Newsletter No. 327

No. 327, 19.11.2008 选择制造什么命题,取决于他对数学和世界的感觉。例如 爱因斯坦一定是对大自然兴起了强烈的感受,才引发他勇 敢地模塑整个宇宙的动机。数学家则敢于用简单的语言 来诠述他们见不到而只能靠推想的事情,这便是数学的感 情。 Everyone has a different view about what’s beautiful. But a common theme is that beauty is a simple and concise statement containing very rich content. That is one of the basic elements of all beauty in nature, in physics, in literature. Something simple that says a lot. However literary beauty tends to involve more emotions. There are emotions in mathematics too, only manifested differently. What distinguishes a mathematician from a physicist or other scientist is that a mathematician can create a topic and the topic he chooses to create depends on how he feels about mathematics and the world. Einstein must have been motivated by strong feelings for nature to be bold enough to think up a model for the whole universe. Mathematicians have the daring to use a simple language to narrate things they can’t see and then speculate what it’s like. And these are, if you will, the sentiments of mathematics. 3 为什么中国留学生总是喜欢选择工程和商科,而不 是数学?你想改变这个现状吗? Why do Chinese students studying abroad tend to choose subjects like engineering and business over mathematics and would you like to change the situation? 中国人比较现实。半世纪以前,在美国的中国留学生念的 是工程,因为找工作比较稳当;你看矽谷里中国工程师多 的是。中国人念医科的也很多。近一二十年,不少中国留学 生念工商管理,因为一毕业便赚很多钱。我希望慢慢改变 这个现象。 The Chinese are practical. Half a century ago, Chinese students studying in the US chose engineering because it was easy to find a job. In Silicon Valley, there are many Chinese engineers. There were many Chinese studying medicine too. For the past one or two decades, many Chinese have been going to business school abroad because they can’t resist the money. But I would like to change that eventually. 4 你会游说一个有数学天分的年轻人念数学吗? Would you persuade a young person with mathematical talent to study mathematics? 不会,就是自己的孩子,我也没有鼓励他们念数学。念什 么应由兴趣决定。如果孩子对数学是有兴趣的,便很容易 发掘和培养。孩子能凭自己兴趣发展的话,成就反而会大 很多。 I wouldn’t. I didn’t, even with my own children. Interest should dictate what a person studies. If a child is interested in mathematics, it won’t be hard to uncover and develop that interest. Kids often accomplish more if you let them be. 5 你曾大胆批评中国大陆的学术剽窃现象。请问剽窃 对大陆的教育发展构成怎样的障碍? You have been outspoken about your criticism of plagiarism in academia on the mainland. How has plagiarism impeded the development of education on the mainland? 如果学生见到大学的校长、主任或大教授抄袭别人却不会 出事,他们肯定模仿。如果人人都抄袭,那便不用读书了。 影响自然是深远的。 If students see the president of their university, their supervisor or a senior professor plagiarizing and getting away with it, they will surely do it. And if everybody is plagiarizing, what’s the point of studying? The consequences are deep and far-reaching. 6 对中大有何深刻印象? Your lasting impression of CUHK? 先父在崇基念书,哥哥弟弟也在中大念书,我也在1966年 进入中大。由李卓敏当校长到现在,中大一直维持良好的 学术气氛,对中国文化的保存,在香港几所大学里算是比 较悠久。在融合中国和西方文化方面,中大在香港和亚洲 有它特殊的地位。 My father studied at Chung Chi College in the 1950s. My elder and younger brothers all went to CUHK and so did I in 1966. The University has managed to maintain a good academic atmosphere since the days of Dr. Li Choh-ming. Its preservation of Chinese culture has been the most 1 你提出了卡拉比—丘空间的数学结构,成为被称 为「万物定理」的弦理论的基石。可否简述一下 其缘起? You invented mathematical structures called Calabi- Yau spaces that underlie string theory, the ‘theory of everything’. Briefly, how did it all begin? 我最初研究几何中的曲线,纯粹是由于它的美,与其后得 出来的物理模型并无关系。我对于曲率如何在量方面控 制几何学的全域特征一向深感眩惑。在五十年代,卡拉比 提出他的猜想来解释其中关系。我觉得很奇妙,但不认为 这是真确的,因为实在是太优美了。之后好一段时间,我尝 试证明它是错的,但却不能。最后,我只有断定它是对的。 1976年,我破解了卡拉比猜想,并由此为很多基础数学的 重大难题寻得解答,包括代数几何里一些颇为著名的问 题。 I began studying curvature in geometry merely for the sake of its own beauty. It had nothing to do with the physical model which came later. It had always been a deep and puzzling question how the behaviour of curvature quantitatively controls the global feature of geometry. In the 1950s, E. Calabi proposed a conjecture to explain the relationship. Like many other people, I was fascinated by it, but did not believe that it is true, because it is simply too elegant and beautiful. Then for a long time, I tried to prove it wrong and I couldn’t. I finally decided it had to be true, and in 1976, I solved it. I then used the solution to solve many important problems in fundamental mathematics, including some rather famous questions in algebraic geometry. 2 数学家是你的公认身分,兴之所至你又是一位诗 人,你怎样比较数学和诗歌的美,以及两者对感情 的体现? As a full-timemathematician and part-time poet, could you compare notions of beauty and manifestations of emotions in maths and poetry? 美的定义人言人殊,但普遍认同美是简洁而内容丰富的命 题,大自然的美、数学、物理、文学,都是一样,用简单的方 式表达深厚的意义,不过文学的美往往牵涉感情。其实数 学也带有感情,只是表达起来不一样。数学家跟物理学家 或其他科学家的分别,在于数学家能够制造一个命题,而 丘成桐教授,1949年于广东出生,菲尔兹奖得奖人,并获颁美国国家科学奖 章,以非线性微分几何研究掀起了几何学的革命,现为哈佛大学数学系系主 任、香港中文大学数学科学研究所所长。 Born in Guangdong Province, China, in 1949, Prof. Yau Shing-tung is a Fields Medalist and holder of the US National Medal of Science, whose contributions to non-linear differential geometry has had a revolutionary impact on geometry. He is chairman of the Mathematics Department at Harvard University and director of the Institute of Mathematical Science at CUHK. 「卡拉比—丘空间有很多种,哪种最好,没有 人说得准,但大多数人认为这一个是最能代表 宇宙的模型。」 ‘There are many Calabi-Yau spaces. Nobody knows which one is the best but most people feel this is a good model for the universe.’