In Memory

I feel very honored to have this opportunity to say a few words on the occasion of the ninetieth birthday of my teacher Professor Y. C. Wong.

Before I entered HKU in 1960 and had the chance of meeting Professor Wong in person, I knew about him from his legendary reputation as one of the "Boxer Rebellion Indemnity Scholars" and one of only two Chinese to be appointed professor in HKU at a time when only Englishmen or Europeans could occupy such positions. Dr. Hou in Pathology was the other professor. Moreover, Professor Wong was appointed at the remarkably young age of 35.

I first met Professor Wong in his office about math courses when I was a freshman. My first exposure to mathematical rigor was in HKU. I saw for the first time the beauty and elegance in mathematical logical arguments and mathematical structures.

I recall a meeting with Professor Wong in the summer of 1961 after my freshman year. There was a Walter Brown Memorial Prize awarded at the end of the freshman year based on an examination in the summer. I took the exam. Even now I remember the problems in the exam. It was about the orthogonal system of Legendre polynomials. Computations of the definite integrals by iterated integration by parts give their inner products. Also some differential equations give recurrent formulas among them. I must have made some mistakes about the integration by parts. I did not get the prize. After the exam, Professor Wong called me to his office to tell me that one person scored higher than me. I later learned that it was Wong Sheung-Kai. The purpose of the meeting was to give me some encouragement and a copy of the book "An Introduction to the Theory of Numbers" by G. H. Hardy and E. M. Wright. He wrote a very nice note to go with the book. I still have the book. Here it is. From its appearance you can tell that I did spend a considerable amount of time on it. Unfortunately, with all the moving I could not locate the note.

I was in the Faculty of Arts program of the Math Department. After the first year a student in the Faculty of Arts could choose all nine papers in mathematics, that is, all courses exclusively in mathematics for the second year and the final year. In my year, besides myself, Lam Tsit-Yuen, Poon Chung-Kong, Wong Tsin-Sze, and Chow Sze-Yung chose nine papers in mathematics. In the summer after my freshman year Professor Wong introduced a summer project of making plastic geometric models under the guidance of somebody with expertise in working with plastics. I participated in that project. The participants designed, cut plastic sheets, and glued them together. The purpose of the project was to help with the concrete visualization of geometric objects.

In many old institutions, for example, G6ttingen and Harvard, there are still glass cases containing professionally made geometric models. Every time I see such glass cases of geometric models, I am reminded of the plastic models of the summer of 1961.

After so many decades of research, I realized more than ever before that, no matter how elaborate and abstract a mathematical theory is, it is like the proverbial "thousand miles' journey with the inevitable first small step." All theories start with some simple concrete models, concrete pictures, concrete examples, and some down-to-earth simple, but possibly tricky, lemmas.

Nowadays all pictures are virtual on the computer screen. However, when I tell my students what matters most is the understanding of what simple pictures and lemmas make the complicated theory click, I still see in my mind Professor Wong's plastic model project.

I took from Professor Wong a course on differential geometry. The textbook is the book by Norden. I still have with me the Chinese version of that book. Here it is. It looks very used. I still remember vividly the way he gave his lectures: engaging, meticulous, serious, and perfectionistic. His infectious love for the subject radiated from his lectures.

Speaking of Professor Wong's being a perfectionist, I would like to inject a story which I heard from Doris Chan. One day Doris Chan treated her entire class to tea in the old canteen which was next to the Jordan Memorial Library. She regaled us with stories about various faculty members of the Math Department. I distinctly remember one she told about Professor Wong. Professor Wong always strives for perfection in whatever pursuit he engages in and is a very inventive person. Before a ball with the future Mrs. Wong, he wanted to first make sure that he had all the dance steps perfectly right. So he carefully studied a book and got the future Mrs. Wong to practice with him. The trouble is that he had to interrupt the practice frequently to consult the book. Finally he found an ingenious solution. By clamping the top of a music stand on the shoulder of the future Mrs. Wong, he could put the book on and read it while following the dance steps illustrated in the book.

When I was in HKU, the whole Math Department was built up by Professor Wong. Chan Hong-mo, Leung Kam-tim, Tsou Siu-tong, Doris Chan, Chan Wing-ming, and Tong Bok-yin were faculty members I took courses from. The department was small, both in terms of the number of students and the number of faculty, but it was a very congenial department with a pleasant and inspiring academic environment. That is why there was the kind of socializing with Doris Chan in the anecdote mentioned earlier.

In keeping with the tradition of British universities, there was a respectful distance between the senior faculty and the students at HKU in those days. Professor Wong appointed a number of demonstrators including Yuen Ping-cheong, Lam Kee-yuen, Chan Kai-yuen. There were also a number of demonstrators who came from Zhongshan University. The demonstrators acted as a kind of bridge between the students and the senior faculty.

Lam Kee-yuen, one of the demonstrators, organized an extracurricular study group with some students. Tsou Sheung-chun, Lai Hon-fai, Lam Tsit-yuen, and I were among the participants. Each student prepared the presentation of a topic when the group met. S. T. Tsou dubbed the group "le petit seminaire de K. Y. Lam." One time I presented the theory of ordinary differential equations when the group met in the house of S. T. Tsou. When I prepared for the presentation, I learned a great deal about differential equations which was useful to my study later. After the presentation, we were served chicken porridge as refreshment. During refreshment Tsou Sheung-chun was still discussing mathematics with great animation. I still remember her extensive gesticulation caused a big spill of the chicken porridge!

There was a staff seminar run by Professor Wong only for the faculty. Out of curiosity I asked around to inquire what was done in the staff seminar. Somebody told me that the staff seminar discussed the book by Helgason on symmetric spaces. I went out to buy a copy of the book and studied it. It was only some time after I left HKU that I could understand it, but the seed of interest was already sown in HKU.

When I was a student in HKU there were only very few mathematics courses offered. Even with a full course load I had only very few lectures per week. Life was very leisurely. I enjoyed the congeniality of the Department and the stimulating academic environment. I could do a great deal of exploring and thinking on my own.

Coincidentally when I finished at HKU, Professor Wong helped chart the next step in the preparation for my mathematical career. At that time the person who taught me German at HKU was recruiting students for graduate study in Germany. He made arrangements for me to get a scholarship from the Deutsche Akademische Austauschdienst to study in Germany. I was almost set to go to Germany. K. T. Leung got his doctoral education in Hamburg and Zurich after the Second World War, so I went to him to inquire about student life in Germany. He told me that life was very hard in Germany immediately after the war and most students just survived on bread and water. Well, as an undergraduate in HKU, I had been pampered in St. John's College for three years. It was like a hotel. One could even order and sign for room service for night snacks. When I shared with my German instructor my second thoughts about going to Germany because of the reportedly Spartan life style, he looked at me with a straight face and said, "Indeed the German government does have scholarships with the stipulation that the scholarship holders must limit their diets to only water and bread, but I can assure you that what you are getting is not that kind." Besides the creature comfort factor, the incompatibility of the British and German higher education systems meant a great deal of uncertainty in the academic arrangements. I finally gave up my plans to go to Germany.

It was rather late and I did not have any U.S. graduate school application forms. I asked Lam Tsit-yuen whether he had some forms left over from his application. He gave me a few. With the forms I went to Professor Wong to seek advice as to which school I should apply to. After looking over the forms, Professor Wong told me that Calabi is an outstanding differential geometer and I could apply to Minnesota to study with him. I followed his advice and went to Minnesota. I studied differential geometry with Calabi and later he recommended me to Princeton. Thus, Professor Wong's advice set the first step of my graduate education.

After his retirement Professor Wong set up a visiting professorship at HKU. I was very honored to return to the Math Department of HKU as the first Y.C. Wong Visiting Professor. Single-handedly Professor Wong built up the Math Department of HKU, not only in teaching but also in research. After several decades in mathematical research myself, I appreciate even more how absolutely amazing it is that, with all the administrative responsibilities of putting together a new department, Professor Wong has continued to pursue his mathematical research all the time, producing results of lasting value. This academic year I have been on leave from Harvard. I spent the Fall semester of 2002 at Columbia University. A faculty member there, Mu-Tao Wang, told me that in his most recent work on the Gauss maps of the mean curvature flow he used the computations of Professor Wong for geodesics of Grassmanians from Professor Wong's 1967 paper in the Proceedings of the National Academy of Sciences of the United States.

Today the students, colleagues, and friends of Professor Wong gather together to celebrate his 90th birthday and his inspiring career as a mathematician and an educator. It is indeed a very joyous occasion. I am privileged to have had the opportunity of not only acquiring mathematical knowledge from him, but also learning from his example as a dedicated scholar and teacher.

I would like to conclude this tribute to Professor Wong with the birthday wish borrowed from the book of Deuteronomy, "As thy days, so shall thy strength be."