[nybsjytm]

> I know they are so close to a computationally-assisted proof of counterexample that it is virtually inevitable at this point.

That's a strong claim. Is it based on more than the linked work on some model problems from fluid mechanics?

I will say that I dread the discourse if it works out, since I don't believe enough people will understand that using a PINN to get new solutions of differential equations has substantially no similarity to asking ChatGPT (or AlphaProof etc) for a proof of a conjecture. And there'll be a lot of people trying to hide the difference.

[hodgehog11]

It's based on knowledge of the related estimates, applying similar techniques to geometric problems, knowledge of all the prior works that lead to the current work, and speaking with members of the team themselves. They are much further along than it appears at first glance. All of the major bottlenecks have fallen; the only concern was whether double precision accuracy is good enough. The team seems to have estimates that are strong enough for this, but obviously keep them close to their chest.

PINNs are different in concept, yes, but clearly no less important, so the additional attention will be appreciated. Asking LLMs for proofs is a different vein of research, often involving Lean. It is much further behind, but still making ground.

[nybsjytm]

> PINNs are different in concept, yes, but clearly no less important

If anything I think they're more important! Whether or not it works out for Navier-Stokes, this kind of thing is an extremely plausible avenue of approach and could yield interesting singularities for other major equations. I am however extremely concerned about public understanding. I know you are well aware that this is worlds away from the speculative technologies like 'mathematical superintelligence' but, if it works out, it'll be like a nuclear bomb of misinformation about AI and math.