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p = np doesn't produce any value though, the stuff you learn solving it might but the fact that they are the same wouldn't be valuable at all.

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sure, agreed, but once you have a proof, you can probably get AI to reduce other problems to that problem in P.

Why wouldn't you be able to do that without a proof? I don't see the value of the proof here, just ask the AI to solve the problem you want and the proof isn't needed.

From my understanding, the two are equivalent; if you can reduce an NP problem to a P problem, you've proven P=NP. The rest is application.

Why would it not be able to find reductions now, but be able to find them just by being told that P=NP is definitely true?

Well then, just tell the AI that the statement is true and it will find reductions!

In reality, it wouldn't depend on the truth value of the statement, but on the AI understanding the proof. If it understands it then it might be able to use it to find reductions.

So the point remains, knowing that P=NP isn't what's important, it's the proof that matters.

Sure, we monkeys don't need to care, though.

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