Bulletin Autumn‧Winter 1980

Q. Is it true that academics o f American universities have to ‘publish or perish '? A. Of course there is always pressure, especially now that competition for jobs has become much keener. In American universities, only posts of at least Associate Professor rank are tenured, and academics below that rank, to be considered for promotion, have to exert themselves in research and publication. It can be seen that the tenure system may have its merits but it also has de merits. To subject the academics to too much pressure is obviously undesirable, but being too lax in this respect, as in certain countries where all university posts are tenured posts, would have undesirable effects as well. Academics w ill be less conscientious once they have secured a post in a university, and may give up research and publishing papers altogether —the last thing we would wish to see in the academic world. There are some academics in American univer sities who put quantity before quality in their publications, often producing papers of dubious merit, but I still think that it is better than not producing anything at all, because in the process of writing the author has at least made an effort to sum up the research he has done. Q. We are always under the impression that mathe maticians are engaged in studies o f a very abstract kind, involving the manipulation o f mysterious figures and symbols. Is this really the case? A. Mathematicians through the ages have striven to seek truth and beauty. On the surface, truth and beauty are very abstract things, having hardly anything to do with practical problems of the physical world; but, in reality, mathematics is not so far removed from the practical world, with which it may even claim a very close re lationship. Practical problems derived from astronomy, engineering, physics, biology, etc. are reduced by mathematicians to mathematical pro blems in the form of equations, etc., which they w ill try to solve. After solving these specific problems, mathematicians may continue with their studies in the area, not out of any immedi ate practical necessity but simply because they are attracted by the beauty which they perceive in the questions, methods and ideas in the field which they may wish to explore further. In other words, mathematical problems spring, on the one hand, from experience in the physical world, and on the other, from the pursuit of beauty in mathematics. We have learnt from experience that pure mathematics, no matter how abstract it is, may eventually have some application in the practical world, if developed in the right directions. For example, Riemann Geometry, once considered by non-mathematicians to be mathematician's play with hardly any practical value, was em ployed by Einstein to explain the time and space of a gravitational field in his general theory of relativity, because of its exactitude, simplicity and beauty. In fact, the physical world has never ceased to provide mathematicians with new problems, especially in an age when science and industry are developing so rapidly. Q. From what you have said, I gather that mathe matics is a very complicated discipline. How many branches are there in mathematics? A. In my opinion, mathematics can be divided into four main branches. First, the study of numbers: this includes the number theory, integer number theory, algebraic number theory and analytic number theory, etc. Second, the study of geo metrical figures: here we have plane geometry, projective geometry, differential geometry and algebraic geometry, etc. Third, the study of function: this involves the study of the relations between numbers and between different kinds of geometry. Fourth, the study of probability. Q. I suppose mathematicians can be divided into pure mathematicians and applied mathe maticians. A. Well, it is in fact quite difficult to draw a line between the two. Before, good mathematicians were usually astronomers, physicists or scientists in other fields aswell. Things had changed by the end of the nineteenth century when mathemati cians developed a strong interest in the study of abstract mathematical problems and basic theories of mathematics, and devoted to them their undivided attention. However, the connec tion between mathematics and the other sciences has become closer again since the fifties. Generally speaking, pure mathematicians seek to conquer their field from the standpoint of aesthetics, having no concern for the practical value of their work. But in recent years, some of them are also willing to take up research on theoretical physics, which, in away, is very much mathematics-related. Applied mathematicians usually concern themselves with practical pro blems derived from or suggested by the other sciences such as computer science and engineering. 12