## Wednesday, February 15, 2006 ... //

### Terence Tao - Fields medal

Terence Tao, the Mozart of math, has just won the 2006 Fields medal. Congratulations!

His honor will be announced on August 22nd, 2006, in Madrid. The other winners will be Andrei Okounkov, Wendelin Werner, and Grigory Perelman.

On the Mozart page, you will see that this medal was already predicted 3 months ago - in 2005. Among other things, he has proved that there exist arbitrarily long arithmetic sequences of prime integers (together with Ben Green in 2004). The Reference Frame is the first public source in the world where you can learn about the new winner.

Incidentally, if Tao is Mozart of math, you may also ask who is Tao of Physics. ;-) Or at least Tao of silly science-oriented puns. :-)

Terence Tao went to high school at age of 8. He received a PhD from Princeton University at age of 21 and at age of 24, he became a full professor at UCLA. He is an expert in harmonic analysis, nonlinear partial differential equations, as well as algebraic geometry.

#### snail feedback (4) :

Awesome! Terence Tao is certainly very deserving of his Fields medal. I am glad he does not waste his talent on something completely irrelevant to reality, like Witten does. The kind of math he does is what I call beautiful math: The problem is so easily understandable that you can explain it to an elementary school student in plain English. Actually any one with a decent physics intuition can see the correct answer already: A set of infinite prime certainly very likely contains an infinite cases of progressive sequences of any conceiveable length. But solving and proving them takes a real genius to do. His Fields winning work can be found here. See how much you can read and understand the paper.

Harmonic analysis is a very important branch of mathematics, and actually very useful in some practical applications.

Quantoken

I followed Quantoken's link above to the Field's medal paper on arxiv.org, and it is 56 pages of beautifully written text and maths. I like the historical introduction, and the way that the various components are described in detail first, instead of referring the reader somewhere else. It's the kind of helpful paper that encourages people who find pure maths a real headache (like me). I'm glad Quantoken has given a very brief explanation above.

Congratulations to Terence Tao! To me what is even more interesting than his childhood story is where he discusses his way of working in an understandable way. See

http://www.college.ucla.edu/news/05/terencetaomath.html -

How does Tao describe his success?

"I don't have any magical ability," he said. "I look at a problem, and it looks something like one I've already done; I think maybe the idea that worked before will work here. When nothing's working out; then I 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 mathematicians faced with a problem, will try to solve the problem directly. 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 I 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.

"If I experiment enough, I get a deeper understanding," said Tao, whose work is supported by the David and Lucille Packard Foundation. "After a while, when something similar comes along, I 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, so 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 of 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, that gnaws at me."