Grigori Perelman isn’t much for prizes. This week Perelman, one of the world best and strangest mathematicians, proved it again by turning down a $1 million dollar prize from the Clay Mathematics Institute Millennium Prize for solving one of the most troubling math problems of the last century.
The Poincaré conjecture, named after prominent French mathematician Henri Poincaré, involves a complex problem in the field of topology — an important area of math that studies the enduring properties of objects that are stretched or otherwise deformed, but not torn or otherwise reconstituted. Scores of prominent mathematicians tried to solve it over decades but failed, leading to its characterization as the Mount Everest of math [Washington Post].
In 2003 Perelman put forth his solution to the conjecture, but not in the traditional way of putting it through the peer review process. Instead, he simply emerged from the shadows and threw his work up on the Internet with in a rebellious, “ta-da,” and waited for the world to catch up.
After a brief barnstorming tour in the United States, during which he refused interviews, Dr. Perelman returned to Russia, leaving the world’s mathematicians to pick up the pieces and decide whether he had really done it. A worldwide race to retrace, explicate and check Dr. Perelman’s proof ensued. In the meantime, Dr. Perelman quit his post at the Steklov Mathematical Institute, moved in with his mother and ceased communicating with the outside world [The New York Times].
Therefore, confirming what Perelman had achieved took several years of work fraught with difficulty understanding his methods (and rivalry with mathematicians like Shing-Tung Yau), as documented in a great New Yorker piece on Perelman from 2006.
It was astonishingly brief for such an ambitious piece of work; logic sequences that could have been elaborated over many pages were often severely compressed. Moreover, the proof made no direct mention of the Poincaré and included many elegant results that were irrelevant to the central argument. But, four years later, at least two teams of experts had vetted the proof and had found no significant gaps or errors in it. A consensus was emerging in the math community: Perelman had solved the Poincaré. Even so, the proof’s complexity—and Perelman’s use of shorthand in making some of his most important claims—made it vulnerable to challenge. Few mathematicians had the expertise necessary to evaluate and defend it [New Yorker].
Perelman turned down the 2006 Fields Medal, and now has officially turned down the Clay prize as well. The reason, according to the reclusive Perelman, is that he built on the work of the American mathematician Richard Hamilton, who deserves as much credit as him. The Clay leaders tried to convince Perelman he should accept, since all great work is built on the shoulders of giants. But, true to form, the eccentric genius stays quiet and hidden away in Russia.
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Image: American Mathematical Society