Monday, May 03, 2010

Discover interview with S.T. Yau

Discover Interview: The Math Behind the Physics Behind the Universe .
There are some slightly technical parts but there also many non-technical interesting responses. I met him often during the academic year 1980-81 in Princeton. He tried to get me to work out a geometric proof of a known topological result. It was clear that it could be done and I did not want to do it and often used to avoid him. But he remained friendly and gracious. Later it turned out that there was a geometric proof much more elegant and basic than I imagined and so he was right afterall. Some excerpts from the interview:

"Q. How did you go from that rough-and-tumble young man to the focused person you are now?
A. In the early 1960s my father was chairman of the department of literature and philosophy at Hong Kong College. The college president wanted to make a deal with the Taiwanese government to send in spies. My father refused to go along and resigned. That created a big money problem because he had eight children by then. My father had to run around among different, distant colleges to support the family. Back in China he’d lent a friend some money, and after the Communists took over, the friend moved to Macau, a city near Hong Kong, and ran his own schools. So he told my father, “I cannot return your money, but your daughter can come to my school, and I’ll give her free room and board and free tuition.” So my older sister went to Macau to study and got some flu, some funny disease, we never knew exactly what. She came back and she was treated, but she died in 1962. Then my elder brother got a brain disease; at the time we didn’t know what it was. My father had all kinds of burdens on his shoulders and then he got a disease, which I believe was cancer, but we didn’t know much in those days. My mother was running around trying to get funding to help my father. Finally we raised some money, but it was too late. He died after two months in the hospital in 1963, in the middle of my studies in the ninth grade. We could no longer afford our apartment, so we were kicked out. That’s when I realized I would have to make decisions for myself.
Q. Disproving the Calabi conjecture would have been a major achievement; how did you announce it?
A. In August there was a big conference at Stanford with the top geometers in the world, including Calabi. I talked to Calabi and told him my idea. He said, “That sounds great. Why don’t you give a discussion about it to me?” It was scheduled for 7 p.m. Calabi brought a few colleagues from the University of Pennsylvania, and then a few others heard about it, and a few others. There was a little crowd. I talked for about an hour, and Calabi was excited. “I’ve been waiting for this for a long time, and I hope it’s right,” he said. All the other people said, “Great, finally we can stop the wishful thinking that Calabi is true.” Then Calabi wrote to me in October. He said, “I’m trying to reconstruct your argument, and I’m having some difficulty. Could you explain the detail?” I started to reconstruct it and I found a problem too. I got totally embarrassed. I did not respond to Calabi at that moment and instead tried extremely hard to patch up the proof. I couldn’t, so I looked around to find other examples where Calabi was wrong. I didn’t sleep for two weeks. But every time I found an example that was close, the proof fell apart at the last minute. Finally I said, gee, this cannot be such a delicate matter. Now I had much deeper insight into the issue and felt there must be some truth to the whole thing. I determined that it had to be right.
Q. So after all that work trying to prove that Calabi’s conjecture was wrong, you decided it was correct after all?
A. I began developing the tools to understand it, and by 1975, only one part of the proof was left. That year my wife got a job in Los Angeles. I moved to UCLA. All in a short time, we got married, bought a car, bought a house in the Valley, and had to look for furniture. My mother came from Hong Kong for the wedding, and then her parents came—they all stayed under one roof and got into fights; it was complicated and crazy. I was fed up, so I locked myself in the study and thought about Calabi instead of the family problems, and I solved the whole thing. I went over the proof three times in detail, and I went to see Calabi in Pennsylvania. On a snowy Christmas Day, he came with me to visit mathematician Louis Nirenberg at New York University. We spent all day Christmas going over it, and I spent the next month writing up the proof for publication."

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