In November , a Russian mathematician named Grigori Perelman posted the first of three short preprints to the arXiv an online repository for drafts of academic papers in math and science , offering a proof for the famous Poincare conjecture —one of the toughest remaining unsolved problems in mathematics, although partial solutions had been made over the decades since it was first proposed in Rumor had it that Perelman did not even plan to publish a formal paper. It was such a momentous achievement that in , Perelman was awarded the Fields Medal, the highest honor in mathematics. All sought to answer the burning question: What would drive a man to shun all fame and recognition—well-deserved, I might add—and withdraw from the world altogether? Certainly, Perelman had always been eccentric.

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In Perelman had left academia and apparently had abandoned mathematics. He was the first mathematician ever to decline the Fields Medal. Perelman earned a doctorate from St. Petersburg State University and then spent much of the s in the United States, including at the University of California , Berkeley.

He was still listed as a researcher at the Steklov Institute of Mathematics, St. Petersburg University, until Jan. In the s Thurston won a Fields Medal for his efforts to extend the geometric classification of two-dimensional manifolds to three dimensions. In the American mathematician Richard Hamilton took up the idea of studying how a manifold develops as its curvature is smoothed out, using what is known as a Ricci flow after the Italian mathematician Gregorio Ricci-Curbastro.

Much was achieved, but Hamilton reached an impasse when he could not show that the manifold would not snap into pieces under the flow.

It is generally believed that the techniques he introduced will have a profound influence on other branches of geometry and analysis. As he had done with the Fields Medal, Perelman refused the prize. Get exclusive access to content from our First Edition with your subscription. Subscribe today.

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## Perelman's Solution

In Perelman had left academia and apparently had abandoned mathematics. He was the first mathematician ever to decline the Fields Medal. Perelman earned a doctorate from St. Petersburg State University and then spent much of the s in the United States, including at the University of California , Berkeley. He was still listed as a researcher at the Steklov Institute of Mathematics, St. Petersburg University, until Jan.

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## Poincaré conjecture

He was particularly interested in what topological properties characterized a sphere. In this way he was able to conclude that these two spaces were, indeed, different. Is it possible that the fundamental group of V could be trivial, even though V is not homeomorphic to the 3-dimensional sphere? Here is the standard form of the conjecture: Every simply connected , closed 3- manifold is homeomorphic to the 3-sphere.

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