Mathematics and its role in Science and Technology
数学与科技
Professor Shing Tung Yau
丘成桐教授
Beijing March 24, 2004
北京 二零零四年三月二十四日
It is a great honor for me to be recognized by the Chinese government on my efforts to promote scientific interchange between China and other counties. I was born in south China and grew up in Hong Kong. I was educated under the colonial system set up by the British. Fortunately, my father was proud of Chinese culture and sent me to a Chinese middle school.
由于促进中国与其它国 家的科技交流而得到中国政 府的表扬，本人深感荣幸。 我生于汕头,长于香港， 接受的是英国式的殖民地教 育。可幸先父重视中国文化， 把我送到中文中学就读。
I was also educated in The Chinese
其后我肄业于香港中文
University of Hong Kong. While my training
大学。相对而言，在那里学
on mathematics and science in Hong Kong
到的数学和科学知识并不算
could not be said to be great, I was fortunate
很多，但却对中国文化有了
to learn Chinese culture in a reasonable
一个比较全面的了解。
thorough manner. The elegance of Chinese literature had deep influence on my thinking. I am proud of the deep and continuous developing civilization of my mother country. While I devoted my whole life to study fundamental science, I also consider promotion of science, especially for
中国文化博大精深，对 我有很大的影响。我引以自 傲的是，祖国源远流长，迄 今犹自欣欣向荣的文明。我 虽然毕生研究基础科学，但 亦以推广、普及科学为己任，
my mother country, to be a responsibility of
对与祖国有关的工作，尤其
my life.
珍惜。
While I left Hong Kong in 1969, I did not
1969年离开香港时，我
have passport of any country. At that time, it
并没有拿英国护照。当时中
was not clear at all that the Chinese
国政府是否会和美国修好， 还是一个谜。尼克松访华，
government would build a good relation with the United States. I did watch with great joy
我在电视上看到了，感到十 分高兴。1979年华罗庚教授
when Nixon visited China. In 1979, I was
邀请我访问中国科学院。早
invited by Professor Hua to visit the Academic
在中学时，我已经读过不少
Sinica. I learnt a lot from Professor Hua’s
华先生的著作，获益良多，
book when I was in high school. I admired
他是我敬佩的人物。他的来
him and was flattered to be invited.
函，令我有受宠若惊之感。
When I stepped out from the airplane in the Beijing airport, I touched the soil of Beijing and
felt great joy to return to my mother country. I am proud to say that when I was awarded the Field’s Medal in mathematics, I held no passport of
any country
and
should
certainly
be
considered as Chinese. I did put in a lot of efforts to help Chinese mathematics. On the other hand, I regretted very much that I still could not settle down in China. Whatever I have done for Chinese mathematics can in no way be compared with those Chinese who have grown up and stayed here or those who returned to China on a permanent basis.
甫 出机 场， 接触 到 首都的泥土，回到了祖国 母亲的怀抱，我心潮澎湃， 激动万分。回想获颁数学 上的菲尔兹奖时，我并无 持有任何国家的护照，因 此我是以堂堂正正中国人 的身份去领奖的。
我为中国数学的发展 出了不少力。不无遗憾的 是，至今我尚未能回国定 居。当然，我对中国数学 的贡献，与在此间土生土 长，或自海外归来，长期 工作的同行相比，是微不 足道的。
It will be an exaggeration to attach too
海外学者对国家发展种
much importance for those who hold a
种意见，虽然每有精警之言，
permanent position in foreign soil to talk
但也不必奉之为金科玉律，
about development of this great country.
全盘接受。 故此，本人谨就亲眼所
I will therefore only make some humble
comments
based
on
my
observations. As we know, China has developed education system since Confucius time.
见，亲耳所闻，略抒管窥之 见，如有一二中的，则于愿 足矣。 我国自从孔子开始，便 建立了完整的教育体系，这 是大家都知道的。从此教育
Knowledge is accessible even to nonnobleman. It was a break through.
不再是贵族的专利，这可是 件石破天惊的大事。
By Han dynasty, the government started to build a system to select educated man and man with virtue to serve the country. Even kids in villages have potential to be in the central government. The system was reasonably fair and China is united partially based on such outreached system. It may be interesting to note that even foreigners were able to hold high position in the court at that time. The system was polished and became system of examinations. The scope of examinations was rather large during early dynasties, like Tang dynasty. Even mathematics was included in the test. However, the examination has been much more focused in the past four hundred years. It was thought that a thorough study of Confucius thinking is enough to run the government. Hence the test has been focused on a very narrow band of knowledge. The damage to the creative thinking in China is almost fatal.
及至汉代，地方举荐贤良 文章之士于庙堂，于是乡党小 子，亦有望大用于朝廷。这种 颇为公允的做法，无远弗届， 整个国家大一统的局面，或多 或少亦由此而维系。值得一提 的是，甚至外国人也曾在朝廷 供任高职。 这种制度逐渐演变,最后便 形成考试制度了。在这种制度 的早期──例如唐代──考试 的范围还是颇为广泛的,数学也 包括在内。但在过去四百年间, 考试的范围便大大地缩窄了。 大家以为熟读四书五经,便足以 治国平天下。因此，考试的知 识面变得异常狭窄，国人思想 上的原创力在这种钳制下，遂 变得奄奄一息了。
It is important to realize that Confucius considered knowledge to be virtue: 大學之道，在明明德， 在新民，在止於至善。 But Confucius did train students on practical matter. Some of his students became diplomats. Some of them became businessman. Some of them became general. The Greek philosophers Socrates also consider knowledge to be virtue. But pursuing of truth and beauty is the essence of Greek education. In this daunting new world, knowledge is the key to human well-being. Any great country will have to substain long term investment in learning, without which social advancement is an empty dream. Knowledge has to be based on the following: 1. Virtue, Ethics 2. Knowledge of humanity 3. Basic science 4. Applied Science
重要的是，孔子以为知识是 一种美德︰
大学之道，在明明德， 在新民，在止于至善。 虽然如此，孔子也传授实际 的学问。他的门人当中，有的当 上外交官，有的作生意，有的做 了将军。希腊哲人苏格拉底也以 知识为善。追求真善美乃是希腊 教育的宗旨。在无畏的新时代 (daunting new world) 里 ， 知 识乃是人类通往幸福的钥匙。任 何大国都必须长期投资于教育， 不这样做，社会的进步只能是空 谈。知识必须建基于 1. 道德伦理 2. 人文知识 3. 基础科学 4. 应用科学
Since the defeat of Opium war in the early nineteenth century, China realized its own weakness in modern technology and tried several times to modernize. The major development was on building ships, railways, mining and building weapons. After two centuries of trial and error, we finally see a true opportunity to develop China into a great country. While economic growth is unpreceding strong in modern Chinese history, we should remember that the true engine of modernization is based on acquisition and application of knowledge. However, for a developing country, knowledge is usually associated to applied science only. One tends to overemphasize short-term payoffs and ignores long-term strength. One should note that Fundamental science is the base of all modern technology. China’s modernization should realize the importance of basic science.
自十九世纪中鸦片战争失败后，
中国便深深感受到技术落后的弱点， 尝试改革、现代化也不只一次了 。
当时主要的做法是造船、筑铁路、 开矿、生产武器等等。经过了差不 多两个世纪的努力与失误，到了今 日，我们终于看到了中华民族复兴 的契机。当前我国经济迅速发展， 是近代史上空前的。但是，我们必 须牢牢记住，汲取知识和应用知识， 才是现代化的真正动力。 然而,发展中国家往往以为知识 只指应用科学而言。人们追求立竿
见影的效果,忽视长期的利益。我们 必须认识到,只有基础科学,才是现
代科技之母。中国的现代化,必须要 意识到基础科学的重要性。
Michael Atiyah who is president of Royal Society of England, told me the
following: For a country like China which has
阿 提 亚 教 授 (Michael Atiyah) 担任 英国 皇家 学会 会长时，曾对我说了这番话:
aspirations to become a world economic
中国既望跻身经济 大国
power, it cannot be lack of ambition. Certainly the Japanese who started off
之列，就必须雄心万丈，志
with the plan of just copying the west soon changed to invest in fundamental
意仿效西洋，但旋即改变方
research. Also the US is the most advanced economically and is supporting fundamental research in a big way. I would think that China world be receptive to the challenge of competing in all respects with Japan and the USA.
不在小。日本维新之初，一 向，致力发展基础研究。 美国虽是当今经济最强体， 但它依然大力注资于科研。 我想中国要与日本,美国分庭 抗礼,就必须在各方面与它们 并驾齐驱。
There are several important branches of sciences and technology that will play fundamental role in this century: – Information technology – Life science – Energy science – Material science – Environment science – Economics and finance – Social science While these branches do interact with each other, they depend heavily on the development of fundamental science who provide the principle: why and how things actually work. Interdependence of scientific disciplines recurs frequently throughout history. A successful merge of ideas of two apparently independent fields always brings unexpected glory to both subjects.
在这个世纪，有几门科技会
发挥根本的作用，它们包括︰ – 信息技术
– 生命科学 – 能源科学 – 材料科学
– 环境科学 – 经济与金融 – 社会科学
这几门学科互相渗透，它们 同样依赖于基础科学的发展，因 为后者指出了事物的根本原理。
回顾历史，科技领域互相依赖， 屡见不鲜。两门看似无关的领域，
其中的概念一旦能成功地融合， 肯定对大家都大有好处。
在十九世纪，人们看到
In the nineteenth century, we saw the great success of unification of electricity and magnetism. In the twentieth century, we saw the great success of application of quantum mechanics to chemistry. We saw application of mathematics and physics to the building of modern computer which in turn become the fundamental tool of all science and technology. Nowadays, we are witnessing the glory of application of physical science to life science.
了电学与磁学的结合；在二 十世纪，人们看到了量子力 学在化学上的应用，同时也 看到了数学和物理如何应用 于现代计算机，使之成为所 有科学技术中不可或缺的工 具。当前人们正在见证物理 科学应用于生命科学。凡此 种种，都是人类文明的伟大 成就。
Each unification started from basic science. By the time when it is successful, great breakthrough in technology was rewarded. It brought great economic growth for those countries who initiated and enhanced such development.
学科之间的融合，始于 其基础部分。当融合完成之 时，往往导致技术上的突破。 对于带动或支持这些发展的 国家，其在经济上的利益， 是不可低估的。
In the past two centuries, we saw the
accumulation countries
in
based
wealth on
of
European
scientific
and
technological advances. The first and second
在过去的两个世纪,欧洲 各国因科学及技术而累积了 大量的财富。二次世界大战
world wars brought a large group of
导致大量科学家及工程人员
international scientists and engineers to the
移民美国。当今之世,美国的
United States.
We saw the American
影响力可说是无远弗届。它
dominance of the world. The unparalleled
空前的繁荣，实归功于技术
prosperity of United States is driven by
工艺的进步，而后者多少源
technology growing out of the investment in
自其在基础科学的投资。美
basic scientific research over the past fifty
国公司和院校所拥有的大量
years. Large portions of the patent rights
专利权，都拜基础科学研究
held by American companies and universities
came from the strength of basic science.
之赐。
The strength as a world power relies on the ability to educate the population in basic science and to recruit the best mend in the world to work for them. In the case of United States, a lot of foreigner talents may not even speak English fluently. I believe China should recruit many nonChinese talents even if they may not understand about China at the beginning. The reason is that science, especially pure science, has no border. We can be benefited much more by foreigners who are not biased. In the twenty first century, mathematics will be the most basic subject to be studied. Mathematics gives the underpinning structure for all science. It is not only the language for all science. It has a life by itself.
一个国家的国力是否强盛， 表现于其国民的科学知识水平，
以及其吸引外来精英的能力。就 以美国为例，很多在美国工作的 海外人材，连英语都说不好。我 认为中国应吸引非华裔人材来华 工作，不管他们是否认识中国， 毕竟科学是没有疆界的。只有不 分中外，兼收并蓄，我们才能取 得成功。 在二十一世纪，数学会成为 最基本的学科。数学会成为所有 科学的框架，它不但是科学的语 言，还有其本身的价值。
I. Mathematics as a basic language :
Geometry is the language of spacetime. Calculus is the language of astronomy. Operator theory is the language of quantum
一.数学是基本语言 时空的语言是几何，天文 学的语言是微积分，量子力学
mechanics. Fourier analysis is the language
要透过算子理论来描述，而波
for wave motion. All these are subjects that
动理论则靠傅立叶分析来说明。
are considered exceedingly beautiful by
数学家研究这些科目，最先都
mathematicians. They were developed in its own right. The common feature of these s u b je ct s t hat w e re u n de r s t oo d b y
由于其本身之美所感召，但最
后却发现这些科目背后，竟有
mathematicians. They then give rise to the
些共通的特性。这个事实说明
most fundamental reason why we have
了看起来并不相关的科目，它
interdiscip lary interactions between
们之间有甚多交缠互倚的地方。
s e e m i n gl y u n re l a t e d s u b je c t s .
Let us look at common language.
While
language may be a symbol, it does convey our
我们先看看通用的语 言。语言是一种符号，用以
emotion and our feeling of the subject that we describe. Chinese poems are not the same as
传情达意。中国诗与西洋诗
Western poems because we do emphasize the use of each Chinese character which carry different
个单字的用法，因为每个单
meanings in general. Even among Chinese poems, the number of characters that are allowed
就算在中国诗内，字体的多
in composing the poem do change the feeling that we want to convey. Ancient Poems were more
古诗较随意，汉诗以五言为
flexible. Han poems used five characters per sentence. Tang poems use seven characters. Sung developed Qi which had different number of characters for each sentences. Each style of poems reflects the feeling of schlors of these dynasties.
不同之处，在于前者着重每 字都具有不同的意义。然而， 寡也左右了要表达的感情。 主，唐代则重七言，到了宋 代，流行的便是长短句─词 了。不同的体裁，微妙地反 映了不同朝代文人的感受。
Hence mathematics research does change the scientific development that we are workin g w ith.
因之，数学的研究改变 了科学发展的航道。举例而言，
For examp le, a deep
understanding of Fourier analysis or wavelet
对付立叶分析的理解越深入，
can give much different understanding of
我们就更能理解波的运动及图
wave motion or technique of imaging.
像的技巧。反之，现实世界也
Conversely, the practical world did influence
左右了数学的发展。波运动及
the development of mathematics. The beauty of wave motions and their spectrum was the
其谱所显示的美，乃是这些科
most basic driving force to develop the
目发展的原动力。这些学科对
subject.
现代技术及理论科学的影响极
Their important application to
modern technology and theoretical science cannot be exaggerated.
其深远。
It is difficult to imagine that Newton can develop classical mechanics without the great language of calculus whose development can be traced back to Archimedes. There is no doubt that Farady understood electricity and magnetism. But the final completion of the theory was due to the Maxwell equations. Its implications for understanding light, radio wave and modern science is tremendous. II. Mathematics as a science of order Besides being a language, and a subject of great beauty on its own right, mathematics is a science of order. Let us read a citation of a Harvard professor, Andrew Gleason:
没有微积分这种起源于亚基 米德的伟大语言，很难想象牛顿 能发展古典力学。 毫无疑问，法拉第精通电学 和磁学。但电磁学的完整理论要 归功于麦克斯维方程。电磁学对 光、无线电波和现代科学的研究 是极为重要的。 二.数学是秩序的科学 除了作为一种语言，以及一 门纯美的学科外，数学还是秩序 的科学 (a science of order)。 我们引一段美国数学学会前会长、 哈佛教授格臣 (Andrew Gleason) 的说话:
“Mathematics is the science of order: its object is to find, describe and understand the order that underlies apparently complex situations. The principal tools of mathematics are concepts which enable us to describe this order. Precisely because mathematicians have been searching for centuries for the most efficient concepts for describing obscure instances of order. Their tools are applicable to the outside world; for the real world is the very epitome of a complex situation in which there is a great deal of order.”
数学乃是秩序的科学， 它的目的是发现、刻划、 了解外观复杂情况的秩序。 数学中的概念，恰好能够 描述这些秩序。数学家花 了几百年来寻找最有效地 描述这些秩序的精微曲折 处。这种工具可用于外在 世界，毕竟现实世界是种 种复杂情况的缩影，其中 包含大量的秩序。
Therefore it is not surprising to see that mathematics has strong applications in economics where several Nobel Laurent’s were awarded based on their works related to mathematics. We expect its application to Social science and history through Data mining and statistic.
由是观之，数学能大 用于经济学，是毫不奇怪 的。好几个诺贝尔经济学 得奖者，其工作皆与数学 有关。
三.作为工具的数学
III. Mathematics as a tool
A lot of important mathematics were
大量重要的数学，原
developed with sole motivation to study
意是为解决工程上的问题。
problems in engineer.
For example, N.
比如，维纳 (N. Wiener)
Wiener and his students pioneer the study of
及其弟子，是讯息科学的
information science. However, the theory of
先驱。他们发展出来的如
stochastic differential equations, the theory of
随机微分方程、维纳测度
Wiener measure, and the theory of entropy have gone far beyond the original purpose of their study. The theory of Bucy-Kalman filter is absolutely fundamental for modern Control theory.
The theory of Shock wave is
important for design of airplanes.
沦、熵论等，最终都远远 超出它们原来的动机。 Bucy-Kalman 滤子理论在 现在控制论中举足轻重， 而冲击波则在飞机设计起 着关键的作用。
IV. Mathematics as a subject of beauty
The purest branch of mathematics is perhaps number theory. It goes back to ancient days in Babylon, in Greece and other countries. It is a subject of great beauty. No great mathematicians can resist the appreciation of it. Yet in the past twenty years, we see its importance in application to question of security. Crytography depends in a large scale on questions related to factorization of integers to prime numbers, development of Self-corrected Codes depends on algebraic geometry. Geometry grew out from the desire to survey land and for navigation. While it still serves the same purpose, its power has gone far beyond the original motivation. It is the basic building block of fundamental physics of spacetime. Its applications include computer graphics, Crystallography and tomography.
四.数学作为纯美的学科 最纯粹的数学，要算是 数论了。其根源可以追溯到 古代巴比伦、希腊及其它国 度。它精美绝伦，没有大数 学家不曾为其倾倒。在过去 二十年间，我们看到了数论 在保安问题上的重要应用。 解码学依赖于大量与因子分 解为质数的问题。自我修正 数码也依赖于代数几何学。 几何来源自土地测量及 航海。虽然它确实解决了有 关的问题，但它的功能远远 超出了两者，它演变成为时 空物理的基石。
Practically all branches of mathematics that were driven by desire to pursue beauty have found great use in practical world.
差不多所有原先为追求 纯美而发展的数学分枝 ，都 在现实世界中找到重要的应 用。
V. Mathematics in industry: In 1995, the Society for industrial and applied mathematics published a report. They survey 75 managers in industry through telephone calls. Nearly half (49%) of them characterized mathematics as an underlying requirement or tool for them. Among those managers, their education background:
五.数学在工业 1995年工业与应用学会 发表了一项报告。 他们透过电话访问了工业界 的七十五位经理。差不多有 一半﹙49%﹚指出数学是他们 必需的背景或工具。这些受 访者的教育背景如下:
Area of manager’s degrees Mathematics Engineering
Ph.D 16% 13%
Masters 11% 6%
Physics Statistics / Biostatistics Business / Management Computer science Chemistry / Biology
13% 9% 0% 0% 0%
3% 5% 11% 6% 3%
专业
博士
硕士
数学 工程 物理
16% 13% 13%
11% 6% 3%
统计 / 生物统计 商业 / 管理
9% 0% 0% 0%
5% 11% 6% 3%
计算机 化学 / 生物
The report found the following: Application of mathematics Algebra and number theory Computational fluid dynamics Differential Equations Discrete mathematics Formal systems and logic Geometry
Optimization Parallel Algorithms Statistics Stochastic processes
这份报告也指出︰ 数学的应用
Cryptography
代数与数论
解码学
Air craft and automobile design Aerodynamics, porous media, finance Communication and information security Computer security, verification Computer-aided engineering and design Asset allocation, shape and system design Weather modeling and prediction crash simulation Design of experiments, analysis of large data sets Signal analysis
计算流体力学
飞机及汽车设计
微分方程
空气动力学、渗流、 金融
离散数学
通讯及讯息保安
形式系统及逻辑
计算保安、验算
几何
计算机工程及设计
最优化
资产投放、形状及 系统设计
并行计算
天气预告模式、仿 真
统计
实验设计、大量资 料的分析
随机过程
讯号分析
VI. Overview of policy on mathematics
in China
六. 中国数学概观 中 国认 识到 现代 科 技的重要，这点是不容置
Chinese government certainly realizes the importance of modern technology. There is no question that Chinese science and technology has experienced tremendous growth in the past ten years in terms of outputs of papers. To look at mathematics alone, we have the following table which shows that the number of Chinese mathematics papers grew from 6% to 10% of the product of the whole world in a matter of ten years. (Although one should note that this figure include Chinese mathematicians all over the world, a lot of them reside in America).
疑的。过去十年间我国科 技的惊人发展，就论文的 数量而言，十分可观。单
就数学一项，从下表可见， 中国人发表文章的百分率， 就从6%上升到10%﹙必须 指出，所谓中国人包括居 于世界各地的中国数学家， 在美国侨居者不少﹚。
Mathematics Review (by American Mathematics Society) The output of papers by Chinese mathematics
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
Number of Papers 3472 3944 4158 4458 4654 5201 5369 5800 6399 6587 6677 6845 7239
Percentage within all published papers 6.1% 6.9% 7.1% 7.9% 8.1% 8.5% 8.6% 8.8% 9.6% 9.5% 9.6% 9.9% 10.4%
美国数学会数学评论 中国数学家的论文
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002
Number of Papers 3472 3944 4158 4458 4654 5201 5369 5800 6399 6587 6677 6845 7239
Percentage within all published papers 6.1% 6.9% 7.1% 7.9% 8.1% 8.5% 8.6% 8.8% 9.6% 9.5% 9.6% 9.9% 10.4%
While quantity of publication does give an
诚然，论文的多寡，可
indication of research activities, more detail
以视为研究频繁疏落的指标。
study of published papers show that only a
然而细心审视下，可以看到
very limited amount of these Chinese papers
发表于一流期刋的文章，毕
appeared in first class journals. The major
竟只属少数。故此当务之急
problem that Chinese scientists are facing is
是提升论文的水平。国人工
how to lift quality of research papers. There are not much Chinese papers that may
pioneer a subject or direction of importance.
作能开拓一领域，或指出一 重要方向者，寥若晨星。过 份重视文章的数量，对研究
The overemphasize of quantity of papers does have negative effect on research.
有 负 面 的 效 果 。
Chinese mathematicians are actually brilliant and creative. In the late fifties and early sixties, Prof. Hua and Prof. Feng had pioneered several subjects of mathematics that lead the world. The fact that they were more isolated in those days actually helps them to look for directions of their own. The government’s overemphasize of the leadership of scientists that reside in foreign countries create a psycological burden on the local scientists who are very capable. Let me give an example. In the last year, a major news appeared in mathematics is the possible resolution of a problem of Poincare in topology. It depends on the understanding of an equation developed by Richard Hamilton. It was a Russian called Perelman who claims to be successful in carrying out Hamilton’s program. He worked on this problem very hard in the past seven years. Become his claim of success, very few people paid attention to this line of research.
我国数学家才华纵横， 兼擅独造。早在五十年代末 期，华罗庚教授及冯康教授 已开拓了某些领域，走在世 界的前沿。当时比较封闭的 环境，不但没有妨碍其工作， 还使他们走出自己的道路。 政府过份依赖海外的学 者，以他们马首是瞻，会对 国内的才俊带来心理的包袱。 试举一例子。 去年数学界宣传的大事， 要数是拓朴学中的彭加莱猜 想可望解决了。解决的方案 基于对理察汉密尔顿 (R. Hamilton) 方程的研究。方 案是由俄国人普雷尔曼 (Perelman) 提出的，他对 此问题苦思七年，但并没有 引起人们的注意。
However, I am a good friend with Richard Hamilton and had also contributed to this program. I recognized the importance of his work in 1996. So I went to China and told all the major leaders in mathematics the importance of Hamilton’s equation. I urged all the experts in the country to study this equation and I told them that the reward of research in this equation would be tremendous. I sent two of my Ph.D students from Hong Kong to run seminars on this work in Beijing.
To my great surprise, experts in Beijing, taking advice from some Chinese mathematician in American (including my former student who was a famous professor in MIT), consider the paper of Hamilton too difficult and not rewarding. They ordered the seminar to go into different directions, against the wishes of many young brilliant Chinese participants.
理察汉密尔顿与我份属
老友。早在1996年，我就了 解到他工作的重要性了。于 是我跑回来，跟这里的同行 说明了这方程的价值，并指 出顺藤摸瓜，硕果累累，因 此必须开展这方面的工作。 我还让两位在香港的博士生， 专程跑到北京来组织有关的 研讨班。 意想不到的是，在北京 的专家，却听从了旅美数学 家﹙其中一位是我的学生， 当时已是麻省理工的名教授 ﹚的意见，说汉密尔顿的文 章太难懂，念后不划算，不 顾一些优秀青年学者的意愿， 硬要研讨班转到别的方向去。
Incidentally, the group of Chinese experts did
顺便说一名，中国该领域
study the field of geometric analysis (closely
的专家八十年代时是在我的指
related to Hamilton’s work) under my guidance
导下研司几何分析的（与哈密
in the eighties. In fact, they took notes of some
尔顿工作密切相关的领域）。
of my lectures with Schoen in America in the
事实上，他们八十年代在美国
eighties. The book was written in Chinese and
为我和舒恩的一些演讲作记录。
published ten years before the English version.
该书的中文版比英文版早十年
A large group of Chinese mathematicians learnt
面世。一大群中国数学家阅读
from the book and they wrote a lot of papers in
了此书，并撰写了大量论文。
the subject. However, due to the drive of mass
然而，由于炮制论文的驱动，
production, only the easier part of the book was
他们仅研读了此书中的易懂部
studied. The leaders of this subject are still yet
分，他们这行的带头人尚需探
to find a direction for their research in China.
求中国自己的研究方向。
Fortunately, mathematicians in south China
幸 好在 南方 的人 没 受 到
were not influenced by this small group of influential mathematics in the North. Prof. Zhu of Zhongshan University was doing research in The Chinese University of Hong Kong. He accepted the challenge and studied this equation deeply. He was able to achieve first rated results. Unfortunately, he is still not recognized in the North.
北方的影响。中山大学的朱教
I believe that in this new century, many important new fields are opening up to be studied. Mathematics will be the major tool. Chinese mathematicians will play a vital role in such development. But they should be open minded and creative in their thinking. They should make up their mind on what is most important, not depending on the urge of mass production and fashion only.
授当时正在香港中文大学访问， 他接受了挑战，开展了这方面 的研究，深入地探讨这条方程 式，最后得到一流的成果。遗 憾的是，他尚未得到北方的认 同。 我深信新世纪必有新学问, 而数学亦会是其主要工具。我 国数学家在其中会扮演关键的 角色。我们要勇闯新天地,一 旦决定自以为重要的方向时 ,
便一往无前，不管能否发表大 量的论文。
The very major problem that
当今中国数学界面对的
Chinese mathematics faces is lack
大难，便是缺乏领导者。陈
of leadership. The only livin g
省身老师德高望重，是国内
world-class mathematician in China is Prof. S. S. Chern and he is over
ninety years old. Many universities
仅存的世界级大师，但他已 经年过九十了。为了解决这
个问题，很多大学向海外招
try to solve the problem by offering 手，聘任一些访问教授，每 many visiting Professors who may commit their time of one to two months to the Chinese institutes.
年回来工作一两个月。
However, scientific leadership can only depend on full time resident in China. Unfortunately, many universities are very proud and content to put famous names on their list of professors without promoting the actual goal of science and technology. Most of them are Chinese mathematicians resided in foreign soil. They cannot devote much time for academic development in China. Some of their scientific achievements are overexaggerated by their counter parts in China. The results of such collaboration have not been as successful as was claimed by the administrators. On the other hand, I do believe international collaboration is very important for China.
I believe scientists with no prior link to Chinese community should be encouraged to be invited. A true international scientific atmosphere will bring Chinese scientific strength to a new plateau.
我觉得学术上的带头人应
该让国内的学者来当。当下许 多大学竞相招揽名教授 ，并以 此自炫。其实，这些名教授大 都任教于海外，他们不可能全 心致力于中国的学术发展。兼 之，他们的学术成就，亦往往 受到其国内同行的夸大 。这种 合作的模式，并不如外界看到 的那样成功。不过，话说回来，
我还是认为国际合作对中国是 相当重要的。 中国可尝试邀请那些与中 国并无渊源的学者来华 。一种 真正的国际化气氛，会把中国 的科学提升到新的境界。
Perhaps this can be achieved by modeling
after the Institute for Advanced in Princeton where Einstein and many great theoretical
一个可行的办法，就是 成立普林斯顿高等研究所式的
leading
机构。当年爱因斯坦及其他伟
theoretical research for the whole world.
大的理论科学家，便是在普林
Most of these leading scientists came from
斯顿进行研究，终其一生的。
scientists
spent
their
life
in
different countries. I believe it is important to form such an institute with a noble goal. It should be open to scientists all over the world.
这个所必须具有崇高的使命， 并面向全世界。在其中长期任
The permanent faculty should have high
职的，必须是学术上的殿堂人
respect from the government and should have
物，受到政府的尊敬。他们自
world-class quality. It should not be limited
然也不必局限于中国人。我希
to Chinese descendent only. I wish China should be world-class in research in a short time.
望中国能在短期内成为研究大 国。
Poincare:Science is no more a collection of facts than a house is a collection of bricks. The architecture of science is provided by mathematics.
Of course without bricks or knowledge of the bricks, there is no way to make a successful design. A close collaboration of mathematicians with other scientists will lay the foundation for science. Mathematicians should be encouraged to interact with other branch of science. It is the nature of mathematics to broaden itself in response to scientific needs and to deepen itself through integral analysis. Therefore it should be the center of all science for this new century. I do hope the Chinese mathematicians to be open minded in both national and interactions with other disciplines.
科学是堆砖头，数学家将之变 成华厦。 ──彭加箂 诚然，没有砖头或有关的砖头 的知识，便不可能有成功的设计。 惟有数学家与其它科学家的紧密合 作，才能为科学打下基础。我们应 该鼓励数学家与其它科学家合作。
数学的本性决定了，它会随着科学 研究的需求而拓宽自身的领域，并 会随着综合分析而更为深入。因此， 在这个新世纪，数学将成为所有科 学的中心。
──完──