The P vs NP Problem – The Millennium Prize Question

P is the set of problems that can be solved quickly (polynomial time). NP is the set where solutions can be verified quickly. The question: does P = NP? If yes, many hard problems (factoring, SAT, travelling salesman) become easy – breaking most cryptography. Most experts believe P ≠ NP. This is the most important open problem in computer science. One consequence: if P = NP, then every creative act of mathematical proof could be automated. The $1 million prize remains unclaimed.