Well then, just tell the AI that the statement is true and it will find reductions!
replyIn 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.
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.
replyWhy 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?
replyFrom 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.
replyYes but it's also possible that there are other proofs. The point remains, the content of the proof is what matters, not that the statement is proven.
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