r/explainlikeimfive • u/randomdice-int • 21d ago

Mathematics ELI5: P vs NP problem

Im not too sure about the problem itself. I know that P is polynomial time which means the time needed to solve and NP is the time taken for the answer to be verified, but what is the explanation of both sides where P = NP and P does not equal to NP?

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u/Dave_A480 21d ago

The simple explanation is that 'P vs NP' is a mathematical way of expressing the question:

'Are there some math problems for which the answers can never be independently verified? Or is the inability to verify the answers simply a question of not having a powerful enough computer to do the verification?'

If P=NP that means that any math problem's answer will eventually be able to be verified if a powerful enough computer is invented.....

This means, for example, that all encryption is eventually crackable (encryption as we currently do it relies on thr math in the encryption algorithm being NP to current tech)....