P versus NP problem

The P versus NP problem is a major unsolved question in computer science. It asks whether every problem that can be quickly checked for a solution (NP) can also be quickly solved (P). To illustrate, if you can easily verify a jigsaw puzzle is complete, can you just as easily piece it together? If P equals NP, it means all problems with quick checks can be quickly solved. If P does not equal NP, there are problems that are easy to verify but hard to solve, which has profound implications for fields like cryptography and optimization.