I’m not sure about the Riemann hypothesis since there’s a likely chance that RH is undecidable in ZFC. But this might be more safe if one adds a time limit to when one wants the answer by.
But simply in terms of specification I agree that formalizing “don’t get out of your box” is probably easier than formalizing what all of humanity wants.
Why? I know certain people (i.e. Chaitin, who’s a bit cranky in this regard) have toyed around with the idea, but is there any reason to believe it?
Not any strong one. We do know that some systems similar to the integers have their analogs to be false, but for most analogs (such as the finite field case) it seems to be true. That’s very weak evidence for undecidability. However, I was thinking more in contrast to something like the classification of finite simple groups as of 1975 where there was a general program of what to do that had no obvious massive obstructions.
I’m not sure about the Riemann hypothesis since there’s a likely chance that RH is undecidable in ZFC. But this might be more safe if one adds a time limit to when one wants the answer by.
But simply in terms of specification I agree that formalizing “don’t get out of your box” is probably easier than formalizing what all of humanity wants.
Why? I know certain people (i.e. Chaitin, who’s a bit cranky in this regard) have toyed around with the idea, but is there any reason to believe it?
Not any strong one. We do know that some systems similar to the integers have their analogs to be false, but for most analogs (such as the finite field case) it seems to be true. That’s very weak evidence for undecidability. However, I was thinking more in contrast to something like the classification of finite simple groups as of 1975 where there was a general program of what to do that had no obvious massive obstructions.