think of balance

TPL: So as a result, what fields are of the concentration of good people right now?

SM: Let’s see. I am not the director. So I don’t know.

TPL: Sorry. I am not trying to give you a quiz.

SM: If you go to the homepage of RIMS, maybe you can get some ideas.

JKC: But usually number theory and algebraic geometry are big parts of it.

SM: Yes, but it does not mean it would be that way forever. Depending on the time, there would be some emphases on particular fields. But depending on the availability of people, it will change.

JKC: So what do you think of the recent development in algebraic geometry. For example, big breakthrough in minimal model program in recent years. (45:30)

SM: Well, I mean, I am very happy about it.

JKC: But their approach is kind of very different from your original approach.

SM: I mean… it depends on what you mean by my approach. My approach is just to use the cone. Still it’s just a cone. (45:12)

JKC: I shall say that for your method, your method is highly dependent on the detail knowledge of singularities individual…

SM: No no… I wanted to classify them completely since I was a student. I didn’t mean to solve higher dimensional case by that. It’s just impossible to classify them. At the time, there was no way to solve it. I was, in a sense, desperate to understand it. So the natural action was to classify them. So to fully understand the threefolds, we have to understand everything. So….

TPL: This is what the general people call the Mori Program, right?

SM: Again, I wasn’t involved in the development. I just stumbled across this notion of extremal rays. What’s called Mori Theory is based on the extremal rays, though people don’t draw pictures. It’s so basic. Before this extremal ray, people did not know how to get to extremal rays and minimum models. (46:25)

TPL: Algebraic geometry as a field, when did it really start? It is generally considered such a core subject of mathematics.

SM: In the middle of 19th century, Riemann studied it. Around 1900, Italian schools studied surface case. But the results of Italian schools are sometimes not accurate. So they did not have a precise notion of various things. So André Weil and Oscar Zariski started building up the foundation. So Weil’s “Foundation” was written in 1950s. Then many people worked on the foundation. For instance, my adviser Nagata constructed a model theory. Then Grothendieck came up with schemes. It was, in a sense, based on Nagata’s work. Nagata expanded it. Again, it’s hard to say when it did start.

SM: So when did you start to be interest in the Threefold?

JKC: My interest in that started maybe two years ago (2007). At that time, we somehow had some methods trying to understand the Threefold of general type. (50:38)

SM: You mean the work with Meng Chen (陳猛)?

JKC: Yes, after that we become more and more interested in the Threefold.

SM: You are working in the explicit algebraic geometry, a new generation.

JKC: It’s kind of following your program to understand Threefold more explicitly.

SM: I like that. I mean to reach the level of the understanding of surfaces you really have to redo many things.

TPL: So algebraic geometry is a field that is developing.

SM: Yes, but it has also been applied in various ways. For example, to String Theory. I don’t know much about it, but it’s quite surprising. In the applied mathematics as well.

TPL: I know it very vaguely, like in the Soliton Theory.

SM: Or in the cryptography. Because of the computers, they can compute things in algebraic geometry. Maybe not in analysis, not so precisely. But in algebra, algebraic geometry things can be precisely computed. But some people found surprising applications. It’s interesting to watch those things happening.

TPL: I know some people are trying to think about that in biology also.

SM: It won’t be so easy, but still, that could be very important.

TPL: So in Japan, where are the important places to start algebraic geometry?

SM: Like Tokyo and Kyoto.

JKC: Is Nagoya also one of the places?

SM: Many people left. So it depends on what aspects of algebraic geometry you want to study. So if you want to study the moduli or to realize the moduli using quotient of a symmetric bounded domain, Nagoya is the place. Nagoya has an expert on that. (53:05)

TPL: You visited Utah for a year?

SM: Many occasions.

JKC: Is that during the period János Kollár was still there?

TPL: Oh, I see. Where is Kollár?

SM: At Princeton.

TPL: He collaborated with you?

SM: He is a very wise guy. Not like me.

JKC: Kollár is always very sharp and very precise.

SM: Yes, he is.

TPL: You are a Zen master.

SM: No no… I don’t intend to be that way. I don’t even try to compete with him.

TPL: So some time ago, I heard from people that they talked about RIMS, because RIMS is so prominent. From time to time, people talked about what would happen to RIMS, but you answered this question already. Things will happen unexpectedly.

SM: Yes, that’s the case. For the institute, it is necessary to plan ahead, but it’s still difficult to say.

TPL: In the past history of RIMS, which you said 40 years. What were the memorable things? Can you think of a couple?

SM: I don’t know much and I don’t feel that I represent RIMS, so ….

TPL: Okay, you went there in 1990. So that has been, 18 years.

SM: So presence in Sato school is sort of enough.

TPL: You mean even now?

SM: Yes with Kashiwara, who was a leading member of Sato school. Unfortunately, Kashiwara is retiring in one year.

JKC: In one year?

SM: He is retiring next March.

TPL: This thing about retirement, in Japan, there is no exception. No matter who you are. A Fields Medalist or something, you have to retire at the retirement age.

SM: Yes, that is correct.

TPL: I am sure in other countries; they make exceptions for people like you. (laughs) There was Kawai?

SM: He retired.

TPL: He was also in generalized Sato school.

SM: That’s right.

TPL: But Sato is still around right. He is still alive.

SM: From time to time, if there is an interesting occasion, he may show up.

TPL: In RIMS, do you give a course?

SM: No. We have graduate students, but we don’t teach them through lectures. We run seminars. As we don’t have that many students, so it’s most effective to run seminars.

TPL: I see. So students present some materials also and the professors direct them?

SM: Yes, that’s right. Usually it’s one or two students with several professors. So the number of professors is bigger than the number of students.

TPL: I see. So how many Ph.D. students all together are there at RIMS do you know?

SM: In Japan, master course and Ph.D. course are separated. For master course, around 10 students for each grade; for Ph. D. course, there is only 5 students in each year. But it’s not constant.

TPL: So this is one function of RIMS. The other function of RIMS, as you have said, is a meeting place for international mathematicians, like Princeton IAS. You also have post-doctorates?

SM: Yes, RIMS also have positions for post-doctorates.

TPL: I see. You have flexibility for travel or not?

SM: Yes, many members of RIMS travel abroad freely.

JKC: So basically, you don’t have constraint, where if you leave for one year, you have to stay at RIMS for one or whatever the duration is.

SM: There is some but no…

JKC: This is what happens in Taiwan basically.

SM: No, not at RIMS. Of course, if the need become higher, then the duties will change. But it is not like that, not at the moment.

TPL: In fact, for past few years, how many months do you stay at RIMS each year?

SM: In that case, most of the time. It’s not because of RIMS, it’s that I am serving at a government committee and I am a member of Japan Academy. So I have to attend the meetings. As I said earlier, I live in Nagoya. But I have to go to Kyoto 4 times a month. Now, I have to go to Tokyo 3 times a month. Sometimes, I can skip, but it’s very rare.

TPL: Jung-Kai was asking that question, but in fact, the people in RIMS, even the younger people, they stay at RIMS most of the time, right?

SM: Probably yes, but I don’t think that’s completely ideal. They should go out freely. I moved to RIMS as a professor, but from ‘91 to ‘93 I stayed at University of Utah. This is a little unusual but I wanted to be away from the aftermath of the Fields Medal. I should add that at RIMS, it is common that professors visit foreign countries for a few months. There are no obvious rules on these probably because there is no teaching duty at RIMS. Although we run seminars but we run it together in algebraic geometry. I don’t know about other fields. But in algebraic geometry, we run it together, so if one of us is away, we can still manage. It’s not a big restriction. But, you see, the research environment, like accessibility to library and chances to talk to joint workers is very good at RIMS, so probably people don’t feel the urge to leave. It’s hard to say. But at least for me, I don’t tend to stop there. At least, that is the way I have been so I cannot say no to a colleague if he/she wants to be away.

JKC: But maybe RIMS is already good enough, people just come to RIMS, so there is no urge to go.

SM: But post-doctorates, generally, they are not very outgoing. I am a little worried about it. Maybe it’s a culture. I don’t know. In old days, people went to foreign countries for longer. Now we have a grant money for foreign travel, so we can go using that. So they can make lots of short trips. But in the old days, this kind of money is not available, so people had to go out for extended period. So it’s hard to say which is better. Personally speaking, it’s good to have an experience of prolonged stay. That is the only way I could have learnt to speak English. I mean, I could have managed, but without the experience of teaching, it’s hard. So in my case, I went to US when I was 26 years old. In the first year, I had to teach, because I was a TP, an assistant professor.

JKC: Yes, teaching professional.

SM: But I never taught in Japan earlier. Not just that, I never even learnt things in a regular way, because my freshman year was at the days of student riots. So the first half year, the university, the college was closed. ,

TPL: Was that the time of Vietnam War year?

SM: No?… it was 1968 to 1969.

TPL: That’s the Vietnam War year in the US. There were a lot of student riots, in places like Berkeley and Wisconsin.

SM: That was a unique year for Japanese universities. That was the only year the University of Tokyo did not have the entrance exam because of the students’ riot. If I say that, the people around my age can immediate identify with it

TPL: Could I change the subject a little bit? You have been in contact with many people. Do you feel like to talk about some other personalities which you have met? You talked about Kollár.

SM: I don’t know…

TPL: How about your teacher, for example? What kind of person is he like?

SM: He doesn’t talk much and I don’t talk much. I talk just because I am forced, otherwise, I don’t talk much.

TPL: He doesn’t talk much either. But nevertheless, he influenced you and he is an important one, you said. He motivated you.

SM: He is a very unique person. He is very quick at thinking. I don’t know how he can think of those. He was famous at thinking up counter examples. He was known to be Mr. Counter Examples.

TPL: I see. Is he still alive?

SM: No, he passed away last year in August.

JKC: How about János Kollár?

SM: Let’s see…. He seems to know almost everything. Have you talked to him?

JKC: Yes, I have. He knows almost every kind of mathematics.

SM: Yes, that’s right. So what do you think of him? As a counter question?

JKC: I don’t know. He seems to me a very sharp person. I mean he knows everything. After talking to him, in 5 minutes, he seems to know how your knowledge and what’s your knowledge, your view of mathematics and in this case, he knows you already.

TPL: scary.

SM: In that sense, he is a scary person.

JKC: I think when he was younger, he was even much scarier. He is nicer in these years.

SM: He has learnt how to be soft, I guess.

TPL: Indeed, it’s nice to be in this mathematical community. We have all kinds of people.

SM: Probably he realizes that in his position, he shall be nice. I mean, in the best way for mathematics, not for him. He does not need to compete.

JKC: Are there any other mathematicians who affect you when you were in the US?

SM: Mumford. In the sense, Mumford is like Kollár. If you talk to him, it seems he knows everything.

TPL: I saw an interview of Hironaka (廣中 平祐), that was on AMS notices, I think. Did you see that article?

SM: No, is it recent?

TPL: Yes, maybe last year. I remember a sentence, he said ‘I am not a genius, Mori is a genius’.

SM: That’s flattering.

TPL: Perhaps your wife is waiting for you to go to Palace Museum. So we continue maybe next time. You have said very unique things and that’s very enlightening.

SM: Actually, I have a couple questions about the review. It shall not take long. For personnel, is there any restriction or regulations for post-doctorate positions can be offered only within after such and such year after getting Ph.D.?

TPL: There is no regulation, but usually it’s within 5 years or something.

SM: Is it usual for post-doctorates to get another post-doctorate position?

TPL: You mean after one year?

SM: No, since it’s difficult to get a permanent position. A person finishes his Ph.D. fellowship; may this person apply for another fellowship? Is it possible?

TPL: You mean someone who has been here?

SM: No, not particular for this case. It’s a general question.

TPL: You mean if someone who has a post-doctorates position and apply for our positions or vice versa. Yes, it’s possible.

SM: How usual ?

TPL: After post-doctorates in our place, usually they would go out and find a job.

SM: So not another post-doctorates fellowship.

TPL: Usually not in our case, because they can stay here up to 3 years. But our post-doctorates that are coming here are sometimes post-doctorates from somewhere else. Usually after the post-doctorates, they would go out and find a job. Most of them get the job.

SM: So job situation is not that hard here?

TPL: For our post-doctorates, in general, the situation is not so bad. Maybe we put a quality requirement, so the quality comes in is okay.

SM: That’s all. Thank you.

TPL: Thank you.

  • Tai-Ping Liu is a faculty member at the Institute of Mathematics, Academia Sinica.
  • Jung-Kai Chen is a faculty member at the National Taiwan University.