- Birch and Swinnerton-Dyer conjecture, (Unsolved)
- Hodge conjecture, (Unsolved)
- Navier–Stokes existence and smoothness, (Unsolved)
- P versus NP problem, (Unsolved)
- Poincaré conjecture, (Solved)
- Riemann hypothesis, and (Unsolved)
- Yang–Mills existence and mass gap. (Unsolved)
If you solve any of the above problem, you will won US $1 million prize being awarded by the institute to the discoverers.At present, the only Millennium Prize problem to have been solved is the Poincaré conjecture, which was solved by the Russian mathematician Grigori Perelman in 2003.
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