Professor, alum nab Fields honor

The International Mathematics Union named professor Andrei Okounkov and Terence Tao GS '96 among the four Fields Medal winners announced last month.

The award, often described as mathematics' equivalent of the Nobel Prize, is given once every four years and is considered the discipline's highest honor. Only 44 medals have been awarded in the Fields Medal's 70-year history.

At age 31, Tao is among the youngest individuals ever to win the award, which is given to mathematicians under the age of 40. "It's quite an honor — very different to anything that's happened to me before. This prize is the highest in mathematics," Tao, now a professor at the University of California at Los Angeles, told the BBC.

The IMU recognized the young Australian for his work on furthering the understanding of prime numbers and his work on wave motion as part of Einstein's general theory of relativity.

"Terence Tao is a supreme problem-solver whose spectacular work has had an impact across several mathematical areas," the IMU said in a statement announcing the recipients Tuesday morning.

"He combines sheer technical power, an otherworldly 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?' "

Observers agree that Tao has proven himself a veritable powerhouse in the realm of mathematical achievement, showing a tremendous gift to penetrate areas of the field others have yet to approach.

Tao taught himself addition at age two by watching "Sesame Street," and began taking college classes when he was nine. At age 13, he was the youngest person to ever win the International Math Olympiad. He earned his Ph.D. from Princeton at 21 and was a tenured professor by 24.

"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."

For his own part, Tao has painted his success as the result of endurance more than speed.

"It's not about being smart or even fast," he said in an interview at UCLA last year. "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."

Get the best of the ‘Prince’ delivered straight to your inbox. Subscribe now »

"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."

Peter Sarnak, a Princeton mathematics professor who was present at the Fields award ceremony in Madrid, called Tao "a technically brilliant problem solver with very few mathematicians in the world in his league."

"I particularly liked his theorem [which] asserts that there are arbitrary long arithmetical progressions in the prime numbers," Sarnak said in an email. An apparently useless theorem, but one which is very appealing especially if you like prime numbers."

Tao plans to continue to work on the research that earned him the Fields Medal. "Now that I am a little less stunned by the last few days' events, I think the feeling that strikes me most now is the sense of responsibility to the field that comes with such a high honour, and I hope to live up to the medal's strict standards for excellence in the future," he said in an email.

'Brilliant contributions'

Okounkov was praised "for his contributions bridging probability, representation theory and algebraic geometry" — different areas of mathematics that had until recently seemed unrelated.

"The work of Andrei Okounkov has revealed profound new connections between different areas of mathematics and has brought new insights into problems arising in physics," the IMU said in a statement. "Okounkov's ongoing research in this area represents a marvelous interplay of ideas from mathematics and physics."

Okounkov remains modest, even after receiving the most coveted prize in his field. "There were many brilliant and highly deserving candidates, several from our own mathematics department alone," he said in an email after a "hectic" day in Spain, adding that he was "somewhat surprised" to learn that he had won when he was notified months ago.

"I don't think my work stands out above the standards of the department. And to support this point of view, I could quote a very long list of medals, prizes and other honors earned by Princeton mathematicians."

Some colleagues beg to differ, however, lauding Okounkov's unique aptitude for mathematics. "I would characterize Okounkov as being very powerful, sophisticated and fast thinker who also has great combinatorial talent and problem solving skills," Sarnak said. "This combination is rather unusual."

Mathematics professor Joseph Kohn has also heaped praise on Okounkov. "Andrei Okounkov has made brilliant contributions to many areas of mathematics," Kohn said in 2002 at the time of Okounkov's appointment to the faculty. "This work is truly spectacular."

Okounkov, who came to Princeton in 2002 from the University of California at Berkeley, was born in Moscow in 1969. He received his doctorate in mathematics from Moscow State University in 1995.

"I am very proud to be a part of the Princeton mathematics department," Okounkov said. "We have not only individual brilliance, but also a great spirit of exchanging ideas."

"I was looking forward to joining this very distinguished group and my expectations came 100 percent true. I absolutely must mention here my friends and collaborators professor Rahul Pandharipande and his student Davesh Maulik."

Okounkov teaches a graduate class on representation theory every semester, in addition to his undergraduate classes.

Asked about future research, he said, "We have a lot of projects going, so instead of planning for the future, I am simply hoping for success, or better, a breakthrough, in one of the directions."

Medal declined

Other mathematicians awarded the medal today included the now famously reclusive Russian mathematician Grigori Perelman, who has solved a key piece of the century-old puzzle known as the Poincaré conjecture.

"I think the work of Grigori Perelman in which he proves the Poincaré conjecture is truly astounding — certainly the best result in mathematics in the last 10 years," fellow medalist Tao said. "I certainly consider his work far superior to my own, and unquestionably the right candidate for the Fields Medal."

Perelman, who gave a lecture at Princeton in 2003, declined to attend the IMU's ceremonies in Madrid to receive his medal, apparently becoming the first mathematician to refuse the prize. Officials at the IMU said Perelman declined the coveted medal because he didn't value the extra attention.

"The reasons center around his feeling of isolation from the mathematical community, and in consequence his not wanting to be a figurehead for it or wanting to represent it," Sir John Ball, president of the IMU, told The New York Times. "I don't think he meant it as an insult. He's a very polite person."

Since the initial publicity surrounding speculation of him being awarded the Fields, Perelman has said that he has retired from the professional mathematics arena.

"Now, when I become a very conspicuous person, I cannot stay a pet and say nothing. That is why I had to quit ... I am not a politician," he is quoted as saying in the Aug. 28 issue of The New Yorker.

Perelman has not said whether he will accept the $1 million prize offered by the Clay Mathematics Institute, based in Cambridge, Mass., to the individual who first proves the Poincaré conjecture.

Weindlin Werner of the University of Paris-Sud was the fourth Fields medalist, recognized by the IMU for his work on some of "the most exciting and fruitful interactions between mathematics and physics in recent times."

Founded at the behest of John Charles Fields, a Canadian mathematician, the Fields Medal recognizes "work already done and as an encouragement for further achievements on the part of the recipient."

The medal was first awarded in 1936 and, after a pause during World War II, has been regularly awarded since 1950. Winners each receive an award of about $13,400.

Previous Fields Medal prizewinners with Princeton affiliations include Atle Selberg (1950), Kunihiko Kodaira (1954), John Milnor (1962), Charles Fefferman (1978), William Thurston (1982), Gerd Faltings (1986) and Edward Witten GS '76 (1990).