양전닝

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Zhang: Why did your work in physics produce such a great impact in mathematics?

Yang: This is, of course, very difficult to answer. Luck is a factor. Beyond that, two points may be relevant. First, if one chooses to look into simple problems, one has a bigger chance of coming close to fundamental structures in mathematics. Second, one must have a certain appreciation of the value judgment of mathematics.

Zhang: Please say more about the first point.

Yang: Most papers in theoretical physics are produced in the following way: A publishes a paper about his theory. B says he can improve on it. Then C points out

that B is wrong, and so forth. Most of the time, it turns out that the original idea of A is totally wrong or irrelevant.

Zhang: In mathematical circles, too, one has this situation.

Yang: No, no. It is very different. Mathematical theorems are proved, or supposed to be proved. In theoretical physics, we are pursuing instead a guessing game, and guesses are mostly wrong.

Zhang: It is, however, necessary to read the newest publications.

Yang: Of course. It is important to know what other research workers in one's field are thinking about. But to make real progress, one must face original simple physical problems, not other people's guesses.

Zhang: Was that what you were doing with Mills in 1954?

Yang: Yes. We asked, "Could we generalize Maxwell's equations so as to obtain general guiding rules for interactions between particles?"

Zhang: What about the Yang-Baxter equation? You were not treating in 1967 a basic important problem in physics.

Yang: This is correct. But I was looking at one of the simplest mathematical problems in quantum mechanics: A fermion system in one dimension with the simplest interaction possible.

Zhang: Why do you emphasize "simplest"?

Yang: Because the simpler the problem, the more the analysis is likely to be close to some basic mathematical structure. I can illustrate this with the following observation: If there is a mathematics-based winning strategy in the game of chess, or in Wei-qi (known in the United States by the later Japanese name of "go"), then it must be in Wei-qi, because Wei-qi is a simpler, more basic game.

Zhang: Please talk about the second point.

Yang: Many theoretical physicists are, in some ways, antagonistic to mathematics, or at least have a tendency to downplay the value of mathematics. I do not agree with these attitudes. I have written:

Perhaps because of my father's influence, I appreciate mathematics more. I appreciate the value judgement of the mathematician, and I admire the beauty and power of mathematics: there are ingenuity and intricacy in tactical maneuvers, and breathtaking sweeps in strategic campaigns. And, of course, miracle of miracles, some concepts in mathematics turn out to provide the fundamental structures that govern the physical universe! [1, p. 74]

관련논문

• Zhang, D. Z. 1993. “C. N. Yang and Contemporary Mathematics.” The Mathematical Intelligencer 15 (4) (December 1): 13–21. doi:10.1007/BF03024319.