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. 你身为中大数学科学研究所所长,一直不遗余力推动 数学普及。数学重要在哪里? 所有顶尖大学如哈佛、普林斯顿,最看重考生的SAT推理 测验成绩。测验内容只有英文和数学两项。数学是最能检 测思维、推理和逻辑能力的科目。若学生对数学一窍不 通,则不可能修读工程、科学或经济学。逻辑与表达是世 界上任何学者任何企业家之根基。 你看到数学推理在香港有衰微之象,何解? 不少教师看重实用。但很多事情表面无用,实则重要,所 以不能单从表面对知识妄加判断。一首诗似乎不实用,却 可以叩动人心。我读高中时,学校还会教不对称平面几何 ─不是因为实用,而是因为可以训练推理。现时香港和 内地的学校多已取消教不对称平面几何,认为不切实际。 讽刺的是,美国多数名牌高中仍在教,而且重点教。 你在普及数学方面做了些甚麽? 媒体和科普作家对真正学者的思考方式一知半解。我唯一 能做的,是还原真实数学家的面貌。数学家的工作要么不 是常人想像那么难,要么并非那般容易。孩子应认识到数 学家并非媒体渲染的怪胎。不少家长误以为孩子学数日 后就找不到工作。事实上,学数的人也是华尔街的人、制 造原子弹的人和送人上月球的人。 这些算是应用数学吗? 未必。对应用科学的最大帮助,来自最纯粹的数学。素因 子分解是密码系统最核心、使用最广泛的运算法则,而密 码系统是网上银行的重中之重。事实证明几何运用在很 多地方,包括3D成像。身体器官的医学造影有助外科医生 确保手术分毫不差。过去四十年,所有改变世界的应用突 破皆源自纯数,而应用意念的孕育正始于我等数学家的脑 袋。 令尊丘镇英是哲学家。哲学对你学数有什么影响? 许多数学家深受哲学思辨影响─家父的哲学观就影响了 我。但单靠哲学是不够的。爱因斯坦对时空连续的理解结 合了莱布尼兹的哲学,然而,具体的分析仍要靠物理和数 学知识。单凭哲学,爱因斯坦不可能获得如此成就。不过 也正因为爱因斯坦有很深的哲学底子,才得以成为举世无 双的物理学家。 数学家在心底里是艺术家吗? 当数学家想推导一个结论,会希望结果不仅正确,而且能 与自然契合─这点和艺术家的愿景相当接近。艺术家以 感性角度描绘自然之美─男人也好,女人也好,月光也 好。数学家也有感性,但得同时保证所立的每个命题须为 真命题。 望着这栋大厦的结构,我想了解它为何如此悦目,只是我 向数学寻求答案,研究对称性。我好奇为什么海浪以某个 模式移动才好看。判断美与不美是艺术行为。蹩脚的数学 家难以分辨漂亮的命题与背离自然的命题。 有什么会阻碍儿童的数学发展? 只要令孩子对某事物雀跃,就会自主学习。然而很多家长 强逼孩子在校争取好成绩,这是大错特错的。孩子很快就 会丧失兴趣,甚至抗拒。有不少家长在孩子不足七岁就叫 我帮他们一把,实为不幸。 这个现象是否发生在中国家长身上比美国家长多? 美国学生八年级之前都轻轻松松,边学边玩。不像香港和 内地孩子,稍不在意成绩就注定失败收场。到了十年级或 十一年级,美国学生开始发力,有时甚至比香港学生更刻 苦。适当的努力很必要,但如果小孩子从幼稚园开始一直 埋头苦读到中学,最后就消耗殆尽了。 丘成桐教授 Prof. Yau Shing-tung 中大博文讲座教授 沃尔夫数学奖及 菲尔兹奖得主 Distinguished Professor-at-Large of CUHK Wolf Prize laureate and Fields medalist 10 No. 436, 19.4.2014