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The problems are, the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap.

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The Millennium Prize Problems were seven unsolved problems in mathematics that were stated by the Clay Mathematics Institute on May 24, 2000.[1] The problems are the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap. A correct solution to any of the problems results in a US$1 million prize being awarded by the institute to the discoverer(s).

To date, the only Millennium Prize problem to have been solved is the Poincaré conjecture, which was solved in 2003 by the Russian mathematician Grigori Perelman. He declined the prize money.

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