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If it is known that A is provably true then one can study the consequences of A being true. It changes things becuase the body of knowledge has expanded.

by czgov 29d ago

mahdi7d1 28d ago
In this case won't this oracle also tell you what is the consequences as soon as it tells you RH is true and also much more? At this point what is the point of you knowing what is true and what is not?
- czgov 28d ago
  There is no actual oracle. In this discussion oracle means Lean.
saithound 28d ago
> If it is known that A is provably true then one can study the consequences of A being true But one can already study the consequences of P=NP right now. You don't need to know that it's provably true in order to do that. Knowing an actual proof would be useful, but an oracle revealing merely that it's true (or even provable) without telling you the proof does not let you do anything you couldn't do before.
- czgov 28d ago
  Some people (almost all mathematicians) wouldn’t want to spend time on consequences of a false statement. In the present discussion it’s not about letting me do something I can’t do now but about whether or not the endeavor is worthwhile. A lot of people spent a lot of time and effort to prove or disprove the Jacobian Conjecture. AI solved it easily. It is increasingly becoming the case that humans are not as good at mathematics as computers. You are free to ignore computer generated proofs but I don’t think this position will win out in the long run.
  - skinner_ 28d ago
    > Some people (almost all mathematicians) wouldn’t want to spend time on consequences of a false statement. No, people constantly prove statements of the form "if P=NP, then strange implication X". They do not consider it wasted effort at all, because of the contrapositive: if X is indeed very strange, they might be able to prove that it is false, and then they've settled P!=NP.
    - czgov 28d ago
      If a counterexample to a conjecture is found then all work toward proving consequences of the conjecture will cease. No one is trying to discover consequences of the Jacobian Conjecture now. At some point an AI will prove a result that is so long and complicated that no human will understand it. This should not preclude people from using that result. In general, whenever the body of knowledge is increased it is a good thing. Even if it isn’t increased by humans.

If it is known that A is provably true then one can study the consequences of A being true. It changes things becuase the body of knowledge has expanded.

by czgov 29d ago

If it is known that A is provably true then one can study the consequences of A being true. It changes things becuase the body of knowledge has expanded.

mahdi7d1 28d ago

In this case won't this oracle also tell you what is the consequences as soon as it tells you RH is true and also much more? At this point what is the point of you knowing what is true and what is not?

czgov 28d ago
There is no actual oracle. In this discussion oracle means Lean.

saithound 28d ago

> If it is known that A is provably true then one can study the consequences of A being true But one can already study the consequences of P=NP right now. You don't need to know that it's provably true in order to do that. Knowing an actual proof would be useful, but an oracle revealing merely that it's true (or even provable) without telling you the proof does not let you do anything you couldn't do before.

czgov 28d ago
Some people (almost all mathematicians) wouldn’t want to spend time on consequences of a false statement. In the present discussion it’s not about letting me do something I can’t do now but about whether or not the endeavor is worthwhile. A lot of people spent a lot of time and effort to prove or disprove the Jacobian Conjecture. AI solved it easily. It is increasingly becoming the case that humans are not as good at mathematics as computers. You are free to ignore computer generated proofs but I don’t think this position will win out in the long run.
- skinner_ 28d ago
  > Some people (almost all mathematicians) wouldn’t want to spend time on consequences of a false statement. No, people constantly prove statements of the form "if P=NP, then strange implication X". They do not consider it wasted effort at all, because of the contrapositive: if X is indeed very strange, they might be able to prove that it is false, and then they've settled P!=NP.
  - czgov 28d ago
    If a counterexample to a conjecture is found then all work toward proving consequences of the conjecture will cease. No one is trying to discover consequences of the Jacobian Conjecture now. At some point an AI will prove a result that is so long and complicated that no human will understand it. This should not preclude people from using that result. In general, whenever the body of knowledge is increased it is a good thing. Even if it isn’t increased by humans.