(Guangming Daily March 26, 2001)
This is the text of a talk given by ShiingShen Chern on December 18, 2000 at the opening ceremony of the International Mathematical Conference held to commemorate the 90th birthday of Hua Luogeng. The last two additional passages were given by Chern on March 9. To preserve the style of the original presentation, minimal editorial changes have been made to the text, and notes have been added. This is the first time that this article has made public. The original version was first published in chinese in Guangming Daily March 26, 2001.
I had a friendship and connection with the late Mr Hua Luogeng that stretched over many years. I first met him 70 years ago on the campus of Tsinghua University at the start of classes in the fall of 1931. During those 70 years, we were at times in the same department and we were destined to have an enduring connection. He was born in 1910 and less than a year my senior.
I remember that when he first joined us in 1931, he had only graduated from junior high school, but his mathematics thesis had attracted much of our attention. Tsinghua was very different from other universities. Not only did it ask him to come but also offered him a position. It was very unusual for a university of that time to do so. Because of his academic background, his position was that of an "assistant" when he first came. At that time the Mathematics Department was called the Arithmetic Department and only became the Mathematics Department later. I was an "assistant" lecturer” in the Arithmetic Department one year ago. The offices of the Arithmetic Department comprised 4 rooms and were situated on two sides of the corridor of a "Gong"(I)shaped hall with two rooms on each side. On one side was the office of Mr Xiong Qinglai, Head of Department. I also had a table in another place and was his assistant lecturer. Another office had two tables, those of Mr Zhou Hongjing and Mr Tang Peijing. When Luogeng came, he shared my office table. Because I was made a "research student" in 1931, he became an assistant and was given the use of this table. Thus our relationship then was of one succeeding another.
Luogeng was an excellent mathematician and hence did not need the general prerequisite mathematical training. Very soon he was able to discuss the problems of mathematics on the same level with everyone else, with research students and even with lecturers. Though he was officially an assistant, he was, in effect, a research student. I was also a research student and we interacted with each other often and attended the same classes. It was an extremely happy period of my student life.
I should add that Tsinghua's Arithmetic Department was a very small department at that time but it had a great influence on the development of arithmetic in China and constitutes an arguably significant chapter in the history of Chinese mathematics. Other than Mr Hua, our classmates at that time included Zhuang Qitai and Shih Xianglin (who later became professors at Peking University and Nanjing University respectively) and also classmates who would become professors at Nankai University. Though Tsinghua operated on a somewhat small scale at that time, it produced a considerable group who would exert some influence on Chinese mathematics. Later, Tsinghua expanded and invited foreign professors, not so much for the purpose of giving seminars as for socialising and showing a few transparencies. They would stay in Tsinghua for a year. The world renowned French mathematician Hadamard and the American Wiener came and gave lectures at Tsinghua. Such arrangements nowadays may not be easy. Starting on a small scale, Tsinghua was able to produce some positive effect on the development of mathematics in China.
In 1934 I left Tsinghua upon graduation and went to Germany for further studies. In 1936 Luogeng went to Cambridge University in England to work with the great mathematician Hardy. He took the TransSiberia railway from Beijing to Berlin. I was in Hamburg at that time and so we met in Berlin in the summer of 1936. Coincidentally, the [Summer] Olympics were held in Berlin that year, and Hitler was at the stand. Interestingly, the fastest runner in the 100metre sprint and 200metre sprint was a black man [the American Jesse Owens]; this was a big blow to Hitler. Regrettably, the Chinese team did not perform well in the Berlin Olympics. The most wellknown team member was the swimmer Yang Xiuqiong, but she did not get any award. The highest ranked member Fu Baolu was in pole vault, but he also did not get any medal. In contrast, China has now made great strides and her athletes have achieved glorious results in international Olympics. I think that similarly China has the potential in mathematics but mathematics requires more time [for development]. Luogeng and I would watch the Olympics as well as discuss a lot of things.
After the 1936 Olympics, I went to Cambridge and was together with Luogeng. His work at that time was in analytic number theory, and its most important tool was the ""circle method". It is strange that though number theory is about the properties of integers, it needs complex variables to unravel the deep properties of integers. The connection between complex variables and prime numbers is mysterious and fascinating. Luogeng has done much work in this area to which he has made contributions. He applied the circle method to the Waring Problem and the Tarry Problem. One of the main contributors to the circle method is the Indian mathematical genius Ramanujan, and the first paper on it was a paper by Hardy and Ramanujan. A very big advance was next made by the Soviet Union mathematician Vinogradov. Luogeng made much improvements and advances on Vinogradov's method. His own work on the estimation of trigonometric sums was a significant contribution. I believe that Luogeng made his deepest contributions to mathematics during his stay in Cambridge from 1936 to 1938. His contributions to analytic number theory were numerous.
When he returned to China in 1938, the SinoJapanese War had begun. Peking University, Tsinghua University and Nankai University were then grouped together in Kunming as the SouthWest United University (SUU). As a professor of Tsinghua, he was a staff of the SUU. Nowadays we like to complain about facilities being inadequate or support inadequate. In fact, at that time we had nothing, even the existing books were all packed in boxes. Since we did not know when we would have to move again, the library staff was reluctant to unpack the boxes. However, in spite of those circumstances, we had a high spirit and good disposition and there was camaraderie at the SUU in Kunming. For example, we held a seminar with Mr Wang Zhuxi of the Physics Department, in 1940 or so. The SUU at that time produced some outstanding students like Wang Xianzhong, Zhong Kailai, Yan Zhida, Wang Hao, and Wu Guanglei. Thus, if we have the people and this spirit, we can still do many things even if the environment is a little unfavourable.
I was with Luogeng [in Kunming] for about five years from 1938 to 1943. When our group first went to Kunming, we did not have any place to stay. Because the original school was not at that place, we had to "Borrow" the rooms of a middle school. The school was very generous and offered some rooms for SUU staff to stay in temporarily. So professors like Hua Luogeng, Wang Xinzhong and I stayed in one room (Wang was an expert on Japanese history). Each of us had a bed, a desk, a bookcase and a chair. So the room was rather congested, but life was purposeful. Even before we got out of bed, we would joke with each other. Although there were material hardships, life was nevertheless purposeful. Nowadays, we wish for unceasing material progress, but I think that there is joy amidst hardship.
In the summer of 1943, I went to the Institute for Advanced Study at Princeton, while Luogeng remained in Kunming. However, we wrote to each other often. When the war effort was victorious and the country was rebuilding itself, I knew that he would be involved in various societal activities. We would only meet in Shanghai in 1946. I had then just returned from the US and he was about to go to US on official business. But we still managed to talk a fair bit of mathematics; our mathematical interests had become closer. In 1950 I left for the US and was at the University of Chicago while he was at the University of Illinois, which was quite nearby. He once came to the University of Chicago to lecture on an elementary proof of the BrauerCartanHua Theorem; it was a beautiful proof. He returned to China in the summer of 1950. He had to pass through Chicago in order to board a ship at San Francisco. We all admired his deep patriotism. When we parted company this time, our two worlds would become worlds apart with hardly any mutual contact. I would only know about some of his activities through the occasional media reports about him.
It was not until 1972 when I was invited by the Chinese Academy of Sciences that we met again in Beijing after a hiatus of 22 years. It was like a dream as we reminisced the past. In 1980 he led a team to the US. When he passed through Berkeley, he stayed at my place for two days. We chatted like in the old days; it was a happy time. In 1983 he visited the California Institute of Technology. I then drove over 400 miles from Berkeley to visit him. That was our last meeting.
Translated by Y.K. Leong January 17, 2011
