The Poincaré conjecture posits that any simply connected, closed 3-dimensional manifold is homeomorphic to the 3-dimensional sphere. It was proven by Grigori Perelman in 2003 using Richard S. Hamilton's theory of Ricci flow, marking a significant milestone in the field of topology and earning Perelman the prestigious Clay Millennium Prize, which he declined.

Poincaré Conjecture

Poincaré conjecture

simply connected

closed 3-dimensional manifold

3-dimensional sphere

Grigori Perelman is a Russian mathematician renowned for solving the Poincaré Conjecture, one of the seven Millennium Prize Problems, which had remained unsolved for over a century. Despite being awarded the prestigious Fields Medal and a million-dollar prize, Perelman declined both, citing a lack of interest in recognition and disapproval of the mathematical community's values.

Grigori Perelman

Richard S. Hamilton's theory of Ricci flow

significant milestone

field of topology

The Clay Millennium Prize is a set of seven unsolved mathematical problems, each carrying a reward of one million dollars for a correct solution, established by the Clay Mathematics Institute to advance mathematical knowledge. These problems, known as the Millennium Prize Problems, represent some of the most challenging and profound questions in mathematics, with only one having been solved to date.

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