As mentioned above, one of the seven problems has been solved. In 2002, Russian mathematician Grigori Perelman proved the Poincaré Conjecture, which had stumped mathematicians since 1904. The CMI describes the problem in full on the prize website, but put simply, it says that a three-sphere—a higher-dimensional sphere, kind of like a tesseract is a higher-dimensional cube—is the only possible type of bounded three-dimensional space that contains no holes. Another astounding piece of this story? Perelman turned down the $1 million prize. In 2002, Perelman also refused to accept the Fields Medal, which is the highest honor in mathematics. No one had ever turned down this distinction before. You're probably wondering why. That's another unanswered question for you to solve.

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