Prof. Sone was born in 1936 in Osaka, Japan. He received his bachelor's degree in 1959 and a master's degree in 1961 from the Department of Aeronautical Engineering, Kyoto University. He has been a faculty member at Kyoto University, where he is now a professor emeritus. He is a life member of the American Physical Society, and served as the President of the Japan Society of Fluid Mechanics. He is the founder of Kyoto School of Kinetic Theory and Fluid Mechanic. His book Molecular Gas Dynamics, Theory, Techniques, and Applications published by Birkhäuser in 2007 offers the authoritative account of the Boltzmann equation in the kinetic theory.

TPL: First I want to thank you for agreeing to do this interview. You have been here four times, so maybe you can start by telling us how you feel about and what are your experiences here.

YS: The first time I came here was about three years ago. I was very interested in the works here about the characters of solutions of Kinetic Theory. It was close to my research direction. I enjoyed very much the discussions with people here. At the time, I was just starting writing a book, and was happy to include new materials found in the Institute so that the content of my book could be more understandable to mathematicians. The last time I came here, there was a workshop on Kinetic Theory. Some people from Europe also attended it. The Institute here was very well prepared to entertain visitors, because most of us, except people from Hong Kong, do not understand Chinese. For Japanese, it is a little bit frustrating since we can a little bit understand what is written but we cannot understand at all what you speak (in Chinese). What I mean that they were very organized is in that sense.

TPL: You were our teacher, and we were lousy students. But lousy students sometimes ask good questions.

YS: Yes, you asked very good questions. Every time I got something here, I then had new materials to add into my previous book. Now I am writing another book, and I expect I also can get new ideas that are appropriate to be included into my new book. For questions like what materials should be included in a book and what shouldn’t, it seems that people working in the same area will think the answer is obvious, but for another group of people they may think differently. This may happen even in some simple situation. For example, when fluid dynamic people take the gravity as an example of external force, but astrophysics people it is not an external force. Even this small matter bothers the reader. So, we have to eliminate these sorts of problems to make it understandable.

TPL: We learn things every time you come. From time to time we asked you to repeat things and you did repeat things. Therefore, we slowly learnt a little bit more. You really have patient.

YS: In fact, I have to be more patient in Japan. This time Professor Yu spoke about generalised Hilbert expansion for Boltzmann equation. It is the first one to use mathematics to make solutions of the equation explicit. Now you are jointly going to work on the Green function, and I hope you will solve some long-time unsolved problems around corners. I very much look forward to your final results.

TPL: Yes, we will have a long-term correspondence on this. You have contacted with lots of mathematicians, yourselves actually is more like a physicist. You do experiment. So, you must have some ……

YS: I was educated as a Classical Fluid Dynamicist. I began my research in the Kinetic Theory at the Department of Aeronautics at Kyoto University. At that time, many people around us did not understand what the subject is, even the name the BGK equation (It is a model equation of the Boltzmann equation where the collision term is simplified. Now, I use the BKW instead of the BGK.). Soon after I had a chance to visit the Courant Institute. It was a very good experience.

TPL: What year was that?

YS: 1966-68. After that I then had a chance to visit Paris. During the stay, Professor Cabannes was kind to introduce some mathematicians to me. My real communication with mathematicians started from that time. When I was in Kyoto, we had some relation with mathematicians, e.g. Professor Masaya Yamaguti　（山口昌哉） (we were in the same building, so we have some chance to discuss), but as far as the kinetic theory is concern, our relation with mathematicians, except Harold Grad, started from Paris. Our works did not have too many overlap, nonetheless, from the way they were doing, we could figure out some way that we could do. In this way we were able to continue our cooperation. Then, Professor Tai-Ping Liu kindly invited me to this Institute for many meetings, and my cooperation with people here became deeper and deeper. The research conducted here focuses more on the structure of solutions, which is closer to our direction. Our study is rather a formal analysis, while the study here is a rigorous analysis. I think we have established a very good bridge between us. Certainly, there are mathematicians in Japan working in related area, but they are a little far away from us. We can communicate with them through those like you.

TPL: We actually do not deserve any compliment, though we try to be better students. I always want to ask you several questions. One of them is that you know Professor Harold Grad well and know Professor Yamaguti well, so do you mind you describe to us your impression about them? What kind of person they are?

YS: First of all, when I was an undergraduate student, I had a chance to talk to a mathematician　（Tamano:玉野）, who was doing topology and belonged to the group of Yamaguti. It was by chance that he came to our class and gave us some exercises. He was kind that I asked him about a question and he explained to us patiently. Then I had chances to talk to Yamaguti and to read some books together with him. Yamaguti was basically a very kind professor. He was active to encourage young people to do research and accepted many people of various characters.
Yamaguti ever visited to the Courant Institute. He had a chance to talk to Harold Grad. He told him there was a person who was working on the subject of Grad. Professor Grad then immediately sent me an application form. Fortunately, Grad already knew me by papers of mine, so very soon they accepted me to the Courant Institute. Professor Grad was a very kind and great person. He did not come to his office very often, twice a week, once for teaching, the other time for discussion. We prepared the material what we would like to discuss. He was so kind to us personally. Superficially he looked so pushing in some sense, but he is modest and very kind person. Japan at that time was not so rich as nowadays. It was a very poor country. The round air ticket to New York from Japan costs my half-year salary. To visit foreign country was a very special thing. After I left the airport, my mother had to report to the bureaucratic office of our university that I had really taken the airplane. It was such a period. There was a big gap between these two countries. I spent a very good time in New York for two years on the research without disturbance. I thought I could do something on the kinetic theory.

TPL: (Laugh) Of course you had done something in the Kinetic theory before you went to New York, right?

YS: A little bit (laugh), in order to have some directions to study the Kinetic Theory. In Courant, there were a lot of courses and a various type studies and researches. If I stayed in Japan, I would follow more or less the same research direction as I had experienced.
Later on, Professor Cabannes invited me to Paris for six months as a visiting professor. After that he invited me again. During that period of time, I had chances to make contact with Bardos, Golse and other French. Cabannes was very keen to make contact between mathematics with mechanics.

SHY: At that time Golse was very young, wasn’t he?

YS: Yes, very young.

TPL: In a lecture in Rome, Golse and his students had some recent results on proving the limit from of the Boltzmann equation to the incompressible Navier-Stokes equations. He said in the lecture that the scaling he learnt to get the incompressible Navier-Stokes equations was from your previous works.

YS: That work was about when I just returned to Japan from Courant. I tried to think how to find the straightforward expansion that the Navier-Stokes equation can be derived from the Boltzmann equation, and I got some results. Later, this approach leads to the incompleteness of the classical fluid dynamic system in describing the behavior of a gas in the continuum limit, and the ghost effects it induces.

TPL: When was that?

YS: I published it in 1971, but I did it much earlier. It was a rather short paper. Unfortunately, at that time I could not afford to attend meetings. You know, at that time Japan was still not so rich, the travel expanse would cost a substantial part of my annual salary. Erwing Yu read the paper for me. (L. Was that paper published in a Proceeding of a conference?) The paper is published in the Proceedings of the conference: Rarefied Gas Dynamics, edited by D. Dini (Edritrice Tecnico Scientifica , Pisa, 1971.

TPL: But, that short paper made several of them to spend many years to prove it. Started by Bardos, Golse, Saint-Raymond, many people involved, and it finally solved recently.

SHY: When you were in Courant Institute, what was Friedrichs’ influence upon your study of fluid dynamics?

YS: At that time, he was very interested in pseudo-differential operators, thus as far as the fluid dynamics is concerned, he did not influence me too much. Nevertheless, his attitude about teaching did. He was a very good speaker. I remember he taught a course of special topics of partial differential equation (title may not be exact), and the way he was teaching was very attractive. He very much enjoyed himself about what he was doing. I would like to add another aspect. Usually, Mrs Friedrichs came to the Institute once a week and taught English to wives of the visitors from non-English speaking countries.

CCC: In what situation you decided to study kinetic theory?

YS: In Kyoto, people interested in, mainly theoretical, fluid dynamics in Engineering and in Science got together every week for a seminar. They are working on classical fluid dynamics and magneto hydrodynamics at that period. At that time in Japan, in fact not only in Japan but also all over the world, computers were not very popular. Because of this, research results in fluid dynamics were limited and seemed not to be so fresh. I had a chance to read a paper of gas dynamics where kinetic effect is mentioned, which seemed to me fresh. I was interested in gas dynamics from kinetic theory when I learned physics in high school. On the other hand, our colleague introduced a paper in a seminar, where the name of the BGK equation appears at end, but no people knew the name. Thus, I read the paper and started from some very simple problems, like the Rayleigh Problem. I was involved in this area more and more. When the director, professor Patterson, of the Institute of Aerospace of University of Toronto, Canada visited Kyoto, I gave him some papers of mine. Later on, during the stay in Courant, I visited Toronto. He told me that my papers were good materials for his textbook, and he put my PhD thesis almost in full into his book. This encouraged me.

TPL: So, you came to this idea that you wanted to do something fresh when you were a graduate student?

YS: I did not attend the PhD course. When I finished my Master degree, the professor offered me the position as a research associate, thus I did not go to the PhD course. In Japan, we could get a PhD just by presenting a paper. Another reason that I had to do by myself was that, at the first year of my research associate after I got master, my professor went to the States and I worked by myself. So I had time to read some papers together with Yamaguti on Stability Problems, Time-independent Problems, Ordinary Differential Equations and so on.

TPL: Basically, you are self-taught, right? Since you not only choose subjects but also do the whole of your research by yourself. And you understand the basic thing of the subject also by yourself.

YS: Um. I was very much influenced by my supervisor, Professor Tamada (玉田), to attack physical problem, although my work was different from him. He is fairly well known in the field of transonic flows. He gave us some problems already formulated and asked us to finish this. It is an easy way for students. Personally, I did not like this way. Things like that were not interesting. Fortunately, he was away later.

SHY: Professor Sone, I am very curious that you said when you were young, Japan was very poor and environment was not as good as now. So, when you returned from Courant Institute to Japan, how did you continue doing your research?

YS: The daily life was poor but University life is not so bad. Japanese university research was not the project system. Some amount of money comes automatically. We are given certain minimal amount of money. Therefore we can steadily do our research and don’t have to pay much attention to such things like funding and projects. Besides, compared with nowadays, we had more time for researches.

SHY: How about people’s attitude and the research environment around you? How did people interact with one another or make good communication to enhance researches?

YS: In the last few years, all the people say that they are busy, busy, busy, and they cannot do thorough study. They are really busy doing something, but it is partially their excuse. It is a problem whether the money they get in such a way is used effectively. When I was a student, professors seemed to have more free time, though facility was poor. There was no telephone in each office and distance call was inconvenient. There was no something like a seminar room like nowadays. I remember when I was a graduate student if we wanted to discuss, we have to find some other places, probably outdoors.

TPL: So, you must find somewhere in the corridors, in the yards and so on…

SHY: And someplace like empty grass. You did not need to write so many proposals, did you?

YS: No, no.

SHY: So, in some sense, it was good since you did not have to burden you mind with pressure and could feel free so as to focus on your own works.

TPL: About computation, you and your associates do more and more calculations by using computers, is that true?

YS: No, we do not do more and more. If it is necessary, we do it. We choose the problem first by our physical interest. But, when we do it, we do it heavily. In the last ten years, one can do about ten thousand times bigger computation… Thus, you may think we are doing more and more. It is a powerful tool. We use it carefully when necessary.

SHY: So, it depends on the problem you are looking at.

YS: Yes.

TPL: So, analytical understanding is what you think important.

YS: Yes. For educations, we must be very careful. Many students are inclined to do numerical computations on the already formulated problem, because the progress of their numerical computation is apparent and it gives them the explicit results but formulation and analysis are tedious for them. The computation requires a lot of time; for simple work that does not train the intelligence. If they spend much time, it does replace the training in formulation and analysis. They are diligently working, and thus don’t notice that they are completely idle in the study of the most important part. If we are not careful about that, we only produce programmers. If one lives on computer life from young, their way of doing things is very much badly influenced by it. When we do some work on computer (e.g. writing a paper on Tex), we don’t put its complete form on computer and respond the reaction of computer. One is too accustomed to it. Then, he does a similar thing when he is asked to present a report from his professor. He is not able to prepare a complete report by himself alone. We have to think what the advantage and the disadvantage it may cause and to prepare for it. It is dangerous to go in one direction without compensation.

TPL: I remember you said something that is about mathematicians do Science, but what we mathematicians have in mind about Science might not be exactly close to the nature.

YS: Usually, mathematicians have a very good brain. They can understand things very fast. Therefore, some think they can do everything. (All laugh!) But in some cases it is dangerous. For instance, they are rigorous mathematically but are not rigorous at all physically. Things are not so simple as they think. I think tight cooperation is very important.

TPL: How do you think about rigorous analysis? You have done a lot of analysis, but you also do experiments and do computations. You just use a complete set of tools for doing the science. How do you feel about the role of the rigorous analysis?

YS: Up to some point, you can say something without rigorous analysis, but beyond that, if you still want to say what you want, then we do need the analysis. That is, one can be satisfied for the present problem but rigorous results are required for the further development. For instance, the problem we discussed this morning (inappropriateness of the heat-conduction equation in describing the temperature field of a gas in the continuum limit), we could understand that some corrections are required by a simple discussion, but we cannot say any beyond that. We need mathematical study.

TPL: Then, it is not satisfactory without rigorous analysis.

YS: No. New good theorems help the further development; in addition they are useful to the present problem. In many cases, the difference of approaches in different fields gives a fresh idea. Every individual usually thinks in limited directions, and each one has fairly different point of view. Even we just refer to other’s idea, we could have a chance to think it over in a different way. I think a thing like this is very important. In criticizing mathematics education, some say “I have never used such a kind of mathematics at all”, also some engineers say “I have never used what I learnt in the university”. But, it is not true. If someone is not educated in that way, I can imagine that he would have gone in a different direction. I learnt mathematics and physics in the school, but I do not use all of them. Many things are not used at all, but the way of thinking is important to me. In daily discussions at various places, including TV, they proudly make some proposal and left its realization in a proper way to others, assuming the realization is only small technical matter. Responsible proposals should take consideration whether it has meaning (existence of solution) and the realization is practically possible (construction of solution). It is not well recognized. Learning mathematics will help in these problems, even though they are not directly related.
In Japan, pupil, in elementary, middle, and high schools, are taught in a special way in preparatory school, because of the exams. This eliminates them the process of thinking. Thinking takes time. Thus, they are taught how quickly to get the answers for entrance exams. I think this is very dangerous. Without such teaching, pupils would think in their own way. In memorizing the year of events in the world history, they will memorize in a way that they like or think efficient. Similarly, how to spell English vocabularies, they would try to find out a good way to memorize them. Such a thinking process is in one’s inside. They are small things but its accumulation is nonnegligible. If the education eliminates all the processes of thinking but only teaches pupils how to efficiently get high score in examinations, then it is dangerous. Now, many people say that we have to teach something and something. But, I think they are different issues.

TPL: I am afraid this phenomenon is not unique in Japan.

YS: Yes, it is worldwide. An experience of mine is the following. I had a chance to read a university textbook on Physical Chemistry for preparing teaching materials for one of my courses. The first part is about kinetic theory, and it is my part, so I know the content very well. But the writing was very bad. (Laugh.) I continued to other parts, and I did not understand them very well. There are exercises for solution at the end of each chapter, and there are formulae in each chapter as well. So, without reading the content of each chapter, I could solve the questions and get correct answers simply by using the provided formulae. It is sure that I did not understand the content, but I can still get scores. I think we have to analyze this point more carefully for education.

TPL: Not just which subject to teach.

SHY: Instead, how to make student think and make student try.

TPL: This is a big subject.

YS: They said “efficiency, efficiency.” But we have to spend time for everything.

TPL: I remember my mother used to say “The faster, the slower.”

YS: To think things again and again is very important. Efficiency is OK, but if the time is saved in such a way, we then need to use the extra time to study, not to go out to play. (Laugh!)

TPL: You probably mentioned it implicitly, or at least I feel somehow I heard it from you that in doing research one needs to concentrate. No matter how smart one is one cannot try to do everything.

YS: Surely, we are not so wise. (All laugh!)

SHY: How did you develop your interest in science? Was it from high school or from Kyoto University? I mean originally you were trained as an engineering student.

YS: I am interested in fundamental things before entering university. As many boys, I am also interested in machine. After some consideration, I chose an engineering department. From the booklet introducing department, I chose the department, where fundamental studies are stressed. Professor Fujimoto (藤本), who founded the department, was a person having long prospects. Our curricula offered only fundamental courses, e.g. Applied Engineering Mathematics, Fluid Mechanics, Solid Mechanics, etc. Some courses taught in the engineering departments are full of too many details. Unlike many other departments, we were not asked to study many descriptive subjects. Therefore, we have enough time for self-study. Fujimoto gave us a big influence. 　Incidentally, recent booklets of various universities are more than exaggerated advertising. The universities are advising to tell a lie to the young.
Of course, some other mathematicians like Yamaguti influenced me as well. I have to mention the role of a young research associate Tamano, who sincerely take care of my exercises when I was a undergraduate student and died later in the USA, unfortunately. He was very kind to help me reading books. One may have experienced that one was very uncertain at some point though one read very carefully and found the solution of the point. But he gave me some good advices in such a case. This brought me confidence and enhanced my interest. He didn’t help me anything directly in research, but in the education, he played a very important role and influenced my later research. I think the role of good young scientists to students is very important.

CCC: How many members were there at the beginning of your department?

YS: Generally, there are about 6 laboratories (or research groups) in each engineering department of a national university. Each laboratory has 1 Professor, 1 Associate Professors, and 2 Research Associates.

TPL: Japanese system is different from the US one.

YS: General speaking, they are different for a long time. Our system is very fixed though it is rather difficult establish one. However, once it is established, it is very stable.

TPL: It has its own advantage.

YS: Yes, we can choose our research subject without paying too much attention to the funding. The government give us a fixed amount of money. We spend much more time on students than in US. In this system, those inactive in research are inevitable. Their excuse is the activity in education. Recent change introduces a lot of work besides research and education. It deprives research and education time, especially from young researchers. If the money is admitted, it is too much, and if not, it is a problem. The results of the new system should wait for some time but it is not comfortable for research at present. In the new system, a new excuse is introduced and deprives important research time from active people. Active people already spend full of his time in research and education. If the new work is introduced, they have no way other than to cut the time of research and education. There is misunderstanding about this.

TPL: Someone has pointed out that Japan is a leg above the rest of the Asian countries and that it is so much better. The funding in Japan is much higher than anywhere else. One says that the funding in the Kyoto university alone is many times greater or equal to the sum of all funding of the universities in Taiwan, some order like that. Also, the Electrical Engineering School in Berkeley has more funding than the total funding of universities in Hong Kong. You mentioned that the situation in Japan was difficult after the World War II, but you still produced Nobel prize laureates and so forth.

YS: What is the most important is not money.

SHY: Yukawa (湯川秀樹*) got the Nobel prize before the War, right?

YS: No, just after the war. But, his work was done before the war. At that time, Japan was very poor and people were encouraged.

TPL: You said that when you were a graduate student, you already decided you want to do something fresh. What do you say to young people theses day?

YS: Young people in Japan? (TPL: OK, say, in Japan.) The students of Kyoto University are supposed to be very good in a general society. In performing thesis of PhD or Master, we have not only to give them the topics but also to formulate them ready to start numerical computation. They prefer to do the most uninteresting part. Some, not rare, ask us to advise the value of parameters. It is effective for them. Most of the students, who passed the difficult examination, do not have working knowledge of what they have learned. A professor of electrical engineering complains that some do not understand the difference of electric current and voltage, and another professor of chemical engineering says that many of their students do not know the three form of transfer of heat, conduction, convection, and radiation. It is hard to imagine from what they learned in high school and the fact that they passed the examination and what they are learning. I imagine they put what they studied in their brain in unorganized way. In this way of working, they cannot be interested in science. This problem should be seriously considered. Now we have to foster the mind of the young that can be attracted in science. The atmosphere of the society is an important factor.
A bit unfortunately, owing to the computer, they have to spend so much time for tedious work. Hence, we have to be more careful about this. Some professors like to ask their students to draw beautiful pictures in this or in that way, but sometimes it takes more time than to do a computation. This also happens to some managers in the industry. Of course, presentation must be clear, but the term ‘clear’ is a matter of content, not of appearance. In industry, people used to have time to study, but now they are so busy.

TPL: All the chairmen are so busy. Somehow, all of them have the habit that every time they think about something, they always think about the bureaucratic convenience or efficiency and so on. We thought that with all the email and other things, life should be better, but it seems not really.

YS: It was an interesting story when I visited Grad’s house, which was very large. There was a corner in his house. He said he like that place very much because he cannot hear the ring of telephone, and can avoid it. I think something like the Internet is very convenient. However, on the other hand, if it is a daily use since we are young, we miss the chance that we are trained to formulated our idea or thought. We have to consider some way to train this.

TPL: Do you use the mobile phone?

YS: No, I don’t have. (All laugh!) The problem is that public telephone booth is decreasing and that the life of poor people become harder if they have to have. Unfortunately it is neglected.

TPL: Now you have retired. Professor Aoki said that Sone is unbeatable now. He was ahead. Now he has become a full-time researcher, he will be further ahead. (All laugh!)

YS: We are getting lazy as getting older, therefore we have to concentrate. I have kept many things aside. This is the only way that I can survive. (All laugh!)

TPL: I once talked to people in this Kinetic Theory meeting about the situation in engineering school about kinetic theory. Someone told me that there are good groups in engineering community. I asked them which group it is. They answered Professor Sone’s group. (Laugh!) They were mentioning about your group as an example that the engineering groups are still concerned about and are doing good in the kinetic theory.

YS: Kinetic theory is getting more and more important in gas dynamic problems. Working only in classical fluid dynamics is insufficient. The ghost effect shows this aspect. We must say that we are very happy to have more and more mathematicians involve so much in the Kinetic Theory, not only just in the existence and uniqueness of solutions (all laugh!), but also in the structures of the solutions. For example, the asymptotic theory you are now investigating is very useful for us. However, up to this, not so many people are interested in the structure of solutions, but increasing by your effort. So we are very happy. We have cooperation also with more applied people. Bird from Australia, who devised the direct simulation Monte Carlo method, had a very bad experience with theoreticians when he was young. At that time the computer was small and his result was not accepted by theoreticians in fluid dynamics. He was not happy with theoreticians and there was a period of time that he did not contact with any theoretician. However, now he and I have a very good relation in cooperation.
Bird is a very interesting person. I had some theorem in free-molecular flow (or the solution of the boundary-value problem of the Boltzmann equation without collision term). When he visited Kyoto, he was interested in flows induced by temperature field and inquired a possibility of that kind of flows in free molecular case. It is proved in my work that flows vanishes in that case. He did not know my result. And I said to him that there is a theorem! He then went to his office in our department. He is very quick in numerical computation, and after few hours, he jumped into my office and said with his Australian accent “It is true.” (All laugh.) Really, recently we have close cooperation. I hope we will have more cooperation in some subject in some way.

TPL: It is nice to hear you say that. In some sense, you are a mathematician. The role that you are playing is rather different from your usual role as a scientist. You are now a strict-analyst. Ok, it is very good. And, perhaps we could stop here.

YS: I am a bit sorry that this interview went through a bit random. I didn’t prepare well for this ‘examination’. (All laugh!)

TPL: No, in fact, the interview has been going on what it is supposed to be. And the patterns often come out of randomness. Thank you again. We look forward to you for coming to Taiwan many, many more times, and look forward to learning from you more.

• Tai-Ping Liu is faculty members at the Institute of Mathematics, Academia Sinica.
• Chiun-Chuan Chen is a faculty member at the National Taiwan University.
• Shih-Hsien Yu was a faculty member at the City University of Hong Kong and is a faculty member at Academia Sinica starting July 2021.