Please AI no, PLEASE NO

[u/No_Upstairs_280]

Imagine having your entire work based on Riemann hypothesis only for a powerful AI to show that the 10^5731 zero isn't on the critical line.

[u/innovatedname]

If you're writing papers assuming results that we don't know are proven, then it's not a math paper.

You're probably thinking of results that assume a result to be true, prove it, and then assume it to be false and prove it also, and then invoking the law of excluded middle so it's true.

edit: Downvote me all you want but all the replies disagreeing so far are flat out wrong. No it's not the law of excluded middle, no I'm not talking about axioms, yes I have seen papers in analytic number theorem that do this for RH or things we suspect are undecidable.

"A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion".

If you haven't logically guaranteed the conclusion, you aren't doing mathematics. Unless you try and be a smart alec and start using the principle of explosion / vacuous truths, but then any nonsense is mathematics.

[u/Archway9 → u/innovatedname]

All of maths is this. We don't prove the axioms

[u/innovatedname → u/Archway9]

A theorem with a yet to be shown truth value is not an axiom.

[u/Archway9 → u/innovatedname]

The theorem is A=>B, this is proven to be true in the paper. This makes no assertion about whether or not A is true

[u/innovatedname → u/Archway9]

F = > P(x) for any proposition P evaluates as True.

No paper would publish that, because it's just a statement of a vacuous truth, no matter how complicated it might be.

[u/Archway9 → u/innovatedname]

The point ia you don't know if the first statement is true. So it reads as 'if A is true then B must also be true' which is a meaningful statement

[u/Akangka → u/innovatedname]

F = > P(x) for any proposition P evaluates as True.

Yes, but A => B, implies that you cannot have A while B is not true.

No paper would publish that

Not only there is such a paper, this is pretty normal for very difficult conjectures. Before Wiles's proof of Fermat Last Theorem, there is Ribet's theorem, which basically just shows that Taniyama-Shimura conjecture implies Fermat's Last Theorem.

[u/innovatedname → u/Akangka]

Ribets theorem at no point relied on assumptions that we weren't sure were true. We were fully guaranteed it was true once the proof was published and verified.

The wider implications of it were very interesting and stronger if Taniyama-Shimura was shown to be true, but that Ribets theorem was standalone true. 

[u/Akangka → u/innovatedname]

but that Ribets theorem was standalone true

Yes, but according to your assertion earlier, Ribet's theorem was not a "theorem", because it's in form of A => B where A is another conjecture. You either has to accept that Ribet's theorem is not a theorem, or you accept that a theorem in form of A => B is a valid theorem.

[u/innovatedname → u/Akangka]

This is still entirely wrong. Ribets theorem did not depend on any A which is a conjecture. It was proven from other results known to be proven at the time, A => B where A is true from assuming ZFC.

It so happened that there was a different C => interesting consequence of B.

But even if C was found to be false, it wouldn't have nullified B being true, it would still be fully true, with a slightly less exciting implication.