"Can we find solutions as easily as we check them?"
P vs NP is one of the seven Millennium Prize Problems in mathematics. Simply put: "If it's easy to check a solution, is it also easy to find one?" Multiplication is easy to calculate and check (P), but prime factorization of huge numbers is hard to solve but easy to check if given the answer (NP).
Modern encryption (like RSA) relies on the assumption that P ≠ NP. If someone proves P = NP (finding a fast algorithm for hard problems), all global encryption systems could be broken instantly.
This problem asks about the fundamental limits of computers. For NP problems like the Traveling Salesman Problem, computation time explodes as inputs grow. If P = NP, efficient shortcuts would exist for all these hard problems. Most scientists believe P ≠ NP, but it remains unproven.