Newsletter No. 327

No. 327, 19.11.2008 選擇製造甚麼命題，取決於他對數學和世界的感覺。例如 愛因斯坦一定是對大自然興起了強烈的感受，才引發他勇 敢地模塑整個宇宙的動機。數學家則敢於用簡單的語言 來詮述他們見不到而只能靠推想的事情，這便是數學的感 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 為甚麼中國留學生總是喜歡選擇工程和商科，而不 是數學？你想改變這個現狀嗎？ Why do Chinese students studying abroad tend to choose subjects like engineering and business over mathematics and would you like to change the situation? 中國人比較現實。半世紀以前，在美國的中國留學生唸的 是工程，因為找工作比較穩當；你看矽谷裏中國工程師多 的是。中國人唸醫科的也很多。近一二十年，不少中國留學 生唸工商管理，因為一畢業便賺很多錢。我希望慢慢改變 這個現象。 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 你會游說一個有數學天分的年輕人唸數學嗎？ Would you persuade a young person with mathematical talent to study mathematics? 不會，就是自己的孩子，我也沒有鼓勵他們唸數學。唸甚 麼應由興趣決定。如果孩子對數學是有興趣的，便很容易 發掘和培養。孩子能憑自己興趣發展的話，成就反而會大 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 你曾大膽批評中國大陸的學術剽竊現象。請問剽竊 對大陸的教育發展構成怎樣的障礙？ 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? 如果學生見到大學的校長、主任或大教授抄襲別人卻不會 出事，他們肯定模仿。如果人人都抄襲，那便不用讀書了。 影響自然是深遠的。 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 對中大有何深刻印象？ Your lasting impression of CUHK? 先父在崇基唸書，哥哥弟弟也在中大唸書，我也在1966年 進入中大。由李卓敏當校長到現在，中大一直維持良好的 學術氣氛，對中國文化的保存，在香港幾所大學裏算是比 較悠久。在融合中國和西方文化方面，中大在香港和亞洲 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—丘空間的數學結構，成為被稱 為「萬物定理」的弦理論的基石。可否簡述一下 其緣起？ You invented mathematical structures called Calabi- Yau spaces that underlie string theory, the ‘theory of everything’. Briefly, how did it all begin? 我最初研究幾何中的曲線，純粹是由於它的美，與其後得 出來的物理模型並無關係。我對於曲率如何在量方面控 制幾何學的全域特徵一向深感眩惑。在五十年代，卡拉比 提出他的猜想來解釋其中關係。我覺得很奇妙，但不認為 這是真確的，因為實在是太優美了。之後好一段時間，我嘗 試證明它是錯的，但卻不能。最後，我只有斷定它是對的。 1976年，我破解了卡拉比猜想，並由此為很多基礎數學的 重大難題尋得解答，包括代數幾何裏一些頗為著名的問 題。 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 數學家是你的公認身分，興之所至你又是一位詩 人，你怎樣比較數學和詩歌的美，以及兩者對感情 的體現？ As a full-timemathematician and part-time poet, could you compare notions of beauty and manifestations of emotions in maths and poetry? 美的定義人言人殊，但普遍認同美是簡潔而內容豐富的命 題，大自然的美、數學、物理、文學，都是一樣，用簡單的方 式表達深厚的意義，不過文學的美往往牽涉感情。其實數 學也帶有感情，只是表達起來不一樣。數學家跟物理學家 或其他科學家的分別，在於數學家能夠製造一個命題，而 丘成桐教授，1949年於廣東出生，菲爾茲獎得獎人，並獲頒美國國家科學獎 章，以非線性微分幾何研究掀起了幾何學的革命，現為哈佛大學數學系系主 任、香港中文大學數學科學研究所所長。 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—丘空間有很多種，哪種最好，沒有 人說得準，但大多數人認為這一個是最能代表 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.’