The P versus NP problem is the determination of whether all NP-problems are actually P-problems. If P and NP are not equivalent, then the solution of NP-problems requires (in the worst case) an exhaustive search, while if they are, then asymptotically faster algorithms may exist.
The answer is not currently known, but determination of the status of this question would have dramatic consequences for the potential speed with which many difficult and important problems could be solved.
In the Season 1 episode "Uncertainty Principle" (2005) of the television crime drama NUMB3RS, math genius Charlie Eppes uses the game minesweeper as an analogy for the P vs. NP problem.
