What will the world look like if P=NP is proven true? I know it's likely not the case, but what if? Would society end?AI advancement is scaring me
It doesn't matter because we won't have an algorithm to solve NP-complete problems in P-time. Even if we did, it would probably have a constant factor of 10^10^100 making it useless in reality.
does every problem have shortcuts that can be quickly checkedsociety will not end, sorry
>>17051734>I know it's likely not the case, but what if? That's what they said about Navier-Stokes too. >"Experts estimate a 10% chance that Al will solve or substantially assist in solving a Millennium Prize Problem by 2027,2 up to 20% by 2030, and 60% by 2040.4 All categories of experts, superforecasters, and the public largely predict"Sorry fags. AI can't be stopped.
>>17051741>That's what they said about Navier-Stokes too. I mean P=NP being true. I know most experts believe it's most likely not true, so if AI solves it (which it very well might), then it'd probably be through disproving it.
>>17051734>Would society end?If it's true AND there is a general algorithm, then yes, we're toast.
>>17051776how would it end society? t. non-mathfag
>>17051777P=NP would mean that solving and verifying a solution can, in principle, take the same amount of time. If a general algorithm for solving problems exists, it could enable arbitrarily rapid discovery of better AI architectures. Basically you get a FOOM scenario like something out of a Yudkowsky story.
>>17051734Absolutely nothing.P=NP doesn't imply you actually know the algorithm to turn any problem NP into P.Even if you did have an algorithm its constant factors could still make it absolutely useless in practice.
>>17051789All instances of NP are reducible onto each other, so if you solve one you solve them all. They just need to solve one NP problem in polynomial time.
