Many a mathematician's richest fantasies were realized last week when:
1.1. The Poincaré conjecture, described as "one of the most burning mathematical questions of all time," was declared almost certainly solved. And:
1.2. This Poincaré plot, full of intrigue, prizes and power plays, transformed the normally anonymous calculations of mathematicians into fodder for headlines worldwide.
The central character in this drama, however, was less than a willing participant. Despite winning the Fields Medal on Tuesday for his work on the Poincaré, reclusive Russian mathematician Grigory Perelman not only declined to attend the International Congress of Mathematicians in Madrid to accept his prize -- from the King of Spain no less -- he refused the medal altogether.
The shy, though obstinate 40-year-old is the first person to reject what is considered the Nobel of math. And, according to an article in The New Yorker, he also resigned from the Steklov Mathematics Institute in St. Petersburg last December, quitting mathematics altogether. His objections: the community's questionable ethics and unseemly politicking around his work.
All of which has raised speculation as to whether Dr. Perelman will also turn down the $1-million (U.S.) Millennium Prize offered by the Clay Mathematics Institute (a think tank in Cambridge, Mass.) for the first person to prove the century-old Poincaré. Or, for that matter, whether any one mathematician in a supremely collaborative field can really claim credit at all.
The Poincaré plot is particularly fraught in this respect, because Dr. Perelman provided only a rough sketch of his strategy to solve the conjecture. He posted two papers on an on-line "preprint" archive, and then ostensibly abandoned his work, deliberately leaving it to stand or fall on its own merit. Three camps of mathematicians rushed in to flesh out the details -- so the question then becomes who really provided a comprehensive and complete proof?
Sir John Ball, the president of the International Mathematical Union, made a not-so-veiled reference to this in his opening address at the ICM. "We freely discuss our work with others without fear of it being stolen, and research is communicated openly prior to formal publication," he said. "Editorial procedures are fair and proper, and work gains its reputation through merit and not by how it is promoted. . . . The exceptions are rare, and they are noticed."
The most notable exception in the Poincaré imbroglio is Chinese mathematician Shing-Tung Yau. Now at Harvard, the 57-year-old is known in the math world for being unpleasantly competitive -- a trait that can be attributed in part to his zeal for building the mathematical enterprise in China.
Dr. Yau is a celebrated mathematician, for a theorem uniting topology and geometry, and seminal work pertaining to string theory. He won a Fields medal in 1982. He has dabbled with the Poincaré since the 1970s, and two of his former students wrote one of the papers explicating Dr. Perelman's results.
But lately, Dr. Yau has been manoeuvring for more photons of the limelight than he deserves, promoting his students' work as an original contribution, rather than a compliment to Dr. Perelman's insights.
In contrast, the purist Dr. Perelman -- who makes quite an impression with nails that are apparently inches long -- is described as living on an "ideal plane," governed, like the discipline of mathematics, by absolute axioms.
Rather than chasing renown, he treasures his privacy and shuns material trappings. In the 1990s, he refused a prize from the European Mathematical Society, and the 6,000 euros that went with it. The current monetary value of the Fields is $13,000 (U.S.).
