In little more than a decade, Tao has also written some 140 papers. By comparison, Chan says, most pure mathematicians would be happy with three papers a year. Just as remarkable is his growing number of co-authors (50 at last count). "I have been lucky to find very good collaborators, who have taught me a lot, have introduced me to several new fields of mathematics or have shown me new insights," he says. Plus, he adds, "they are just plain fun to work with."
It's easy to put a genius on a pedestal, to ascribe his success to otherworldly talents. But mathematical research can be more like running a marathon, where sheer determination often prevails. "If he decides to prove something, he will," says Gigliola Staffilani of MIT, a sometime collaborator. Knutson says that Tao has shown him how to chip away at a large problem a little bit at a time. "I'd say I don't understand why this thing would be true. He'd say it reduces to checking these 17 cases, and they all work. I'd say that's awesome, but we obviously can't publish that. But after a while, we'd unwind it to three cases, and then we could publish."
The heart of Tao's gift may simply be his ability to let his thinking roam freely toward an unseen horizon. "Terry is unusual in how open-minded he is," says Ben Green, his collaborator on the prime-number problem. "When we started, a lot of senior mathematicians probably would have said that the idea won't work, that it was ludicrously ambitious. He was willing to try all lines of inquiry."
Willing, you might say, to trace an umbrella in the evening sky.
Dana Mackenzie has a PhD degree in mathematics from Princeton University. He writes about science and mathematics.