Terence Tao - 'Mozart of Math'

"Terry is like Mozart; mathematics just flows out of him," said John Garnett, professor and former chair of mathematics at UCLA, "except without Mozart's personality problems; everyone likes him. Mathematicians with Terry's talent appear only once in a generation. He's an incredible talent, and probably the best mathematician in the world right now. Terry can unravel an enormously complicated mathematical problem and reduce it to something very simple."

Tao was awarded the Fields Medal "for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory." In honoring Tao, the organization said, "Terence Tao is a supreme problem-solver whose spectacular work has had an impact across several mathematical areas. He combines sheer technical power, an other-worldly ingenuity for hitting upon new ideas, and a startlingly natural point of view that leaves other mathematicians wondering, 'Why didn't anyone see that before?' "

Tao's genius at mathematics began early in life. He started to learn calculus when he was 7, at which age he began high school; by 9 he was already very good at university-level calculus. By 11, he was thriving in international mathematics competitions. Tao, now 31, was 20 when he earned his Ph.D. from Princeton University, and he joined UCLA's faculty that year. UCLA promoted him to full professor at age 24.

Speaking of this work, Tao said, "Other mathematicians gave the impression that the puzzle required so much effort that it was not worth making the attempt, that first you have to understand this 100-page paper and that 100-page paper before even starting. We used a different approach to solve a key missing gap."

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.'"

Tao concentrates on one math problem at a time, but keeps a couple dozen others in the back of his mind, "hoping one day I'll figure out a way to solve them."

"If there's a problem that looks like I should be able to solve it but I can't," he said, "that gnaws at me."

Most of Tao's work is pure theoretical mathematics. Of what use is that to society?

"Mathematicians often work on pure problems that do not have any applications for 20 years, and then a physicist or computer scientist or engineer has a real-life problem that requires the solution of a mathematical problem and finds that someone already solved it 20 years ago," Tao said. "When Einstein developed his theory of relativity, he needed a theory of curved space. Einstein found that a mathematician devised exactly the theory he needed more than 30 years earlier."

Will Tao become an even better mathematician in another decade or so?

"Experience helps a lot," he said. "I may get a little slower, but I'll have access to a larger database of tricks. I'll know better what will work and what won't. I'll get déjà vu more often, seeing a problem that reminds me of something."

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."

Read more at: http://phys.org/news75479793.html#jCp