Professor Ivan Gutman, member of the Serbian Academy of Science and the international Academy of Mathematical Chemistry, visited the CFC from Oct. 15 to Oct. 25. He gave a lecture entitled " Recent Results in the Theory of Graph Energy and Related Quantities ".

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Interview

Question: What's your impression of our center?

Gutman: I have visited this center about two years ago, and now I have the pleasure to visit it again. First, I must say that I have been to many places all over the world, and I visited many universities and academic institutions. This center for combinatorics is one of the, I would say, biggest places and outstanding places for combinatorial research. Combinatorics is a part of mathematics, which is done all over the world. There are several centers of combinatorics, I think this one in this university can be considered as one of the major centers, not the only one, there are several others. I don't know if in China there is a stronger center of combinatorics, this center is certainly a very distinguished place. I must say this is one of the reasons why I come here.

Question: Thank you! So, do you like our center?

Gutman: After all, as what I said, I of course like this center. There is a very stronger researching. This is not only seen when you come to the center, but you can see this when you read papers which are published in scientific publications, because the results which are produced in this center for combinatorics are known all over the world. So you don't even need to come here to realize that this is a distinguished place for research, because the papers are published available on all major mathematical journals. Again, this is the reason how I got in touch with Professor Li and so how we started our corporations.

Question: Is it the first time you contacted with Prof. Li because of the papers?

Gutman: I started corporations with Prof Li good maybe 10 maybe more maybe even 15 years ago. We started to exchange letters because we realized that we have some very similar research interests. Then we exchange letters, and exchange letters, and finally he was able to arrange for an invitation, it's two years or three years ago I came here to visit Nankai University for the first time. Let me tell you that then we agreed to write a joint book, so we have at the mean time finished a book, so we have a big book. Prof. Li can easily show you this book, so you can make a picture of this book. This book was initiated during my stay here, and then when I returned home, we, by exchanging further information by email, completed the book and the book has in the meantime been published.

Question: Do you like the research condition here?

Gutman: Yea, well, the conditions for research in mathematics are more or less the same everywhere in the world. You need an office, you need a blackboard, you need some paper, you need a computer, and you need people. The most important thing which should be given is not only to give me a desk but we can exchange ideas between these people. Because here, there is a big concentration of high quality mathematicians, this is a very interesting and important place. This is the main condition. I can meet here other people and ask him a question, then he can answer me a question. This persons of meetings are important. Otherwise, the technical conditions for working here is the same as everywhere else. Mathematicians don't need expensive equipment, but, I would say, something here (in the head). So they have to exchange ideas.

Question: I have a question here, when you do your research in mathematics, how do you find a new problem or a good problem.

Gutman: It is difficult to say. Well, some problems simply emerge. Science, not only mathematics, is developing. It's a system of knowledge, and at a certain moment some questions are simply occurring. Then you have to answer these questions in order to continue to work. This is also in mathematics. So after some time, some questions simply had to be answered. Then, people are working on such problems.

Question: We have the saying like that the problem is first or the basic knowledge is first in research. Which one do you think is more important?

Gutman: I think these are connected. Basic knowledge is not independent of applications. The questions you mentioned before is always come somehow from applications, from real world, from problems which you call them techniques in other fields of science, in human activity, and then it is there simply formulated in mathematical form which you can sometime see the relation, but the relation always comes from real life. The results which mathematician are obtained are sooner or later applied somewhere. Sometimes you do such some research which are directed to some application. But sometimes you do some such pure mathematics. But history of mathematics always showed that after some times any pure mathematical research found application. Researches should not intended to have any application in any place, which is just a pure intellectual game. After some time, it found somewhere a very important application. Here I could tell you many examples from the history of mathematics that they are absolutely show that what we are doing now if you can't see direct application at this moment, then it will come sometime, maybe 5 years, maybe 50 years, maybe 500 years.

Ok, what we are doing has direct applications. We are doing, as you know, good mathematical chemistry. We apply our mathematics research directly to chemistry. So in our case, this question is not applicable to us, because we are working in a field which is applied mathematics. But even if we would work in the field of pure mathematics, it will not be long that some of these results will find somewhere an application.

Question: What's your opinion on our center's students?

Gutman: Ok, you must first understand that I am coming from a small country. My whole country has about 10 million people, which is comparable with the population of Tianjin. The universities are also small. The number of students compared to what you have is small. For instance, I work with only three students. And here the number of students is much bigger. I just found from Prof Li that he has about 20 students. So, again the concentration of clever mathematicians here is much higher than in my country. Also, the competition here is higher, because the students know that there are many such students, if they are not to do some work, and solve some problem, then very soon somebody else will do it. So my opinion about the students is that they are outstanding, excellent and hard workers. I would say that in my country, the students are also outstanding, excellent, but they are not hard workers. Because they know that if they don't do something in this week, they can do it next one. Here you can not, here you have to do work every day, because there are many students do the same and you will lose the game. But of course, this is also well-known that the best mathematicians are collected from China. So, you should expect that the students here are very good mathematics.

If I may say a small criticism, the students here are really excellent and outstanding in mathematics, but they are not so good in English. English today is simple a language of science. It's not my mother language, so I had to learn English. But, all publications are published in English, all books are written in English, all conferences use English, all visitors, like me, speak English. I don't speak Serbian, because nobody will understand me. So I think that the students should learn hard to be much better in English than they are now, because if they don't speak English, they can't communicate with the rest of the world. China is big, but there is also a world outside China. Sometimes it is important that you exchange opinions, exchange ideas with people outside China, and then you have to do in English today. Maybe a hundred of years later it will be another language, but now this is the language in which people communicate all over the world. And here the students are very weak in English.

Question: How do you think the future of the chemical graph theory? We know that you did many superb works in this field.

Gutman: Well, this is difficult to say, but there is no sign of decline of this theory. So, the theory is still in expansion. In general, mathematical theories can sometimes go up, and then sometimes go down. This chemical graph theory in this moment is still going up. How far it will be, I don't know. But, in the next 5 or 10 years you can be quite sure that the research will continue with great activity. What will come later, we should say that I am not a predictor to predict what will be in the far future. Things are changing. I am now in this field of research about thirty years and I remember when I was young we did completely different things than we are doing now. So this chemical graph theory thirty years ago was quite different than it is now. So it is certainly be also very different in next twenty years. But I think it will continue to exist, and this is what I am going to sure you.

Question: What do you think the most shining or most interesting point of this field?

Gutman: OK, well the most interesting part of this field, it is not only chemical graph theory but closely connected with and somehow related to understanding of the meaning of the DNA sequence. Because the DNA sequence from mathematical point of view is a string of four symbols, a very long string of four symbols which somehow contains information about everything in our body. Of course, it can't be completely decoded by mathematical methods, but mathematical approach is certainly necessary to understand what this book written by these four characters says. I think this is the main problem which has to be treated now and in the future to understand as much as possible the mathematics of the DNA code, including, of course, the physics and chemistry, and related subjects.

Question: In the chemical graph theory, there are two theories: chemistry and graph theory. What do you think for the students how to study chemistry and graph theory, how can they combine these two things together.

Gutman: This is a typically multi-discipline scientific field. As the name says, it is chemistry and mathematics, graph theory is a part of mathematics. And so, to do this, you have some knowledge in mathematics and some knowledge in chemistry. There are very few people who have knowledge of chemistry and knowledge of mathematics. So, the best thing is to work together, to make a team work, in which there are some experts in chemistry who know almost nothing in mathematics and some experts in mathematics who maybe don't know anything about chemistry. Then there must be some people, and I think I am one of them, who knows a little bit chemistry and a little bit mathematics. I can serve as a bridge between the chemists and the mathematicians. So, a team work is actually needed in such multi-discipline fields like chemical graph theory. This is also enough, this is not a big thing to say, because it exists already. So there are groups of people who are doing just such researches as I mentioned. Corporation between mathematicians and chemists, and those who know both a little bit can serve as a bridge.

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