succinctly: it is supposed, but not yet proved, that P != NP. where P is the class of problems with optimal algorithmic solution that is polynomial time complexity and NP is the class of problems where proposed solutions can be checked in polynomial time complexity but...
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The main benefit, in my experience, to learning about complexity classes (P, NP), is understanding when I'm _wasting my time_ trying to solve an impossible problem.
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So even if it takes you a few hours upfront to understand the P=NP problem statement, you'll end up avoiding hours spent thinking up bad/wrong algorithms for NP-complete problems.
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It also teaches you how to _frame_ problems more correctly, which is important if you want a shot at solving them. But I guess in practice you can hire an ex-Ph.D. student to do these things for you.
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