Saturday, June 19, 2010

Discover Interview: The Math Behind the Physics Behind the Universe

Shing-Tung Yau is a force of nature. He is best known for conceiving the math behind string theory—which holds that, at the deepest level of reality, our universe is built out of 10-dimensional, subatomic vibrating strings. But Yau’s genius runs much deeper and wider: He has also spawned the modern synergy between geometry and physics, championed unprecedented teamwork in mathematics, and helped foster an intellectual rebirth in China.

Despite growing up in grinding poverty on a Hong Kong farm, Yau made his way to the University of California at Berkeley, where he studied with Chinese geometer Shiing-Shen Chern and the master of nonlinear equations, Charles Morrey. Then at age 29 Yau proved the Calabi conjecture, which posits that six-dimensional spaces lie hidden beneath the reality we perceive. These unseen dimensions lend rigor to string theory by supplementing the four dimensions—three of space and one of time—described in Einstein’s general relativity.

Since then Yau has held positions at the Institute for Advanced Study, Stanford University, and Harvard (where he currently chairs the math department), training two generations of grad students and embarking on far-flung collaborations that address topics ranging from the nature of dark matter to the formation of black holes. He has won the Fields Medal, a MacArthur Fellowship, and the Wolf Prize.

Through it all, Yau has remained bluntly outspoken. In China he has called for the resignation of academia’s old guard so new talent can rise. In the United States he has critiqued what he sees as rampant errors in mathematical proofs by young academics. Yau has also strived to speak directly to the public; his book The Shape of Inner Space, coauthored with Steve Nadis, is scheduled for publication this fall. He reflected on his life and work with DISCOVER senior editor Pamela Weintraub at his Harvard office over four days in February.

You’ve described your father as an enormous intellectual influence on you. Can you tell me about him?
He went to Japan to study economics, but he came back to help the Chinese defend themselves before the Japanese invaded in 1937. By the end of the war he was distributing food and clothes to the poor for the U.N. After the revolution in 1949, he worried about getting in trouble with the Communists, so he brought the whole family to Hong Kong. We were very poor—at first we were almost starving—but my father had a large group of students constantly at home to talk about philosophy and literature. I was 10, 11, 12 years old, and I grew accustomed to abstract reasoning. My father made us memorize long essays and poems. At the time I didn’t understand what they meant, but I remembered them and later made use of it.

Did part of you ever rebel?
I read most of the Kung Fu novels in secret. I quit school for more than half a year. I’d wake up and say I was going, but I’d spend the whole day exploring the mountains and then come back—but I did the homework that my father assigned to me at home.

I heard you led a gang at one point.
I had a group of friends under me. I’d go around, and sometimes we ended up in fistfights with some other groups. So?

How did you go from that rough-and-tumble young man to the focused person you are now?
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.

What did you do then?
After a while the government leased us some land, and we built a small house thanks to money from friends, but it was in a village far from school. The other kids looked down on us for being poor, and I had to ask the school president to allow me to pay tuition at the end of the year, when my government fellowship came through. It was humiliating. But I studied hard and did very well, especially in math. Then a former student of my father started a primary school in a town closer to school. He said I could help teach math and stay there at night. I had to take care of myself, I had to wash things and all of that, but I learned how to survive.

What happened once you made your way to college?
I had fallen in love with math early on, but at the Chinese University of Hong Kong I realized that mathematics was built on standard actions and logic. Soon I had arranged to take tests for the required math courses without actually attending while sitting in on more advanced classes, and no one seemed to mind. In my second year, Stephen Salaff, a young mathematician from U.C. Berkeley, came to teach in Hong Kong. He liked to talk to the students in the American way: He gave lectures and then he asked students questions. In many cases it turned out I could help him more than he helped me, because there were problems he couldn’t solve during class. Salaff suggested I apply to graduate school early. I was admitted to Berkeley and even got a fellowship. I borrowed some money from friends and flew to San Francisco in September 1969.

What did you think of California when you arrived?
The first thing that impressed me was the air. In Hong Kong it’s humid, hot, but in California it was cool and clear. I thought it was like heaven. A friend of Salaff’s came to the airport to pick me up and took me to the YMCA, where I shared a big room with four or five people. I noticed that everybody was watching baseball on TV. We didn’t have a TV at home. My neighbor who was sleeping there was a huge black man. He was talking in a language I had never heard before. He said, “Man, where the hell you come from?” It was fun, but I had to look for an apartment. I was walking around the street when I met another Chinese student from Hong Kong and we decided to share, but we couldn’t afford a place. We looked around and found another Chinese student, from Taiwan, so there’s three of us and it’s still not enough. Then we found an Alaskan also studying math, also on the street. So four of us went in together and the rent for each was $60 a month. My fellowship gave me $300 a month, and I sent half of it home.

What about your math studies?
There were many holes in my knowledge so I’d wake up early and start class at 8 a.m. I took three classes for credit, and the rest I audited. I brought my own lunch so even at lunchtime I was in class. I was especially excited about topology because I thought it could help reveal the structure of space. Einstein used geometry in his equation to give us the local picture: how space curved around our solar system or a galaxy. But the Einstein equation didn’t give the overall picture, the global structure of the whole universe. That’s where topology came in.

What is topology? Is it like geometry?
Geometry is specific and topology is general. Topologists study larger patterns and categories of shapes. For example, in geometry, a cube and a sphere are distinct. But in topology they are the same because you can deform one into the other without cutting through the surface. The torus, a sphere with a hole in the middle, is a different form. It is clearly distinct from the sphere because you cannot deform a torus into a sphere no matter how you twist it.

Does that mean geometry and topology are really two perspectives on the same thing?
Yes. It is like Chinese literature. A poem might describe a farewell between lovers. But in the language of the poem, instead of a man and woman, there is a willow tree, where the leaves are soft and hanging down. The way the branch is hanging down is like the feeling of the man and the woman wanting to be together. Geometry gives us a structure of that willow tree that is solid and extensive. Topology describes the overall shape of the tree without the details—but without the tree to start with, we would have nothing.

It has always amazed me to observe how different groups of people look at the same subject. My friends in physics look at space-time purely from the perspective of real physics, yet the general theory of relativity describes space-time in terms of geometry, because that’s how Einstein looked at the problem.