> If AI advances more and becomes smarter it can be used on both sides.
Yes, and that's true even if it doesn't advance or become smarter. It's happening already that people are using AI on "both sides" both adversarially and defensively and that is improving software, and hopefully mathematics as well.
> I am not sure about the Navier-Stokes proof but in general it sounds highly unlikely that many well-known theorems turn out false.
I'm talking about the LLM Navier-Stokes proof specifically because it's very long and complicated and an LLM is not the same as a human mathematician. A human mathematician is trying to use the tools in a truth-seeking way, whereas LLMs are trying to satisfy the goal of presenting a proof that convinces people it is correct. Maybe naively, it seems to me the failure modes of proof assistants would be amplified under adversarial conditions (i.e. driven by LLMs).
Completely agree that there seem to be many ways that relying on proof assistant software can go wrong.
Yes, and that's true even if it doesn't advance or become smarter. It's happening already that people are using AI on "both sides" both adversarially and defensively and that is improving software, and hopefully mathematics as well.
> I am not sure about the Navier-Stokes proof but in general it sounds highly unlikely that many well-known theorems turn out false.
I'm talking about the LLM Navier-Stokes proof specifically because it's very long and complicated and an LLM is not the same as a human mathematician. A human mathematician is trying to use the tools in a truth-seeking way, whereas LLMs are trying to satisfy the goal of presenting a proof that convinces people it is correct. Maybe naively, it seems to me the failure modes of proof assistants would be amplified under adversarial conditions (i.e. driven by LLMs).
Completely agree that there seem to be many ways that relying on proof assistant software can go wrong.