Science history: Russian mathematician quietly publishes paper — and solves one of the most famous unsolved conjectures in mathematics — Nov. 11, 2002
QUICK FACTS
Milestone: Poincaré conjecture solved
When: November 11, 2002
Or: St. Petersburg, Russia
WHO: Grigori Perelman
On a cold November day, a man living quietly in Russia posted an article on a public server.
The newspaper was the first of three published the following year, resolving the long-standing Poincaré conjecture, a hypothesis posed almost a century earlier by Henri Poincaré.
Simply put, Poincaré theorized that if you were to take any type of 3D space – from a cat to the Empire State Building – and draw a 2D loop on it, if you could shrink that loop down to a point without breaking either the loop or the shape, then the space is mathematically equivalent to a sphere.
Proving this conjecture was crucial to topology, the mathematical study of shapes. The mathematician Stephen Smale had solved the five-dimensional conjecture in 1961thus winning the prestigious Fields Medal in mathematics. But the case of 3D proved to be the most intractable.
In the 1980s, Richard Hamilton, a mathematician at Columbia University, proposed solving the conjecture using a mathematical technique called Ricci flow, which had been useful for Einstein’s theory. general relativityas well as string theory.
In 2006, New York Times reporter Dennis Overbye compared Ricci flow technique of using the heat of a hair dryer to smooth the shrink film. In the same way, Ricci flow could smooth out wrinkles and bends and reduce a complicated shape to a more fundamental one.
Ricci flow helped simplify rounded shapes into spheres, but singularities – points of infinite density – continued to appear in more complex shapes. Topologists can perform a sort of “surgery” to excise these singularitiesbut it was always possible that the singularities would continue to emerge forever. The researchers were stuck.
Perelman’s work solved the singularity problem. Perelman (whose first name is Grigori, also spelled Grigory; Grisha was a nickname) had spent the previous decade doing postdoctoral research in the United States at several institutions. In the mid-1990s, he turned down highly prestigious mathematics scholarships in the United States and Europe, returned to St. Petersburg, and accepted a position at the Steklov Institute of Mathematics.
Look on it
The friendly but shy and “preternatural” mathematician “looked like Rasputin, with long hair and nails,” and he told colleagues that he enjoyed hiking in the woods around St. Petersburg, hunting mushrooms, Robert Greenemathematician at UCLA, told Overbye in 2006. He seemed completely uninterested in wealth or material success, his colleagues reported.
Perelman faded into obscurity after returning to Russia in the mid-to-late 1990s, and many of his colleagues thought he had abandoned mathematics altogether.
Then Perelman published his 2002 paper. Over the next year, he published two more papers and gave a series of lectures at several colleges on the East Coast, explaining his approach. Then he retreated into the background again.
Perelman’s work showed that all singularities were actually reduced to simple shapes, like spheres or tubes, and that if one could follow Ricci’s process through to the end, one would find the 3D shape reduced to a sphere. He had proven Poincaré’s conjecture, but it would take a few more years for mathematicians to go through his brilliant, original and highly technical demonstrations and confirm that the great topographical problem had indeed been solved.
In 2006, mathematicians John Morgan and Gang Tian published a 473 page paper showing that Perelman’s work, building on that of Hamilton, actually proved this elusive conjecture.
Perelman was awarded the prestigious Fields Medal and the Clay Millennium Mathematics Prize, who came with a million dollar reward. He turned them down, apparently because of objections to how credit was given for fixing the problem.
Perelman resigned from his position at the Steklov Institute in 2005 and has since fiercely avoided the limelight. It is unclear whether he still works in mathematics in his St. Petersburg apartment, where, as early as the early 2010s, his neighbors said he took care of his elderly mother.
When a journalist tried to contact him in 2010, he refused an interviewsaying: “You’re bothering me. I’m picking mushrooms.”
