Grisha Perelman Courtesy International Congress of Mathematicians Press Office
Grigory Perelman lives with his mother in an undistinguished apartment in St. Petersburg, Russia. On Tuesday, August 22, rather than being honored at a palace in Madrid, where he would receive a gold medallion from King Juan Carlos of Spain, he was probably in his flat, enjoying a late lunch of borscht or writing equations in solitude.
Perelman is the first person in history to turn down the Fields Medal, mathematics' biggest prize. It's an honor he won the right to refuse by audaciously solving the hundred-year-old Poincaré conjecture.
The week-long International Congress of Mathematicians has attracted nearly 5,000 mathematicians from 100 countries to the Spanish capital. Like the Olympics, the very best travel to the host city from all corners of the globe every four years, where they put their hard work and talents on display and see who takes home the gold medals.
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"There are always lots of rumors swirling around before the Congress," said Columbia University mathematician John Morgan. "And basically everybody is there to see the Fields."
This year's Congress is not unlike a major sporting event--there's the pre-event buzz, not to mention the tender age of most of the competitors.
Like athletics, math is a game for the young. According to an unwritten, but strictly enforced rule, the Fields Medal is awarded to up to four mathematicians 40 years of age or younger. While the Fields is often referred to as the "Nobel Prize of mathematics," at just around $13,500, it's not quite the windfall that a million dollar-plus Nobel would be. (Alfred Nobel actually scrapped the idea of a math prize because of an adversarial relationship with a certain mathematician.)
Around 1994, after having some initial success working on the Soul conjecture, a classical problem in differential geometry, Grisha (as Grigory is called in the Russian tradition of diminutive nicknames) quietly dropped off the mathematics community's radar.
In November of 2002, he emerged from his seclusion, publishing a 39-page missive on the site arXiv.org—a repository for math and physics papers yet to be published in peer-reviewed journals—and alerting a few of his fellow mathematicians to its presence. In March of 2003, another 22 cryptic pages appeared. Four months later, seven more followed. Though he never mentioned it by name, in a mere 68 pages Perelman had apparently solved the Poincaré conjecture, a problem so difficult it had stymied mathematicians for 100 years. (In addition, Perelman had also ostensibly resolved the much bigger Thurston Geometrization Conjecture, of which, Poincaré is just a small piece.)
In 2000, the Clay Mathematics Institute deemed it one of the seven most important unsolved problems in math, placing a $1 million bounty on its head. Bruce Kleiner of the University of Michigan told Nature that Perelman's effect on the landscape of mathematics was similar to "waking up one morning after an earthquake."
Brevity is hardly the soul of wit in mathematics, and the monkish Perelman proved almost too concise.
"In some sense, Perelman did enough, but just barely enough so that any expert in the field could figure it out," said Columbia's Morgan, who, with Gang Tian of MIT, published a 473-page, expanded demonstration of Perelman's proof of the Poincaré conjecture.