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On the Navier–Stokes Millennium Prize Problem

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Re: On the Navier–Stokes Millennium Prize Problem

#231

Post by pbhjpbhj »

rfgplk wrote: post #154
lambda wrote: post #129

Earlier quoted context omitted.

Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data? This is one of the major problems with these enormous closed models, and even most open-weights models, which don't disclose their training process or training data. You can never be sure what went into its training. Did it come up with an idea originally, or is it just plagiarising its training data? Are there ma…

> Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data? Probably? I have a few hundred TB of training data for various small scale models and I can attest that I have _no idea_ what's in them. As in, literally zero. Half is scraped from GitHub and other hosting sites, other than that, I couldn't tell you anything else. At OpenAI's scale their entire pipeline is likel…

Aye, but do they train on user data in these circumstances or not? If they do, then almost certainly the model was influenced by the input of the allegedly plagiarised material.

Re: On the Navier–Stokes Millennium Prize Problem

#233

Post by tedsanders »

contemporary343 wrote: post #131
tedsanders wrote: post #41

Earlier quoted context omitted.

Yes, that was the allegation last night. I work at OpenAI, though not on the team that did this, and my understanding is: - we decided to ask our model for Millenium problem solutions because of two reasons: (a) our new model was looking incredibly good and (b) we heard rumors that some Millenium problems had been solved and were curious if our models could solve them (the goal here was not to scoop any particular in…

"I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a num…

All of those statements sound true, based on what I've heard.

- "very little human" input feels ambiguous, and if someone spends a few days prompting a model to solve a super hairy problem requiring a 100-page proof, I can understand reasonable people interpreting that as both "very little" and "not very little" human input

- it's all true that a team worked on this, a bunch of compute was burned, and the problem was solved in stages and pieces

I'm not sure how any of this provides evidence that OpenAI took any of their work.

As evidence against, we never looked at any of their ChatGPT conversations and our model's proof is quite different from theirs.

(I work at OpenAI, but not on the team that did this proof.)

Re: On the Navier–Stokes Millennium Prize Problem

#234

Post by blake__dev »

arctic-true wrote: post #35

Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra, which was only made public a week ago. Even if this improvement is limited to mathematics, that is an astounding feat.

Yeah I'm surprised they posted a chart, you would think they would keep specifics like that hidden until they're closer to launch

Re: On the Navier–Stokes Millennium Prize Problem

#235

Post by Kotlopou »

For now I think more or less the same thing as with all recent math announcements: This is in a range where human work still exists (see Terry Tao, (1)). I wonder whether the trend will extend into the problems that (as far as I can tell) are considered complete brick walls right now -- P vs. NP, Collatz, Goldbach, odd perfect numbers, problems that aren't part of any research program. (2) In other words, is the progress coming from putting together vast amounts of existing work and computational power, or is it more from RLVR and self-play and autonomous effort?

The answer to this will obviously shape the near future of mathematics, but there's also something even bigger than that at play: It has always been the case that the questions in math were stronger than the answers; you have stuff like Fermat's great theorem that is easy to state but monstrous to prove. This seems to be a property of mathematics, not of humans... but is it true?

A question by Scott Aaronson from 2011 (3) about P vs. NP seems relevant here: "Will humans manage to prove P≠NP before they either kill themselves out or are transcended by superintelligent cyborgs? And if the latter, will the cyborgs be able to prove P≠NP?" Later, he notes that if P≠NP, "once the robots do overtake us, they won’t have a general-purpose way to automate mathematical discovery any more than we do today".

---

(1) https://mathstodon.xyz/@tao/117207849921390904

(2) I'm not sure whether this is a hard distinction -- e.g. Tao also has some partial results towards Collatz (https://terrytao.wordpress.com/2019/09/10/almost-all-collatz...).

(3) https://scottaaronson.blog/?p=690

Re: On the Navier–Stokes Millennium Prize Problem

#236

Post by liberian »

slibhb wrote: post #119
dorjoycb wrote: post #13

It seems like some other mathematicians (not affiliated with openAI) have also (or close to) done this. A statement was posted about the surrounding events by one of the them: https://cims.nyu.edu/%7Etristanb/statement.pdf Also Terrence Tao's post: https://mathstodon.xyz/@tao/117233528517340774

Worth noting that Tao's post says the authors had "significant AI input" but are reworking them into "acceptable form". Either way, it seems AI was involved.

[dead]

Re: On the Navier–Stokes Millennium Prize Problem

#237

Post by QuesnayJr »

cv5005 wrote: post #104

Maybe a naive question, but how does one know that a particular lean proof is actually a proof of what one thinks? Like, ok the logic checks out and it proves something , but there's still the problem of does this logical result actually prove the initial question that was asked?

Someone has to actually check this. I'm guessing OpenAI had someone check it internally, but it's possible to get it wrong.

Re: On the Navier–Stokes Millennium Prize Problem

#238

Post by ameliaquining »

QuesnayJr wrote: post #156
jrflo wrote: post #110

Earlier quoted context omitted.

I'm so tired of this "It's just marketing!!" commentary. An AI model just proved one of the top 3 unsolved problems in mathematics, they have a Lean certificate showing it's valid. How much more evidence do you need that these models are actually highly capable?

Of the seven Millenium problems, Navier-Stokes was the one most thought to be in reach. I'm not sure what the top 3 problems are. You can make a case for the Riemann Hypothesis and P != NP, but I'm not sure what #3 would be. Maybe the Langlands program? (That one is not as precisely stated as the other two.)

There were also some people talking about the Hodge conjecture, because it has some similarities to some LLM-assisted breakthroughs that were considered impressive in the distant past of [checks notes] July 2026. See, e.g., https://xenaproject.wordpress.com/2026/07/20/human-mathemati...

Re: On the Navier–Stokes Millennium Prize Problem

#239

Post by AlexErrant »

recitedropper wrote: post #10

Sad turn of events for our world. After watching the behavior of the most senior OpenAI researchers on twitter, I feel even less confident in them as a team to be shepherding this much capital and compute. The dark forest awaits..

1. What does the dark forest have to do with this? Because "the most senior OpenAI researchers" are shitposting on social media, we've an answer to the Fermi paradox???

2. The dark forest is fun for scifi stories, but is mathematically bunk anyway https://www.noahpinion.blog/p/the-dark-forest-hypothesis-is-... https://www.reddit.com/r/IsaacArthur/comments/1l06cnk/cool_w... https://www.projectnash.com/aliens-the-fermi-paradox-and-the...

When doomposting please actually say something substantive. Negative news always gets clicks/updoots; fight that human tendency.

Re: On the Navier–Stokes Millennium Prize Problem

#240

Post by achierius »

applicative wrote: post #95
int3trap wrote: post #55

Earlier quoted context omitted.

This is the academic equivalent of Trump saying "they stole the election". There's no proof of it but rah rah fuck OpenAI. It's incredibly tiresome and you'd think people could put more effort into it than just following whatever vibes they agree with. Oh well.

No, its a pure outrage. I defended OpenAI til today. I now affirm they must be totally destroyed, burned utterly to the ground.

I mean it's definitely an outrage, but I find it hard to believe that you went from "yay OpenAI" to "literally destroy the company" over... accusations of academic misconduct?
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