My Past Experience in

1
My Past Experience in Mathematics
Shing-Tung Yau
The Chinese University of Hong Kong Sep. 19, 2003
2

• I grew up in the (farming) countryside of Hong
  Kong Yuen Long and Shatin.
• There was no electricity and no pipe water.
• I took bath in the river when I was very young. I
  have eight brothers and sisters and food was
  scarce.
• When I was five years old, I took an entrance
  examination to a good public school. I failed
  mathematics because I made the wrong convention
• I wrote 57 to be 75,
• 69 to be 96.

3

• So I entered a very small village school.
• There were many rough kids from the farm.
• In a matter of half a year, I got serious sick
  because of the intimidation of the rough kids and
  mistreatment of the teacher.
• I rested at home for half a year. I started to
  learn how to deal with difficult situation with
  classmates and teachers.
• By the time when I entered sixth grade, I was a
  leader of a small group of students to wander on
  the street.

4

• My father was a professor. He taught me a lot of
  Chinese literature at that time.
•  
• However, he did not realize that I did not
  attend school for a period of time.
•  
• (Perhaps because I did well at home as I can
  recite most of the essays that he asked me to do.)

5

• The reason that I did not go to school was that
  the teachers did not really teach. I got bored in
  school. Then after a while I got bored on the
  street, also.
•  
• There was a joint examination for all primary
  schools. I did poorly. However, I was exactly on
  the borderline case.
•  
• The government allowed these borderline kids to
  apply for private school and gave them tuition.
•  
• I got into Pui Ching Middle School.

6

• ??
• ??? ? ??? ?
• ???????,???????,???????,???????,???????,???????
  ,???????,???????,???????!
• ?????
• ????,????????????,???????????,????????????,??????
  ?????,???????
• ????,?????????????,?????????????,????????????,???
  ????????,???????

7

• This is probably one of the best middle school.
•  
• Nothing was exciting in the first year of middle
  school. I did not do too well that year.
•  
• However, I learnt much more at home Chinese
  literature, Novels (Chinese and Western),
  Philosophy, history. All from my father and his
  conversations with his students.
•  
• Although I did not understand Greek Philosophy.
  It started to impress me after listening to many
  conversation of my father with his students.

8

• I started to read the famous Chinese history
  books
• ?????
•  
• I am especially fascinated by ??.
•  
• Not only by its beautiful writings, but also by
  its original and responsible way to report the
  ancient history.
•  
• Up to present days, I read this book.
•  
• The global view of history from a great master
  resonants with the thinking of a great scientist.

9

• The following essay strikes me
• Though indulged in reading, I do not pursuit
  precise meanings. Nonetheless, every time I hit
  on something I was so overwhelmed with joy that I
  forgot my meals.
• ?????
• ???,????,
• ????,??????
• I am not bitter for being poor and obscure, nor
  am I keen on being rich and famous.
• ??????,???????

10

• In following years, this has been the guiding
  principle of my study of many different subjects.
• With my fathers teaching, I started to set the
  goal of my life. An important quotation

11
 

• Zuo's Book of History
• On Immortality
• The first place is to reign benevolently, the
  next to gain victory, and the last to say
  valuable words. These achievements will stand
  for long and not be abandoned. Thereafter they
  are called immortal.
• ??
• ???????
• ?????,?????,?????,????,??????
• One needs being humble and simple to reach these
  goals. A former student of mine recently recited
  the following lines from a Tang poem during a TV
  interview in China
• ????????,?????????
• ??????,??????,????????
• I would rather be at the summit,
• So all mountains will become tiny under me.
• I think he was a bit too arrogant.

12
Sima Qian (???) on Confucius (??)

• There are so abundantly many kings and men of
  virtue! Widely known by their contemporaries,
  their names feel into oblivion soon after they
  perished. And yet Confucius, a man in plain
  cloth, has been held in great esteem by scholars
  of more than ten generations.
• ????????,??!
• ????,????,????,
• ????,?????

13

• During conversations of my father with students,
  many important points of history of philosophy
  were mentioned.
• Basic principles
• The root of the very existence of matter (basic
  axioms, etc)
• General phenomena
• Unification of all principles (unified field
  theory)
• Methods of understanding truth based on logic and
  reasoning
• How to combine different knowledge and different
  phenomena under a general principle
• The great philosophers did not simply follow
  others in developing their views, not even from
  their teachers. They created their own thoughts
  (based on previous works.)

14

• The goal of writing history of philosophy
• (??) The origin of a philosophical thinking must
  come from different sources. It is our goal to
  find out such sources.
• (??) There are many complicated philosophical
  thoughts in the history. It is important to
  figure out the treads of their thoughts.
• (??) A cortical comments of the occurrence of all
  philosophies and their consequences.

15

• I also learnt the way to do research with lasting
  importance.
• Wang Guowei (???)
• The Three Levels To Achieve Breakthrough in
  Research (borrowing some lines from Song Ci or
  lyric poems from the Sung dynasty)
•  
• Level One
• ... Last night the west wind withered the
  greenery of the trees
• In loneliness, I mounted the tall building
• Casting my eyesight along all roads to the edge
  of the earth
• ??
• ???????,????,??????

16

• Level two
•  ... For my loosening waist belt I feel no
  regret,
• For her it is worth being haggard and thin.
• ??
• ???????,????????
• Level Three
• Looking for her a thousand times
• In a crowd
• All of a sudden
• As I turned my head
• There she was
• Standing in the shades of fading lights
• ???
• ???????,????,????,??????

17

• In my second year of Pui Ching, I got into a
  problem with my teacher. The teacher was a very
  devoted head master of my class and clearly meant
  well for me. She was shocked to find out that my
  father was a professor and poorly paid.
•  
• Her passion for my future changed my behavior in
  classroom.
•  
• I studied plane geometry in second year of high
  school.

18
My classmates were not used to reason
abstractly. The mere fact that I listened to my
fathers philo-sophical discussion at home made
me feel at home with axiomatic approach.   In
fact, I felt I can understand my fathers
conversation better after I learnt
geometry.   The charm to prove elegant theorems
based on simple axioms excites me.
19

• With the passion for geometry, I started to
  develop my taste for mathematics, which included
  algebra. Everything became easy after I found
  the subject exciting.
•  
• I also found the subject of history interesting.
•  
• It taught me a global view of everything that I
  learnt.
•  How events happened?
• Why they happened?
• What may happen in the future?

20

• At this time, my father just finished writing his
  book on history of Western philosophy. His
  conversations with students taught me the way
  that we should see history in a global manner.
•  
• This kind of practice deeply influence my way of
  looking at my research projects in the later time.

21

• Around 400 A.D.
• Liu (who wrote the first book on comparative
  literature on Chinese writings up to that period)
  ???? ??
•  
• My body may perish along with time.
• My goal and my ambition will extend with my
  theory.
• My heart is in resonance with those great men in
  ancient days.
• My feeling and my theory will go forward for the
  next thousand years.
• ????,????????????,?????????

22

• When I was fourteen, my father passed away. This
  was perhaps the greatest shock to my life. For a
  long time, I could not believe that my father
  left me and the family.
•  
• The financial situation of the family was really
  bad. It was not clear at all that we could still
  go to school. The tremendous will of my mother
  and the helps of my fathers friends and students
  made it possible.

23

• This disastrous change of family situation made
  me much more mature. The extreme hard-ship
  showed difficulty of human relationship, what I
  learnt from my father became practical.
•  
• The poems and the classical essays that I learnt
  became much more meaningful. I spent half a year
  to read classical literature and history of
  China. It became a way for me to relax during
  very tense situation in life. The beautiful
  poems guided me to appreciate the beauty of
  nature.

24

• ???????
•  
• ????!??????????,??????????????,???,???,???????????
  ???????????????,?????????????????,??????
•  
• ??????!??????????!??????????,?????????????????????
  ?????,????????????,??????
•  
• ?????

25

• From Byrons Don Juan II -- A variation edition
  by Steffan Pratt
• Canto III, 86
• 1. The isles of Greece, the isles of Greece!
• Where burning Sappho loved and sung,
• Where grew the arts of war and peace,
• Where Delos rose, and Phoebus sprung!
• Eternal summer gilds then yet,
• But all, except their sun, is set.
• 2. The mountains look on Marathon
• And Marathon looks on the sea
• And musing there an hour alone,
• I dreamd that Greece might still be free
• For standing on the Persians grave, I could
  not deem myself a slave.

26

• I read a lot of books in mathematics. I thought
  about the problems in those books. When I
  exhausted all those problems, I started to create
  my own problems as I thought that they may be
  challenging.
• The practice of creating my own problem had been
  the most important part of my research in the
  future. The textbooks in school did not satisfy
  me. I went to library and I went to bookstores
  to read books. I spent hours and hours in
  bookstore to read books that I could not afford
  to buy.

27

• When I was fifteen, I started to teach lower
  grade level students to earn money. I was proud
  that by teaching in a novel way, I was able to
  transform some very poor student to become the
  best student in class.
•  
• It was an experience to train young people. I
  also learnt that it is beneficial to myself to
  teach.

28

• My high school teachers in mathematics were
  excellent. We studied rather advanced topics in
  mathematics. I had no difficulty with them.
•  
• However, I was rather disappointed that my
  physics teacher was not good enough. The
  fundamental intuition in physics was not
  established during my high school year. I
  regretted it up to now.
•  
• I had an excellent teacher in Chinese. He was my
  fathers friend he taught us to think in a
  non-traditional manner.

29

• We were asked to think creatively. He said that
  we should read good books but also bad books as
  possible comparisons. So I read everything.
  This is true even for my scientific career.
•  
• A typical topic for our essay in our Chinese
  writing the philosophy of a pig.
•  
• So we start to dream about anything interesting.
•  
• I was not the best in my high school. I did not
  have the highest grade in mathematics. But I
  think deeper than my classmates and I read much
  more books.

30

• I entered The Chinese University of Hong Kong in
  1966. I chose mathematics as my career although
  I was also very interested in the subject of
  history.
•  By this time, I started to digest those advanced
  level mathematics books that I read in high
  school. I did not quite understand those books
  at the beginning. Suddenly I understand them and
  I was much better than the contemporary students.

31

•  
• ??????
•  
• ??????????????????
•  
• ??????????????????
•  
•  

32
Chung Chi College Anthem Men from four seas
founded Chung Chi so that here might youth Honour
Christ, eternal teacher, who Himself is
truth. Through the long night keep the torch
bright and the work begun Till the lights of
faith and knowledge show the world made
one. China's still evolving culture, grateful,
we retain East and West, through freely sharing,
further strength obtain, By the Church upheld and
nurtured, minds to duty drawn, Chung Chi, toward
the very highest, lead us on, and on!
33

• College mathematics opened my eyes. The fact
  that one can derive every statement in
  mathematics from simple axioms really excited me.
  After I understood how mathematics was built, I
  got so excited that I wrote a letter to my
  professor showing my great pleasure. It was a
  cornerstone for my appreciation of mathematics.
•  
• A new Ph.D came from Berkeley to Hong Kong. His
  name is Stephen Salaff. He was so impressed by
  my performance that he wrote a book with me
  together. Its topic is on ordinary differential
  equations.

34

• Another teacher Dr. Brody came from Princeton.
  He had a rather unique way of teaching. He
  picked an advanced book in mathematics. He
  assigned a chapter for the students to find
  mistakes in the book and corrected the mistakes.
•  
• It is a good method to train us not to depend on
  textbook. At the same time, I trained myself to
  be critical about the established theorems in the
  book. Sometimes I generalized the theorems.
  Brody was very pleased by my performance when I
  showed what I could do in class.

35

• The importance of such trainings is that
• I learnt how to think independently.
• I found out how important it is to express
  mathematics in front of an audience.
• These points have been important for me and for
  my teaching.

36

• With the help of Dr. Salaff, I was able to enter
  the graduate school of Berkeley despite that I
  did not finish my college in Hong Kong.
•  
• Of course, Berkeley has the leading mathematics
  department in the world. I arrived in August. I
  met Prof. S. S. Chern who become my thesis
  advisor later.

37

• When I was in Hong Kong, I was too much
  fascinated by very abstract mathematics.
  (Although I was trained quite solidly in
  analysis.) I thought mathematics covering a very
  general area is best mathematics. I thought I
  would study functional analysis. I learnt a lot
  in that subject. I read a big fat book of
  Dunford-Schwatz on functional analysis. I also
  read a lot of books on operator algebra.
•  
• When I arrived in Berkeley, I met some best minds
  in mathematics. I changed my view.

38

• When I met those first rated mathematicians, I
  was rather thirsty in learning different subjects
  from them. I attended many classes from 8am to
  5pm. (Sometimes I ate lunch in class.) These
  are subjects ranging from topology, geometry,
  differential equations, Lie groups, number
  theory, combinatorials, probability theory to
  dynamical system. I did not understand all of
  them. But I focus my efforts on several of them.

39

• When I learnt topology, it was so differently
  from what I learnt before. There were fifty
  students in class. All of them seem to be smart
  and far better than me. They could perform and
  talked nicely.
•  
• However, I did my home work well and in a short
  time, I found out that I was not bad, after all.
  The key is to work out all those tough home works
  and think about them thoroughly.

40

• I read a book of John Milnor and was fascinated
  by the description of the concept of curvature.
  John Milnor is an excellent topologist.
•  
• I started to think about problems that is related
  to questions in the book. I spent a lot of time
  in the library.
• There was no office for graduate students. There
  were many famous professors in Berkeley. Soon I
  realize that they are human beings after all. I
  read many journals and books in the library.

41

• I started to be able to prove some nontrivial
  theorems in the second quarter. They are related
  to some theorems in group theory that I learnt
  over some casual conversation with a teacher in
  college. I applied it to geometry. My
  professors were surprised and pleased by my
  progress. One of the professors started to work
  with me. We wrote two papers. Professor Chern
  was on sabbatical leave. When he returned, he
  was very pleased.

42

• I did not think what I did was great. I was very
  impressed by Prof. Morrey on his teaching of
  nonlinear partial differential equations. He
  taught nonlinear technique. It was not
  fashionable. The book he wrote was difficult to
  read. I thought those technique that he
  developed are very deep and must be important for
  the future of geometry. I learnt those
  technology. Despite of Prof. Morreys big name,
  very few students or faculties cared about his
  course. At the end, I was the only student in
  class and Prof. Morrey taught me in his office.
  This course built the foundation of my
  mathematics career.

43

• After I wrote several papers, Prof. Chern told
  many people how brilliant I was although I did
  not think he knew my works well. I started to
  think more thoroughly about mathematics and
  geometry in particular. I worked on other parts
  of geometry. However, results did not come easy.
•  
• My friend S. Y. Cheng came from Hong Kong that
  summer. We shared an apartment right next to the
  campus and I became more relax.

44

• In that summer, I asked Prof. Chern to be my
  advisor. He agreed and after one month, he said
  that my papers in the first year should be enough
  for my thesis. I was surprised because I thought
  they are not good enough and I wanted to learn
  more.
•  
• In any case, in the second year, I learnt more in
  the field of complex geometry and topology.
  Prof. Chern had a great expectation on me. He
  suggested me to work on Rieman hypothesis.
  Unfortunately up to now, I never thought about it.

45

• Instead I pursued the general understanding of
  curvature of space. I decided a key to
  understand such a concept was a proposal made by
  Calabi in early fifties. Nobody believed what
  Calabis thought is true. I started to think
  about it. It is not the standard thing that a
  geometer would do in those days. It is clearly a
  hard question of analysis. Nobody would touch
  such problem.

46

• I started to develop my taste into learning how
  to introduce analytic methods into geometry.
  Previous to this, there were attempts to apply
  nonlinear theory to surfaces in three space. I
  wanted to deal with an abstract space in
  arbitrary dimension.
•  
• Because of Prof. Morrey and Cherns interests in
  minimal surfaces, I also developed interest into
  this fascinating subject. In particular, I was
  interesting into harmonic maps. In general, I
  studied Calculus of variation.

47

• I was interested in all analytic aspects of
  geometry. The basic idea is to merge the subject
  of nonlinear differential equation and geometry.
  In order to understand nonlinear equation, it is
  fundamental to understand linear equations.
  Hence I establish the first major theorem for
  harmonic functions on manifolds. I got my friend
  S. Y. Cheng to look into eigenvalue and
  eigenfunction problems. Together we wrote
  several important papers on the subject. They
  are still fundamental for modern research.

48

• When I graduated, I got several offers. My
  teacher Chern suggested me to go to Institute for
  Advanced Study. The salary was less than half of
  what I could have gotten from Harvard. But I
  went to the Institute for Advanced Study. I met
  some other group of distinguished mathematicians.
  I developed some taste into topology, especially
  the theory of symmetries of space. I did solve
  some important problems in this subject based on
  analytical ideas I developed (group actions on
  manifolds).

49

• Because of problem of visa, I went to New York
  State University of Stony Brook. At that point,
  it was supposed to be the center of metric
  geometry. It was indeed a good place, full of
  energetic young geometers. I learnt their
  technique. But I did not think that was the
  right direction for geometry.
•  
• After one year, I went to Stanford where there
  was no geometer. It is a very peaceful
  environment and is very good in nonlinear partial
  differential equations. I met my very good
  friend Leon Simon and my former student Richard
  Schoen. Together we developed the subject of
  nonlinear analysis in geometry.

50

• Tao Yuan-Ming (?????)
• Long I lived checked by the bars of a cage. Now
  I have turned again to Nature and Freedom.
• ?????,??????

51

• When I arrived at Stanford, there was a big
  conference in geometry. A physicist was involved
  to give a talk on general relativity.
• Although I did not understand Physics well, I
  immediately fell in love of the geometry problem
  associated to general relativity. It is
  fascinating to give physical meaning of space
  that we saw and vice versa.

52

• The problem was too difficult to solve at that
  time. But I kept that in mind.
• During the conference, I thought I found a way to
  disprove the proposal of Prof. Calabi. I was
  asked to give a presentation of my thoughts. It
  all sounded good. Nobody objected. So every
  people was happy that the general expection was
  true the Calabi Conjecture is wrong after all.

53

• After two months, Prof. Calabi wrote to me for
  clarification of my thoughts.
• I found a serious gap on my reasoning. It was
  the most painful period of my research life. I
  could not sleep.

54

• For about two weeks, I could not sleep as I
  considered that my reputation was badly damaged
  by not able to reproduce what I claimed.
  (Although I never wrote any announcement of it.)
  However, the pain of going through of each single
  details of the problem convinced me that the
  opposite direction should be right. The argument
  to give counterexample to the Calabi Conjecture
  was that if it were true, something must happen.
  Hence a few years later, when I settled this
  problem, I knew many natural consequences of it.

55

• After I decided that it must be true, I worked
  towards the right direction. Many preparatory
  works were done to prepare for the final proof.
  I worked with Cheng on understanding my questions
  related to Monge-Ampere equations, affine
  geometry, maximal surfaces and many related
  problems. Richard Schoen worked with me on
  harmonic maps. Schoen, Simon and I worked on
  minimal surfaces. In a matter of two years, we
  understood a great deal of nonlinear analysis
  related to geometry. It was an exciting period
  of time in geometry.

56

• Qu Yuan (??)
• This is what I am after.
• I will not turn back even nine deaths are ahead.
• ???????,????????

57

• Right after I got married, I got the right idea
  to finish the proof of the Calabi Conjecture. I
  felt I finally understood curvature of Kahler
  geometry.
• Many important applications were found to solve
  some old problems in algebric geometry.

58
September 2, 2003
One Cosmic Question, Too Many Answers
One problem is that string theory requires 10
dimensions of space-time, whereas we appear to
live in four. Dr. Strominger remembered being
excited when he found a paper by the
mathematician Dr. Shing-Tung Yau, now of Harvard
and the Chinese University of Hong Kong. It
proved a conjecture by Dr. Eugenio Calabi, now
retired from the University of Pennsylvania, that
the extra dimensions could be curled up in
microscopically invisible ways like the loops in
a carpet.
59

• When I finished the proof of the Calabi
  Conjecture, I felt I have set up a framework for
  mathematicians to merge two important fields
  together nonlinear partial differential equation
  and geometry.
• In 1976, I was in UCLA and I met my friend Meeks
  who was my classmate in graduate school. He was
  not in good shape. But he was a very original
  mathematician. So I proposed to work with him on
  relating ideas from minimal surfaces and
  topology of three dimensional manifold together.

60

• We had a great success. We solved two classical
  problems in both fields
• If the boundary of a soap film is convex, the
  soap film cannot cross itself.
• Together with works with Thurston, the famous
  problem of Smith Conjecture is solved.
• Once the direction was set in the right way, many
  classical questions can be answered.

61

• Next year, I visited Berkeley where I gave
  seminars on nonlinear problems in geometry. Both
  Richard Schoen and S. Y. Cheng were there. With
  Schoen, we finally solved the problem that I was
  excited about in general relativity.
• The problem is called positive mass conjecture
  and is fundamental for general relativity. (Only
  if the mass is positive that spacetime can be
  stable.)

62

• In 1978, I returned to Stanford, I applied ideas
  of minimal surfaces to solve a famous problem
  (Frenkel Conjecture) in complex geometry with
  Y.T. Siu. I also introduced ideas of harmonic
  map to studying discrete group symmetries. These
  ideas are still useful up to now.
• Schoen and I developed the structure theory of
  manifolds with positive scalar curvature based on
  our works on general relativity.

63

• In 1979, we had a special year in differential
  geometry in the Institute for Advanced Study.
  Practically all geometers came. We set a good
  direction for geometry. I proposed one hundred
  interesting open problems for the field of
  geometry. Some of them were solved and some of
  them were not.
• The 1970s have been one of the most fruitful era
  of geometry.

64

• By late seventies, I was well-recognized by my
  colleagues. There were many news coverage on
  problems that I solved.
• However, it will be misleading to think that my
  goal is to earn medals and gain recognition. It
  has never been the priority of my study.
• I am interested in Mathematics because it is so
  exciting to see how human thought can be extended
  to understand nature. The beauty of nature from
  the point of view of geometry is everlasting.

65

• Together with my friends Schoen, Simon, Cheng,
  Meeks, Uhlenbeck, Hamilton, and later by
  Donaldson, Taubes and Huisken, and others,
  Nonlinear Analysis in Geometry has been
  established as a rich subject. Its importance in
  understanding beauty of nature can never be
  underestimated. The most recent developments
  show their importance in Physics and in Applied
  Science.

66

• Once a natural merge of several great subjects
  Geometry, Non-linear Analysis, Algebraic
  Geometry, Mathematical Physics, is done,
  classical and difficult problems were naturally
  solved. Problem solving can be considered as
  lampstands on our road to understand nature.

67

• Confucius (??)
• Studying without thinking goes nowhere thinking
  without studying leads to bewilderment.
• ??????,???????

68

• Han (?? 600 AD) on the process of learning
• When general people praise my writing, I am not
  pleased.
• When general people slight my writing, I am not
  depressed.
• ???????,????????

69
C.F. Gauss (1817)

• I am becoming more and more convincing that the
  necessity of our geometry cannot be proved, at
  least not by human reason nor for human reason.
  Perhaps in another life we will be able to obtain
  insight into the nature of space which is now
  unattainable.
• Until then we must place geometry not in the same
  class with arithmetic which is purely a priori,
  but with mechanics.

70
Lets now demonstrate an old concept of geometry
to computer graphics

• An abstract two dimensional space with complex
  coordinates is called Riemann surface.
• In the following pictures, we use these concepts
  to draw a map over the surfaces of a teapot, a
  bunny, and a minimal surface. Note that this map
  is a generalization of latitude and longitude of
  the globe. They are orthogonal to each other.

71
Application of Gaussian Curvature to Face
Recognition
Note that the color on the face corresponds to
level sets of the Gaussian curvature of the face
72
Riemann Surface

• Holomorphic transformation between surfaces

demo
73

• In the last ten years, my coauthors and I are
  very much involved in understanding the role of
  fundamental physics in geometry. In order to
  gain the intuition behind the motivation from
  physics. I spent a lot of time attending their
  seminars in physics department. We were able to
  obtain deep theorems in mathematics based on this
  interaction. A very important concept is duality

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• Duality is a beautiful and elegant concept.
• It says that some theory with strong coupling is
  the same as other theory with weak coupling.
• It is very similar to Chinese Taoism or Yingyang.
• But the concept of duality is more rigorous and
  quantitive. It enables us to calculate some
  mathematical quantities that are otherwise
  difficult to calculate.

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• I do not hesitate to say that mathematics
  deserves to be cultivated for its own sake, and
  that the theories of not admitting applications
  to physics deserve to be studied as well as
  others.
• - H. POINCARE
• ??????,????,???????????????????,??????,??????????
• - ???

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• and, believe me, if I were again beginning my
  studies I would follow the advice of Plato and
  start with mathematics.
• - GALILEO
• ?????,????,?????????,?????
• - ???

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My father took part in the establishment of the
Chinese University in its early stages. His
three sons, including the speaker, were educated
in the same school. I am deeply honored to be
able to make contribution towards the university.
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Hong Kong has played an important role in modern
history. There are many outstanding scholars
from Hong Kong who are now working all over the
world. Among the four Hong Kong professors in
Harvard, it is interesting to observe that three
of them have been professors of the Chinese
University. I firmly believe that under the
support of our government and our society with
vision, Hong Kong is the city with the greatest
potential to nourish future Nobel or Fields
laureates. Our university should see this as a
goal, not a burden.
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Alumni of Mathematics Department http//www.math.
cuhk.edu.hk/alumni
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Thank you !