@LexYeen@snouts.online
In summary, P is the number of problems that can be checked/verified easily by computers. NP is the number of problems that can be _solved_ by computers computationally. If those sets are the same, the implication is thought to be that there are no problems that can't be solved if enough computing horsepower is thrown at it.
https://simple.wikipedia.org/wiki/P_versus_NP has a more indepth look at the issue. If you solve it, you get $1 million USD!
@kelseyhusky @LexYeen In short, this would be a Big Deal and a lot of things we think of as "safely in the realm of humans because they're too hard for computers to think about like we do" suddenly become computer-solvable.
@orrery @kelseyhusky @LexYeen I doubt humans can solve NP problems either. P != NP wouldn't be an endorsement of humanity's superior abilities over computers. humans "solve" NP problems by approximation, and so can computers. so we are in the same boat
@SuricrasiaOnline @kelseyhusky @LexYeen to be sure, I don't think we "solve" NP problems so much as we perform a level of inductive analysis on them that computers can't do (insert Church's Theorem here, recursively enumerable and recursive languages here).
I'm not arguing humanity is "better" than computers, so much as humanity has the ability to think about problems in ways that computers as yet can't.
@SuricrasiaOnline @kelseyhusky @LexYeen (( Cribbing heavily from Douglas Hofstadter's "Goedel, Escher, Bach": ))I suspect that the big thing separating P and NP problems -- and humans and computers, presently -- is the ability to perform inductive reasoning in finite time.
@kelseyhusky @LexYeen Every problem on this page can now be solved by a computer in human-timescale time: https://en.wikipedia.org/wiki/List_of_NP-complete_problems