More information at http://www.math.princeton.edu/Thurston60th/
And a write up about Thurston: http://www.bookrags.com/William_Thurston
IMO William Thurston is the greatest low-dimensional topologist ever. During Thurston60th, I will be in Princeton area; may be I will go and say hello to the great man.
It seems a strange route from Gudavalli to Princeton. I grew up in villages like Gudavalli, dominated by independent farmers who treated Dalits like dirt and considered Brahmins parasites (Added 5/29/07: This is my impression of those days. I am of the opinion that caste is an abomination and must go). There was not much talk of arts or science; just a few street performances, films and some songs. Those who could afford or borrow enough for university education mainly tried engineering or medicine. Some who finished engineering did not like working ‘under’ others and came back to farm. I finished school too early and could not enter an engineering college. My father decided that I should study mathematics and try for IAS. In the second year, I was exposed to some of Cantor’s set theory and suddenly it seemed that mathematics was not just formulae and calculations but was full of exciting ideas. Then I saw Felix Hausdroff’s ‘Set Theory’. There were statements like ‘invariance of dimension’, ‘invariance of domain’ which sounded metaphysical and I wondered how anybody could prove such things. That was what I wanted to study and understand. And went on to do just that. After a few years John Stallings who was visiting TIFR in 1967 said that Papakyriakopoulos did some great stuff. After Stallings left, I started reading Papa’s papers, the first papers in three dimensional topology I studied I felt at home and never really left the subject.
Then around 1977, Thurston fresh from killing ‘Foliations’ entered the subject and showed that we were just scratching the surface and the subject was completely different from what we were looking at. It was a stunning combination of geometry, imagination, seeing limiting behaviour and sometimes quantifying it. It did not seem worthwhile working in the subject without learning his ideas and techniques and they were new, strange and hard. In 1980, there was a conference in Maine to explain his ideas. Some of us old timers were discussing a well known problem that all of us worked on and did not make any progress. Thurston came by and asked what we were discussing. When we told him the problem, he immediately told us the solution using techniques we never heard of and none of us understood. There was complete silence only broken when Hatcher started scratching something on a piece of paper. It took us years to realize that the solution was simple and beautiful.
I always wondered why Thurston did not prove the Poincare conjecture. Some like Mikhail Gromov, who has broader sweep than Thurston, were more interested in theories and scope of theories than specific problems. But Thurston did show interest in solving specific problems. In some sense, the question was too narrow for him and he generalized it to the Geometrization problem for three manifolds. Perhaps getting in to Haken manifolds in the very beginning did not help. When Hamilton’s ideas came along, perhaps Thurston did not want to follow up on somebody else’s ideas.
In a peripheral way, I had a few encounters with Thurston. Around 1979, I had some minor results on some thing called Smith conjecture, not my main area of research and also spent a few weeks thinking about the general problem. Around the same time, the problem was solved by a combination of Thurston’s work and the work of Meeks and Yau on minimal surfaces. I asked Thurston in 1980 how he handled a specific case and I described a possible (theoretical) example. Thurston said that there was no such example. I went home, checked the theory behind the possible example and asked Thurston again the next day. This time, he passed and immediately drew the knot that I had in mind. And then he exclaimed that he had been ignoring such cases in his lectures. But with his broad sweep and power, such exceptions did not matter when he saw the general picture. By 1986, I picked some bits and pieces of Thurston’s work, just about enough that kept me going. I worked on a a problem for a couple of years and finally proved result using his techniques. When I met him again, I told him of my new result. He looked surprised for two seconds, then stared in to space for ten seconds and said ” of course”. I still treasure that two seconds of surprise that I caused him.
Since my Gudavalli days, I met many mathematicians, some of them like Gromov are considered great, and I even collaborated with a few brilliant ones. May be it is my rustic background, somehow I was never in awe of any of them. But Thurston seems to be a person who could have easily carried on mathematical conversations with Reimann or Poincare. Some say that he used to work hard.
