Whether P and NP are equal
The Clay Mathematics Institute will pay one million U.S. dollars to whomever can prove whether the problems whose solutions are efficiently found ( Class P) are the same as the problems whose solutions are efficiently verified ( Class NP).
It is known that all problems in Class P are contained within Class NP, since one can efficiently solve the problem and compare it to the proposed solution. But it is unknown if NP contains any problems that are not in P.
The general conjecture is that $P \neq NP$.