The Fifth Annual Brilliant 10

Terry Tao, 31


Math's Great Uniter

He searches the mathematical universe for his next big trick

The code breakers who are about to employ a powerful new method to piece together broken messages have UCLA day care to thank. While waiting to pick up their kids, Terry Tao, a UCLA mathematician, and Emmanuel Candes, a mathematician from the nearby California Institute of Technology, wondered if it was possible to reconstruct
a garbled message even if you inter-
cepted only bits and pieces of it. Using ideas from fields as diverse as geometry, statistics and calculus, they not only proved it possible (in special cases), they showed how to do it. Their technique is being adopted by anyone trying to clean up a jumbled signal, be they CIA agents tapping phone lines or doctors restoring spotty brain scans.

The work is quintessential Tao: a breakthrough in a new field that requires a mastery of techniques from across the mathematical spectrum. It´s this kind of ingenuity that won Tao this year´s Fields Medal (announced as this issue went to press), the Nobel Prize equivalent in mathematics. He´s the youngest person to receive the Fields since 1986, which was two years before the then-13-year-old Tao became the youngest person ever to win the International Math Olympiad. In the decade since he earned his Ph.D. from Princeton University at age 21, â€he´s really taken the math world by storm,†says Tony Chan, the dean of physical sciences at UCLA. Tao has made major discoveries in at least five branches of mathematics, and, Chan says, â€the senior people in these fields are scratching their heads in awe.â€

Tao´s most famous result brought an end to a mathematical search that had lasted for centuries [see box, left], in which he used techniques from several fields to uncover an astonishing pattern among primes. But to Tao, the tradi-tional boundaries between different mathematical fields don´t seem to exist. â€They´re interconnected in some way,†agrees John Garnett, his colleague at UCLA. â€You have to be Terry Tao to see all this, but they are.â€-Lauren Aaronson

Tao´s Infinite Primes

Terry Tao and Ben Green at the University of Bristol in England found a surprising pattern among prime numbers. Here´s the condensed version of their 35-page proof.

First, Find a Prime

A prime is a number divisible only by 1 and itself, such as 3, 11 and 421.

Then, Create a Prime
Arithmetic Progression (PAP)

That´s a sequence of prime numbers in which each number is separated from the next by the same difference. The PAP â€5,11, 17, 23†is four numbers long, and each number differs from the next by six.

What did Tao and Green prove?

There are infinitely many PAPs of every length. So â€5, 11, 17, 23†is just one of an infinite number of PAPs with four numbers in it. There´s also an infinite number of progressions that are five, 10 or even 1,936,046 numbers long.