Lost in Mathmagic Land

I rarely balance my checkbook, but I can read about theoretical mathematics all day long. This story has an added dimension—a missing-person subplot worthy of a Holmes story—that, unforunately, makes it essentially irresistible:

Three years ago, a Russian mathematician by the name of Grigory Perelman, a k a Grisha, in St. Petersburg, announced that he had solved a famous and intractable mathematical problem, known as the Poincaré conjecture, about the nature of space.

After posting a few short papers on the Internet and making a whirlwind lecture tour of the United States, Dr. Perelman disappeared back into the Russian woods in the spring of 2003, leaving the world’s mathematicians to pick up the pieces and decide if he was right.

Now they say they have finished his work, and the evidence is circulating among scholars in the form of three book-length papers with about 1,000 pages of dense mathematics and prose between them.

As a result there is a growing feeling, a cautious optimism that they have finally achieved a landmark not just of mathematics, but of human thought.

“It’s really a great moment in mathematics,” said Bruce Kleiner of Yale, who has spent the last three years helping to explicate Dr. Perelman’s work. “It could have happened 100 years from now, or never.”

In a speech at a conference in Beijing this summer, Shing-Tung Yau of Harvard said the understanding of three-dimensional space brought about by Poincaré’s conjecture could be one of the major pillars of math in the 21st century.

Quoting Poincaré himself, Dr.Yau said, “Thought is only a flash in the middle of a long night, but the flash that means everything.”

But at the moment of his putative triumph, Dr. Perelman is nowhere in sight. He is an odds-on favorite to win a Fields Medal, math’s version of the Nobel Prize, when the International Mathematics Union convenes in Madrid next Tuesday. But there is no indication whether he will show up.

Also left hanging, for now, is $1 million offered by the Clay Mathematics Institute in Cambridge, Mass., for the first published proof of the conjecture, one of seven outstanding questions for which they offered a ransom back at the beginning of the millennium.

“It’s very unusual in math that somebody announces a result this big and leaves it hanging,” said John Morgan of Columbia, one of the scholars who has also been filling in the details of Dr. Perelman’s work. …

Let’s hope Perelman appears in three-dimensional space to collect his prize. I do love the math, but I’m likewise drawn to physics and astronomy (particularly the pop stuff about M-theory and Inflation Theory), though I’m no better at those particular hard sciences than I am at math. For anyone who’s interested, Fantasia Mathematica was the book that first started this particular fascination (and Donald Duck of course) and Genius (James Gleick’s biography of Richard Feynman) boosted it along. Perhaps mathematicians who enjoy a good political satire will holla back.

THRILLING UPDATE! So the elusive Grigory Perelman did indeed win and turned down the prize — !! — after being visited in St. Petersburg, Russia, by Sir John Ball, the president of the International Mathematical Union (they’re unionized! who knew!). According to Ball in Kenneth Chang’s NY Times account, “The reasons center around his feeling of isolation from the mathematical community… and in consequence his not wanting to be a figurehead for it or wanting to represent it.”

Wow! Now *that’s* an awkward afternoon tea. I can hear the hungry playwrights sharpening up their pencils now!

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