Understanding NP-Hardness and Its Impact

In this video, we discuss NP-hardness. If we solved any NP-hard problem in polynomial time, we could solve millions of problems in NP in polynomial time. NP-complete problems are NP-hard problems which are also in NP. That makes NP-complete problems the most difficult problems in NP. Discovering a polynomial time algorithm for an NP-hard problem would be a major scientific breakthrough.