Have the Poincaré Conjecture and the Thurston Geometrization Conjecture been proved? This question has been on the minds of mathematicians for more than three years, ever since Grigory Perelman posted his now-famous papers on the Web. In midsummer 2006, as the International Congress of Mathematicians in Madrid approaches and speculation about the Fields Medalsis buzzing, some experts who had been making cautious statements for the past three years sound increasingly confident that the conjectures are finally yielding. In particular, many believe the Poincaré Conjecture is now a bona fide theorem. The picture is slightly less clear for the Geometrization Conjecture, but there is much optimism thatthis result will soon be established as well.
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