> Leven and Tristan worked over several months on one of the Millenium Prize Problems with various AIs to reach final interesting results. OpenAI apparently heard about it in the last days and prompted their latest models to work on the direction Leven and Tristan found fruitful. They then tried to push for controlling communication of the result and dropping Leven from authorship with some very bad taste social pressure.
The thing about these math proofs is that they really add nothing of value. Its a cool tech demonstration on how LLMS can search the trained space, but fundamentally, LLMS haven't "discovered" anything groundbreaking.
For NS equations, they are trying to model something that is discrete (i.e molecules colliding) in a continuous manner. You can easily think of a condition where they fail - imagine a vaccum where there is sufficient space between air molecules, so that collisions aren't always possible. NS won't be able to predict the state of the fluid in every single point in space.
In practice, when you do CFD, no package uses direct differential simulation of NS equations, you usually have simpler approximations that are good enough for the space you are working for. And if you want accuracy, you usually do something like LBM which simulates particle collisions using probability distributions.
whoarewethen 14 hours ago
There is value in knowing (as opposed to hypothesizing) whether some interesting claim is true or false.
Actually, just knowing that a claim is true may motivate people to search simpler proofs, as it happened in mathematics in the past.
runeblaze 14 hours ago
I can't wait to tell my pure maths professors that their most of their research adds nothing of value. I mean I am sure most of them would agree to some extent, but like, dude, have some more faith in the utility of pure maths, esp. centuries down the line
publlus_enigma 9 hours ago
My read was that "these proofs" was referring to AI generated proofs specifically, not all mathematical proofs.
runeblaze 4 hours ago
sure I get that, but like, my field has plenty of counterexample as proofs. we have had non-constructive proofs like probabilistic arguments. i don't think we can play the game of "oh this proof is useful that proof is not useful" well
ActorNightly 8 hours ago
There is plenty of work that goes on in the math field that is super important. But any field has research that is irrelevant. So far, all the proofs done by ai have been largely irrelevant.
secretsatan 17 hours ago
I do wonder if perhaps LLMs take credit from some mathematicians working in obscurity in some dark corner of the web, it’s not unheard of for some to be reclusive. Perhaps someone completely unaware that they might have sovled something someone else considers important.
