Maybe the real question is whether polynomial time is quick.

P versus NP is one of computer science’s central unsolved problems. It asks whether every problem whose solution can be verified efficiently can also be solved efficiently. Problems in P have algorithms that run in polynomial time, while problems in NP have proposed solutions that can be checked in polynomial time. If P equals NP, many notoriously difficult search and optimization problems would suddenly become tractable in principle. If not, some problems are fundamentally easier to verify than to discover. That simple question marks a deep boundary around efficient computation. It is used primarily in computational complexity, algorithm design, and cryptography.