P vs. NP problem

The P vs. NP problem asks is it's possible to finding a solution to a problem as quickly it is to verify it. P and NP refers to the complexity classes of these problems.

P vs. NP is one of the seven Millennium Prize Problems

The question Does every problem that can be quickly checked (NP) can also be quickly solved (P) ? If you can efficiently verify an answer, can you also efficiently find the answer in the first place?

The answer We don't know the answer yet. There is 2 possible scenarios.

$P=NP$ It means that all problems for which we can check solutions in polynomial time can also be solved with the same time complexity.

$P\ne NP$ It means there are problems where checking solutions require polynomial time, but finding solutions is inherently more complex.