Academics & Faculty

Terence Tao to receive National Science Foundation's highest honor

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Terence Tao, the first mathematics professor in UCLA history to win the Fields Medal, will be awarded the National Science Foundation's prestigious 2008 Alan T. Waterman Award on May 6 at the U.S. State Department in Washington, D.C.
 
Tao, who holds UCLA's James and Carol Collins Chair in the College of Letters and Science, said he is "very honored" to accept.
 
The annual Waterman Award, the highest honor the NSF bestows, recognizes an outstanding young researcher in any field of science or engineering supported by NSF with a research grant of $500,000 over three years. Congress established the award in 1975 to mark the 25th anniversary of the foundation and to honor its first director.
 
Tao won the Fields Medal, often described as the "Nobel Prize in mathematics," in August 2006 at the International Congress of Mathematicians in Madrid. In the 70 years the prize has been awarded by the International Mathematical Union, only 48 researchers have ever won it.
 
Born and raised in Adelaide, Australia, Tao, 32, was awarded the medal "for his contributions to partial differential equations, combinatorics, harmonic analysis and additive number theory." In selecting Tao, the International Mathematical Union 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?'"
 
Christoph Thiele, UCLA professor and chair of mathematics, said outstanding graduate students from as far as Romania and China, as well as throughout the United States, have come to UCLA for the opportunity to study with Tao.
 
One of the branches of mathematics on which Tao focuses is a theoretical field called harmonic analysis, an advanced form of calculus that uses equations from physics. Tao also works in a related field, nonlinear partial differential equations, and in the entirely distinct fields of algebraic geometry, number theory and combinatorics — which involves counting. His research has been supported by the David and Lucille Packard Foundation, the Clay Mathematics Institute and the National Science Foundation.
 
In 2004, Discover magazine praised Tao's research on prime numbers, conducted with Ben Green, a professor of mathematics at the University of Bristol in England, as one of that year's 100 most important discoveries in all of science. A number is prime if it is larger than one and divisible by only itself and one. The primes begin with 2, 3, 5, 7, 11, 13 and 17.
 
Euclid proved that the number of primes is infinite. Tao and Green proved that the set of prime numbers contains infinitely many progressions of all finite lengths. An example of an equally spaced progression of primes, of length three and space four, is 3, 7, 11; the largest known progression of prime numbers is length 23, with each of the numbers containing 16 digits. Green and Tao's discovery reveals that somewhere in the prime numbers, there is a progression of length 100, one of length 1,000 and one of every other finite length, and that there are an infinite number of such progressions in the primes.
 
To prove this, Tao and Green spent two years analyzing all four proofs of a theorem named for Hungarian mathematician Endre Szemerdi. Very few mathematicians understand all four proofs, and Szemerdi's theorem does not apply to prime numbers.
 
"We took Szemerdi's theorem and goosed it so that it handles primes," Tao said. "To do that, we borrowed from each of the four proofs to build an extended version of Szemerdi's theorem. Every time Ben and I got stuck, there was always an idea from one of the four proofs that we could somehow shoehorn into our argument."
 
Tao is also well known for his work on the "Kakeya conjecture," a perplexing set of five problems in harmonic analysis. One of Tao's proofs extends more than 50 pages, in which he and two colleagues obtained the most precise known estimate of the size of a particular geometric dimension in Euclidean space. The issue involves the most space-efficient way to fully rotate an object in three dimensions, a question of interest to theoretical mathematicians.
 
"Terry is the world's expert on this set of five problems and has been since he finished graduate school," said John Garnett, UCLA professor and former chair of mathematics. "When Terry made a new estimate of how big the dimension must be, he also produced the solutions, or partial solutions, to many other problems."
 
Tao and colleagues Allen Knutson at UC Berkeley and Chris Woodward at Rutgers solved an old problem (proving a conjecture proposed by former UCLA professor Alfred Horn) for which they developed a method that also solved longstanding problems in algebraic geometry — describing equations geometrically — and representation theory.
 
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."
 
Tao said 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."
 
In naming Tao one of the world's "Brilliant 10" scientists, the October 2006 issue of Popular Science magazine called him "math's great uniter" and said that "to Tao, the traditional boundaries between different mathematical fields don't seem to exist." The magazine described as "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, the Nobel Prize equivalent in mathematics. He's the youngest person to receive the Fields since 1986."
 
The article also quoted Tony Chan, the National Science Foundation's assistant director for mathematics and physical sciences, as saying of Tao, who has made major discoveries in at least five branches of mathematics, "the senior people in these fields are scratching their heads in awe."
 
In naming Tao was named a MacArthur Fellow in September 2006, the John D. and Catherine T. MacArthur Foundation said: "Terence Tao is a mathematician who has developed profound insights into a host of difficult areas, including partial differential equations, harmonic analysis, combinatorics and number theory. His work is characterized by breadth and depth, technical brilliance and profound insight, placing him as one of the outstanding mathematicians of his time."
 
For more on Tao's research, visit www.math.ucla.edu/~tao/index.html and
 
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