The Millennium Prize Problems consist of 7 profound, unsolved mathematical puzzles curated by the Clay Mathematics Institute of Cambridge, Massachusetts (CMI) in 2000. A prize fund of $7M has been allocated to award to winners, with $1M set aside for the solver(s) of each big problem.
All told, the set includes:
- Yang–Mills and Mass Gap
- Riemann Hypothesis
- P vs NP Problem
- Navier–Stokes Equation
- Hodge Conjecture
- Poincaré Conjecture
- Birch and Swinnerton-Dyer Conjecture
Of these monster math problems, only one has been officially solved--the Poincaré Conjecture, by Grigori Perelman. Per Medium:
[Perelman] is the first and only one to have solved one of the Millennium Problems and, according to many, this situation may not change for a long time. He is also the first and only to have declined both the Fields Medal and the Millennium prize. His justification highlights both his peculiar personality and his deep commitment to mathematics for their own sake: "I’m not interested in money or fame. I don’t want to be on display like an animal in a zoo. I’m not a hero of mathematics. I’m not even that successful; that is why I don’t want to have everybody looking at me."
At some point, one assumes, at least one of the other problems will fall. (Other geniuses have already come close and banged on the door of success.)