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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.”

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So, I can't tell if this work is correct.

But it is interesting in connection with Kant, of all people. He claimed that the categories of experience, such as the perception of space, could never be placed on a scientific basis.

At first blush, this theory might have implications for that, and thus for deeper philosophical issues.

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Originally posted by jeff house:
[Kant] claimed that the categories of experience, such as the perception of space, could never be placed on a scientific basis.

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I get confused with any mathematics which insists on more than two decimal points for the value of pi.

So, I can't tell if this work is correct.

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Can't resist - that's why you're a lawyer??

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]By the way, it's way kewl when an important mathematical conjecture is closed. Ever see the Nova episode on Fermat's Last Theorem?

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The book by Simon Singh is a really good read.

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Fact is, the discussion has apparently been reduced to a few thousand pages of mathematics. Stuff at this level is never straightforward.

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I doubt there are more than a few dozen people in the world who will ever understand the whole thing.

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Originally posted by abnormal:

Fact is, the discussion has apparently been reduced to a few thousand pages of mathematics. Stuff at this level is never straightforward.

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Dear God. I really hope the Catholic Church is wrong about the whole hell thing, because I think I just had a flash of what mine would be.

'Solve this, sinner!'

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Poincaré conjectured that three-dimensional shapes that share certain easy-to-check properties with spheres actually are spheres. What are these properties? My fellow geometer Christina Sormani describes the setup as follows:

The Poincaré Conjecture says, Hey, you've got this alien blob that can ooze its way out of the hold of any lasso you tie around it? Then that blob is just an out-of-shape ball. [Grigory] Perelman and [Columbia University's Richard] Hamilton proved this fact by heating the blob up, making it sing, stretching it like hot mozzarella, and chopping it into a million pieces. In short, the alien ain't no bagel you can swing around with a string through his hole.

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A maths genius who won fame last week for apparently spurning a $US1 million prize is living with his mother in a humble flat in St Petersburg, co-existing on her $A75-a-month pension because he has been unemployed since December.

The eccentric recluse stunned the maths world when he solved a century-old puzzle known as the Poincare Conjecture. Grigory "Grisha" Perelman's predicament stems from an acrimonious split with a top Russian mathematical institute in 2003.

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