New mathematical mystery replaces old one...

The Poincate conjecture, in mathematics, can be explained as follows...

(It) is a conjecture about the characterisation of the three-dimensional sphere amongst three-dimensional manifolds. Loosely speaking, the conjecture surmises that if a closed three-dimensional manifold is sufficiently like a sphere in that each loop in the manifold can be shrunk to a point, then it is really just a three-dimensional sphere. The analogous result has been known to be true in higher dimensions for some time.

An easier to understand definition...

It asserts that if any loop in a certain kind of three-dimensional space can be shrunk to a point without ripping or tearing either the loop or the space, the space is equivalent to a sphere.

First presented by Henri Poincare, in 1904, it is widely acknowledged as one of the few outstanding questions in mathematics. Three years ago, a Russian Mathematician, Grigory (Grisha) Perelman, from St. Petersburg, announced by posting a few papers on the internet, that he has solved this intractable problem, and then after a few brief lectures and talks, disappeared from plain sight !

Most experts believe that he is a serious candidate for the Fields medal, the highest honour in mathematics, if he shows up ! Some excerpts...

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.
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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.
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Mathematicians have been waiting for this result for more than 100 years
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once he was back in St. Petersburg, he did not respond to further invitations. The e-mail gradually ceased.
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Recently, Dr. Perelman is said to have resigned from Steklov. E-mail messages addressed to him and to the Steklov Institute went unanswered.

So, it seems that the new mystery is to find the mathematician who cracked one of the more famous mysteries in mathematics...

The list of Perelman's papers that present the solution.

[Images obtained from here and here.]