Four hundred people packed into an auditorium at U.C.L.A. in January to listen to a public lecture on prime numbers, one of the rare occasions that the topic has drawn a standing-room-only audience.Another 35 people watched on a video screen in a classroom next door. Eighty people were turned away.The speaker, Terence Tao, a professor of mathematics at the university, promised "a whirlwind tour, the equivalent to going through Paris and just seeing the Eiffel Tower and the Arc de Triomphe."His words were polite, unassuming and tinged with the accent of Australia, his homeland. Even though prime numbers have been studied for 2,000 years, "There's still a lot that needs to be done," Tao said. "And it's still a very exciting field."

After Tao finished his one-hour talk, which was broadcast live on the Internet, several students came down to the front and asked for autographs.Tao has drawn attention and curiosity throughout his life for his prodigious abilities. By age 2, he had learned to read. At 9, he attended college math classes. At 20, he finished his Ph.D.Now 31, he has grown from prodigy to one of the world's top mathematicians, tackling an unusually broad range of problems, including ones involving prime numbers and the compression of images. Last summer, he won a Fields Medal, often considered the Nobel Prize of mathematics, and a MacArthur Fellowship, the "genius" award that comes with a half-million dollars and no strings."He's wonderful," said Charles Fefferman of Princeton University, himself a former child prodigy and a Fields Medalist. "He's as good as they come. There are a few in a generation, and he's one of the few."Colleagues have teasingly called Tao a rock star and the Mozart of Math. Two museums in Australia have requested his photograph for their permanent exhibits. And he was a finalist for the 2007 Australian of the Year award."You start getting famous for being famous," Tao said. "The Paris Hilton effect."Not that any of that has noticeably affected him. His campus office is adorned with a poster of "Ranma ½," a Japanese comic book. As he walks the halls of the math building, he might be wearing an Adidas sweatshirt, blue jeans and scruffy sneakers, looking much like one of his graduate students. He said he did not know how he would spend the MacArthur money, though he mentioned the mortgage on the house that he and his wife, Laura, an engineer at the NASA Jet Propulsion Laboratory, bought last year.After a childhood in Adelaide, Australia, and graduate school at Princeton, Tao has settled into sunny Southern California."I love it a lot," he said. But not necessarily for what the area offers."It's sort of the absence of things I like," he said. No snow to shovel, for instance.A deluge of media attention following his Fields Medal last summer has slowed to a trickle, and Tao said he was happy that his fame might be fleeting so that he could again concentrate on math.One area of his research — compressed sensing — could have real-world use. Digital cameras use millions of sensors to record an image, and then a computer chip in the camera compresses the data."Compressed sensing is a different strategy," Tao said. "You also compress the data, but you try to do it in a very dumb way, one that doesn't require much computer power at the sensor end."With Emmanuel Candès, a professor of applied and computational mathematics at the California Institute of Technology, Tao showed that even if most of the information were immediately discarded, the use of powerful algorithms could still reconstruct the original image.By useful coincidence, Tao's son, William, and Candès's son attended the same preschool, so dropping off their children turned into useful work time."We'd meet each other every morning at preschool," Tao said, "and we'd catch up on what we had done."The military is interested in using the work for reconnaissance: blanket a battlefield with simple, cheap cameras that might each record a single pixel of data. Each camera would transmit the data to a central computer that, using the mathematical technique developed by Tao and Candès, would construct a comprehensive view. Engineers at Rice University have made a prototype of just such a camera.Tao's best-known mathematical work involves prime numbers — positive whole numbers that can be divided evenly only by themselves and 1. The first few prime numbers are 2, 3, 5, 7, 11 and 13 (1 is excluded).from..IHT

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