Terence Tao, in a UCLA press release about his Fields medal:
What are Tao’s secrets for success?
Tao, who was raised in Australia, offered some insight. “I don’t have any magical ability,” he said. “I look at a problem, and it looks something like one I’ve done before; I think maybe the idea that worked before will work here. Nothing’s working out; then you think of a small trick that makes it a little better but still is not quite right. I play with the problem, and after a while, I figure out what’s going on.
“Most people, faced with a math problem, will try to solve the problem directly,” he said. “Even if they get it, they might not understand exactly what they did. Before I work out any details, I work on the strategy. Once you have a strategy, a very complicated problem can split up into a lot of mini-problems. I’ve never really been satisfied with just solving the problem. I want to see what happens if I make some changes; will it still work? If you experiment enough, you get a deeper understanding. After a while, when something similar comes along, you get an idea of what works and what doesn’t work.
“It’s not about being smart or even fast,” Tao added. “It’s like climbing a cliff: If you’re very strong and quick and have a lot of rope, it helps, but you need to devise a good route to get up there. Doing calculations quickly and knowing a lot of facts are like a rock climber with strength, quickness and good tools. You still need a plan — that’s the hard part — and you have to see the bigger picture.”
His views about mathematics have changed over the years.
“When I was a kid, I had a romanticized notion of mathematics, that hard problems were solved in ‘Eureka’ moments of inspiration,” he said. “With me, it’s always, ‘Let’s try this. That gets me part of the way, or that doesn’t work. Now let’s try this. Oh, there’s a little shortcut here.’ You work on it long enough and you happen to make progress towards a hard problem by a back door at some point. At the end, it’s usually, ‘Oh, I’ve solved the problem.'”
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What does Tao think of his success?
“I’m very happy,” he said. “Maybe when I’m in my 60s, I’ll look back at what I’ve done, but now I would rather work on the problems.”
It’s all very well for super smart people like Tao to say that it’s “not about being smart”, but I have never met or heard of an average person who contributed to mathematical knowledge. He’s probably a nice person and is just being modest. Genius is almost everything. At best, stupid … sorry, less intelligent people like me are resigned to sit on the sidelines and cheer for geniuses like Tao and Perelman. And then spend the rest of the day trying to understand 1 percent of what they actually did, the other 99 percent being beyond our level of comprehension.
“It’s not about being smart” is always code for “It is about being smart” — just like “It’s not you, it’s me” is always code for “It’s not me, it’s you.”
Indeed! BTW, I do think their are differences between how people are smart. Tao suggest that he is (1) stragetic and (2) not the quickest thinker. (1) reminds me of conversations I’ve had with Umesh Vazirani. Sometimes we do associate brains with being quick, but, I myself being slower than a slug, hope that there is more to it than that!