Newsletter No. 436

You have been pushing for the popularization of mathematics through your work as director of the Institute of Mathematical Sciences. Why is this important? All the top universities, like Harvard and Princeton, give top priority to candidates’ SAT 1 results. The exam involves only English and mathematics. Math is the major subject to test your way of thinking, reasoning and logic. If a student knows no math, it’s impossible to take up subjects in engineering, science, and even economics. Reasoning and expression are the basics for any scholar or entrepreneur in any society. You said you’ve observed a decline in mathematical reasoning in Hong Kong. Why is that? Many educators think application is very important. But a lot of things that are important may have no superficial use. You can’t judge knowledge superficially. A poem may seem useless but it resonates with many people. When I was in high school, we learnt asymmetric plane geometry—not because it was useful, but because it taught us how to reason. Most schools in Hong Kong and China are not teaching that anymore; they think it’s useless. Ironically most elite high schools in the US still teach that and teach that well. What have been your achievements in the popularization of math? The media and popular scientists have no in-depth knowledge of how a researcher thinks. My only contribution, if any, is to show them a mathematician’s reality. We do a lot of things that are tougher or easier than what people think. Children should know that mathematicians are not freaks as portrayed by the media. Many parents think their children will be jobless if they study math. But the fact is that mathematicians are involved in the workings of Wall Street, in making the atomic bomb, in sending people to the moon. Is this applied math? Not necessarily. The most important contribution to applied science comes from very pure math. Prime factorization is at the heart of most widely used algorithms in cryptography. Cryptography is crucial to Internet banking. Geometry turns out to be useful for a lot of things, including 3D imaging. Medical imaging of bodily organs helps surgeons to make sure that the surgery is accurate. In the last four decades, all world- changing breakthroughs in application have come from pure math. Yet at the beginning, application couldn’t be further from the minds of us mathematicians. Your father, Mr. Chin-yin Chiu, was a philosopher. How has philosophy influenced your studies in mathematics? Many mathematicians are deeply influenced by philosophical discussions—I was by my father’s philosophical point of view. Yet philosophy alone is not enough. Einstein’s understanding of the space-time continuum had to do with Leibniz’s philosophy yet the detailed analysis required knowledge of physics and math. He couldn’t have achieved what he did on philosophy alone. That said, Einstein is a more advanced physicist than most because he was much more deeply influenced by philosophy. Are mathematicians artists at heart? When mathematicians derive something, we want it to be not only correct, but compatible with nature—that part is certainly very close to what an artist wants. The artist describes the beauty of nature from an emotional point of view—be it a man, a woman, or the moon. Mathematicians are also emotional but every statement we make has to be true. I look at the structure of this building and I want to understand why it’s so pretty, but I derive my answers from math. I look at symmetry. I wonder why it is that only when the waves of the ocean move in some ways that they look pretty. The idea of choosing what is pretty is very artistic. A poor mathematician cannot distinguish between a beautiful statement and a non- beautiful statement that is far away from describing nature. What impedes mathematical development in children? Children learn out of interest. You should get them excited about something and learn it for its own sake. Yet many parents push their children to get better grades in school. This is a big mistake. They lose interest after a while and may even rebel. Many parents of children of only seven or younger ask me to help their kids. That’s really unfortunate. Does that apply more to Chinese parents than American parents? In the US, students are very relaxed up to about Grade 8. They have fun while learning. They don’t lose out in the end even though they don’t take grades seriously, unlike Chinese kids in Hong Kong or mainland China. By Grade 10 or 11, they are working extremely hard, in some cases harder than Hong Kong students. Students should work hard some time, but when small kids from kindergarten toil all the way to middle school, they burn out. 你身為中大數學科學研究所所長，一直不遺餘力推動 數學普及。數學重要在哪裏？ 所有頂尖大學如哈佛、普林斯頓，最看重考生的SAT推理 測驗成績。測驗內容只有英文和數學兩項。數學是最能檢 測思維、推理和邏輯能力的科目。若學生對數學一竅不 通，則不可能修讀工程、科學或經濟學。邏輯與表達是世 界上任何學者任何企業家之根基。 你看到數學推理在香港有衰微之象，何解？ 不少教師看重實用。但很多事情表面無用，實則重要，所 以不能單從表面對知識妄加判斷。一首詩似乎不實用，卻 可以叩動人心。我讀高中時，學校還會教不對稱平面幾何 ─不是因為實用，而是因為可以訓練推理。現時香港和 內地的學校多已取消教不對稱平面幾何，認為不切實際。 諷刺的是，美國多數名牌高中仍在教，而且重點教。 你在普及數學方面做了些甚麽？ 媒體和科普作家對真正學者的思考方式一知半解。我唯一 能做的，是還原真實數學家的面貌。數學家的工作要麼不 是常人想像那麼難，要麼並非那般容易。孩子應認識到數 學家並非媒體渲染的怪胎。不少家長誤以為孩子學數日 後就找不到工作。事實上，學數的人也是華爾街的人、製 造原子彈的人和送人上月球的人。 這些算是應用數學嗎？ 未必。對應用科學的最大幫助，來自最純粹的數學。素因 子分解是密碼系統最核心、使用最廣泛的運算法則，而密 碼系統是網上銀行的重中之重。事實證明幾何運用在很 多地方，包括3D成像。身體器官的醫學造影有助外科醫生 確保手術分毫不差。過去四十年，所有改變世界的應用突 破皆源自純數，而應用意念的孕育正始於我等數學家的腦 袋。 令尊丘鎮英是哲學家。哲學對你學數有甚麼影響？ 許多數學家深受哲學思辨影響─家父的哲學觀就影響了 我。但單靠哲學是不夠的。愛因斯坦對時空連續的理解結 合了萊布尼茲的哲學，然而，具體的分析仍要靠物理和數 學知識。單憑哲學，愛因斯坦不可能獲得如此成就。不過 也正因為愛因斯坦有很深的哲學底子，才得以成為舉世無 雙的物理學家。 數學家在心底裏是藝術家嗎？ 當數學家想推導一個結論，會希望結果不僅正確，而且能 與自然契合─這點和藝術家的願景相當接近。藝術家以 感性角度描繪自然之美─男人也好，女人也好，月光也 好。數學家也有感性，但得同時保證所立的每個命題須為 真命題。 望着這棟大廈的結構，我想了解它為何如此悅目，只是我 向數學尋求答案，研究對稱性。我好奇為甚麼海浪以某個 模式移動才好看。判斷美與不美是藝術行為。蹩腳的數學 家難以分辨漂亮的命題與背離自然的命題。 有甚麼會阻礙兒童的數學發展？ 只要令孩子對某事物雀躍，就會自主學習。然而很多家長 強逼孩子在校爭取好成績，這是大錯特錯的。孩子很快就 會喪失興趣，甚至抗拒。有不少家長在孩子不足七歲就叫 我幫他們一把，實為不幸。 這個現象是否發生在中國家長身上比美國家長多？ 美國學生八年級之前都輕輕鬆鬆，邊學邊玩。不像香港和 內地孩子，稍不在意成績就注定失敗收場。到了十年級或 十一年級，美國學生開始發力，有時甚至比香港學生更刻 苦。適當的努力很必要，但如果小孩子從幼稚園開始一直 埋頭苦讀到中學，最後就消耗殆盡了。 丘成桐教授 Prof. Yau Shing-tung 中大博文講座教授 沃爾夫數學獎及 菲爾茲獎得主 Distinguished Professor-at-Large of CUHK Wolf Prize laureate and Fields medalist 10 No. 436, 19.4.2014