Sunday, August 27, 2006

Noble, not Nobel...


Prestigious Award, ‘Nobel’ of Mathematics, Fails to Lure Reclusive Russian Problem Solver

by Kenneth Chang

Grigory Perelman, a reclusive Russian mathematician who solved a key piece in a century-old puzzle known as the Poincaré conjecture, was one of four mathematicians awarded the Fields Medal yesterday.

But as with previous honors, Dr. Perelman refused to accept this one, and he did not attend the ceremonies at the International Congress of Mathematicians in Madrid.

“I regret that Dr. Perelman has declined to accept the medal,” Sir John M. Ball, president of the International Mathematical Union, said during the opening ceremonies.

The Fields Medal, often described as mathematics’ equivalent to the Nobel Prize, is given every four years. The other Fields medalists this year are Andrei Okounkov, a professor of mathematics at Princeton; Terence Tao, a professor of mathematics at the University of California, Los Angeles; and Wendelin Werner, a professor of mathematics at the University of Paris-South in Orsay, France.

Dr. Perelman, 40, is known not only for his work on the Poincaré conjecture, among the most heralded unsolved math problems, but also because he has declined previous mathematical prizes and has spurned offers from Princeton, Stanford and other universities. He has shown no interest in pursuing the $1 million that the Clay Mathematics Institute in Cambridge, Mass., is offering for the first published proof of the conjecture.

In June, Sir John went to St. Petersburg, Russia, where Dr. Perelman lives, and spent two days trying to persuade him to travel to Madrid to accept the Fields. “He was very polite and cordial and open and direct,” Sir John said in an interview.

And Dr. Perelman was resolute in saying no. “The reasons center around his feeling of isolation from the mathematical community,” Sir John said, “and in consequence his not wanting to be a figurehead for it or wanting to represent it.” He added: “I don’t think he meant it as an insult. He’s a very polite person. There was never a cross word.”

Despite Dr. Perelman’s refusal, he is still officially a Fields medalist. “He has a say whether he accepts it, but we have awarded it,” Sir John said.

Beginning in 2002, Dr. Perelman, then at the Steklov Institute of Mathematics of the Russian Academy of Sciences in St. Petersburg, published a series of papers on the Internet and gave lectures at several American universities describing how he had overcome a roadblock in the proof of the Poincaré conjecture.

The conjecture made by Henri Poincaré in 1904 essentially says that any shape that does not have any holes and fits within a finite space can be stretched and deformed into a sphere. That is certainly true looking at two-dimensional surfaces in the everyday three-dimensional world, but the conjecture says the same is true for three-dimensional surfaces embedded in four or more dimensions.

Dr. Perelman solved a problem other mathematicians had encountered when trying to prove the conjecture using a technique called Ricci flow that smoothes out bumps in a surface and transforms the surfaces into simpler forms.

Dr. Okounkov, born in 1969 in Moscow, was recognized for work linking different fields of mathematics that had seemed unrelated. “This is the striking feature of Okounkov’s work, finding unexpected links,” said Enrico Arbarello, a geometry professor at the University of Rome.

Dr. Okounkov’s work has found use in describing the changing surfaces of melting crystals. The boundary between melted and nonmelted is created randomly, but the random process inevitably produces a border in the shape of a heart.

Dr. Tao, a native of Australia and, at age 31, one of the youngest to win a Fields Medal, has worked in several fields, producing significant advances in the understanding of prime numbers, techniques that might lead to simplifying the equations of Einstein’s theory of general relativity.

Dr. Werner, born in Germany in 1968, has also worked at the intersection of mathematics and physics, describing phenomena like percolation and shapes produced by minute particles jittering randomly in a process known as Brownian motion.

The medal, first awarded in 1936, was conceived by John Charles Fields, a Canadian mathematician, “in recognition of work already done and as an encouragement for further achievements on the part of the recipient.” That stipulation has been interpreted to mean that the award should usually be limited to mathematicians 40 or younger.

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