My Memories of S. S. Chern

By Chung Tao Yang (as told to D. Yang)

In China

Chern was born in Jiaxing, Zhejiang but his father moved his family to Tianjin. Chern did very well there and entered Nankai University when he was only 15. At that time the Nankai math department consisted of one person, Jiang Lifu (1890-1978), who taught all of the courses. Jiang was from the same county as me, Pingyang County in Zhejiang. After graduating from Nankai, Chern went first to Qinghua University, but soon left for Germany, where he studied with Blaschke, and France, where he studied with Elie Cartan. He then returned to China. By then the war had forced the three major universities in Beijing to relocate temporarily in Kunming as a single combined Southwest Associated University, where Chern became a professor. Also there at that time was Hua Loo-Keng1. At that time, Hua and Chern were viewed as the two top young mathematicians in China.

The Academia Sinica started an Institute of Mathematics in Shanghai and appointed Jiang to be the head of the institute. Jiang in turn named Chern as the acting head of the Institute and returned to Nankai. Chern recruited the best students in China to come to the Institute as research assistants. They had no official duties, except to study mathematics. Chern himself would lecture twelve hours a week. One was the well-known topologist Wu Wen-Tsun. During Chern’s tenure at the Institute, he was very successful in training a whole generation of Chinese mathematicians in a broad range of fields.

I got to know Chern just by accident. I was probably the last research assistant brought to the Institute by Chern. I had graduated from Zhejiang University in 1946 and spent two more years there as a teaching assistant. I wanted to be a research mathematician, but had no means of pursuing this. I just read by myself. It just happened that a good friend of mine was at the Institute, and he told me how interesting Chern’s lectures were. He told me it would be good for me to go there. He also told Chern about me and said that, when we were in college, I was better than him. Chern knew that university math departments were always reluctant to let their best students go elsewhere, so he said that if the head of the math department would write a letter to him agreeing to let me go to the Institute, Chern would take me. Luckily, the department head, Su Buchin, who — like Jiang and me — was also born in Pingyang County, agreed to write the letter.

I went to the Institute in the summer of 1948. By then the Institute had moved with the Nationalists to Nanjing. Chern had been invited to visit the Institute for Advanced Study in Princeton and left Nanjing soon after I arrived. I did not get to attend any of Chern’s lectures, but was able to study topology and algebraic topology from notes taken by the other students of Chern’s lectures. I had always had a strong interest in geometry, so I had no difficulty switching to topology.

By the end of 1948, the Communists were winning the war, and the Institute followed the Nationalists to Taiwan. Only three senior mathematicians, (Jiang, Hu Sze-Tsen, and Wang Hsien Chung) and three junior mathematicians (Liao Shantao, Chen, and me) went to Taiwan. Jiang and Chen would return to the mainland in 1949, while Hu, Wang, and I went to the U.S. Hu first went to Tulane as an assistant professor and later became a full professor at UCLA. Wang started at LSU and later became a professor at Cornell. Both were outstanding mathematicians, Hu in homotopy theory and Wang in Lie groups. Liao would go to Chicago, where he worked with Chern.

With the help of Chern, Wang, and Hu, I was offered a teaching fellowship at Tulane. To get a visa for the U.S., I had to provide evidence of enough financial means to stay for at least two years. The stipend was not enough for the visa requirements. Chern deposited $2,400 into a bank account and sent me the receipt, so that I could get the visa.

In the U.S.

I did not see Chern much in the U.S. I visited him a few times in both Chicago and Berkeley.

In 1952, right after I received my Ph.D., I visited Chern in Chicago, where he helped me gain access to the university library.

In 1953 I asked Chern for advice on a problem I faced. I was a research associate at the University of Illinois. A professor and his graduate students were working on a conjecture of Freeman Dyson. I attended their seminars, learned about the conjecture, and started working on it myself. Soon after that, I produced a proof. When the professor heard about it, he told me he almost had it, too. But I knew he didn’t. Our ideas were close but different. I didn’t know what to do. I went to see Chern and asked him how to handle this situation. Chern said that the best way would be to write a joint paper, but that I should wait until the professor suggests it. He also told me that if the professor does not suggest it within a few months, I should go ahead, write it up, and publish it. And that’s what I did. This was one of my best results. Of course, the professor in question was upset, because he and all of his students had been working on it for several years.

In China

Chern had a close relationship with Nankai University. The university started an institute of mathematics, and Chern was the first director. The university built visitor housing, including a residence reserved primarily for Chern. We also stayed in the same building, whenever we visited Nankai. From ’89 to ’95 I visited Nankai every year for several weeks, mainly because Chern asked me to. That happened because Chern once was invited to give some special lectures at Drexel around ’88. He heard I would retire in ’91. He told me it was too early to do nothing. He asked me to visit the new institute at Nankai.

In China Chern was a famous person. So from time to time there would be somebody who would want to visit him, but he wouldn’t try to see everyone. But he did make some interesting friends, including someone who was one of the top go players in China and a bridge partner of Deng Xiao Ping. In ’95 we visited Nankai, while Chern was also there. Chern invited the go player to stay for a few days as his houseguest.

We would have all of our meals together with Chern. My wife usually planned the menu in advance and bought the ingredients. She would cook, even though we had a kitchen staff. Chern loved to play mah-jong, but we wouldn’t play for money. We would just keep track on paper. Also, Chern was not walking well, but he needed to take walks. During those few weeks, every morning we took him for a walk for twenty minutes. This was the last time we were together with Chern and his wife.

[1]: Hua himself had an interesting background. He had maybe only 9 years of formal education, but had to return home to work in his father’s store. But he studied math and managed to publish two articles in a journal. A professor recognized his talent and made arrangements for him to work at Qinghua University as an assistant. He was soon promoted to a research assistant. G. H. Hardy learned about Hua’s talent and made arrangements for Hua to visit Cambridge for a year during which Hua wrote at least fifteen papers. Afterwards, Hua returned to China and became a professor at the Southwest Associated University from 1936 until 1945. Hua went on to have a distinguished career as a mathematician and a leader in the Chinese academic community. (Some of the details of Hua’s life are taken from: Sheng Gong, The Life and Work of Famous Chinese Mathematician Loo-keng Hua, Advances in Applied Clifford Algebras 11(2001) 9-20.)