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Poincaré conjecture

The Poincaré conjecture, before being proven, was one of the most important open questions in [topology] . It is one of the seven [Millennium Prize Problems] , for which the [Clay Mathematics Institute] offered a $1,000,000 prize for the first correct solution. Perelman's work survived review and was confirmed in 2006, leading to his being offered a [Fields Medal] , which he declined. Perelman was awarded the Millennium Prize on 18 March, 2010. The Poincaré conjecture is the first solved [Millennium problem] .

On December 22, 2006, the journal [Science] honored Perelman's proof of the Poincaré conjecture as the scientific " [Breakthrough of the Year] ", the first time this had been bestowed in the area of mathematics.

Poincaré's question
At the beginning of the 20th century, [Henri Poincaré] was working on the foundations of topology—what would later be called [combinatorial topology] and then [algebraic topology] . He was particularly interested in what topological properties characterized a [sphere] .

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