Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

On the Navier–Stokes Millennium Prize Problem

openai.com

Post reply on HN
Print view View original

671–680 of 1001 posts

Re: On the Navier–Stokes Millennium Prize Problem

#671

Post by fer »

irthomasthomas wrote: post #615
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.

Or they trained a LoRA on the victims chats in order to launder their plagiarism.

The timing makes it the most likely, not only them but potentially more. Comparatively quick, instant results. "Here's Astra! BTW our internal model is 10x better at math!" It'd be interesting to see academics having giving deeper looks at whatever OpenAI publishes from now on.

Re: On the Navier–Stokes Millennium Prize Problem

#672

Post by ImPostingOnHN »

modeless wrote: post #169

So the timeline is: Aug 28: OpenAI starts training a new model. Sep 1: OpenAI sees a rumor on Twitter that two Millenium Prize problems were solved and starts their own effort to attack all the prize problems using the new (4 day old!) model. Sep 3: The new model makes some progress toward Navier-Stokes. Based on this progress, OpenAI focuses on Navier-Stokes over the other Millenium Prize problems, using several app…

> There is a caveat that they "can't rule out" the possibility that Tristan's Codex data could have been part of the training set of the new model, though it is described as "unlikely"

This is the lynchpin behind everything, and I would describe it as "likely". Since I am not employed by any party to this dispute, my 1 opinion is more trustworthy than OpenAI blog poster's 1 opinion.

Re: On the Navier–Stokes Millennium Prize Problem

#673

Post by nhatcher »

tedsanders wrote: post #41
pavel_lishin wrote: post #8

Is this the one that was allegedly based on someone else's actual work & prompts? https://news.ycombinator.com/item?id=49605915 https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd... https://cims.nyu.edu/~tristanb/statement.pdf

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…

Some millennium problems? Are there more coming?

Re: On the Navier–Stokes Millennium Prize Problem

#675

Post by peri-cl »

Terence Tao has some observations that seem to be directed at this,

https://mathstodon.xyz/@tao/117237320796901560

> "We have now seen that even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential. The incentives may now be pointing in the direction of no longer sharing any promising research directions with the broader community, which would reverse centuries of traditions of open science and do serious long-term damage to the future of the field."

Re: On the Navier–Stokes Millennium Prize Problem

#676

Post by QuesnayJr »

ameliaquining wrote: post #241
QuesnayJr wrote: post #158

Earlier quoted context omitted.

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...

I brought this up here at HN, and in the ensuing discussion Buzzard himself replied saying he was somewhat joking (https://news.ycombinator.com/item?id=49011950).

Re: On the Navier–Stokes Millennium Prize Problem

#677

Post by 8note »

thorum wrote: post #153
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

It reminds me of the Cognitive Dark Forest hypotheses recently shared here: > “You are creating your cool streaming platform in your bedroom. Nobody is stopping you, but if you succeed, if you get the signal out, if you are being noticed, the large platform with loads of cash can incorporate your specific innovations simply by throwing compute and capital at the problem. They can generate a variation of your innovati…

but what do i lose if somebody else is making money?

im still having fun making something

Re: On the Navier–Stokes Millennium Prize Problem

#678

Post by lossolo »

tedsanders wrote: post #621
Imnimo wrote: post #252

Earlier quoted context omitted.

>we did not read any private chats The question I am interested in is not "did we read private chats", but "was this new model trained using any of Tristan and Levent's chats, regardless of whether they were marked private". Can you comment on that?

If they opted out of training, then we definitely did not train on them. If they did not opt out, then I don't personally know if training signals came from their chats, and I don't think we'd be able to tell without their cooperation in identifying them. And even if signals were trained on in some manner, I highly doubt it made a difference to a problem as challenging as the NS proof. Reasons for my doubt: - I know…

> If they opted out of training, then we definitely did not train on them.

Can't you guys just check their account settings so the public knows what was set?

EDIT: Why was this downvoted? I'm genuinely asking because I have no idea. Opting out is just a normal setting in the profile, It's not like I'm asking for their private conversations or PII. If I were the person claiming that they trained on my conversations, I'd make sure to disclose that I had opted out and hadn't given them permission to do so. And if I were the accused party, I'd disclose whether that setting was turned on or off to provide evidence against the accusation.

Re: On the Navier–Stokes Millennium Prize Problem

#679

Post by flir »

zem wrote: post #664
20k wrote: post #233

Earlier quoted context omitted.

It isn't a priority dispute, the more concerning allegation is that OpenAI may be training their models on prompts that mathematicians were using to solve this problem, and then surprise surprise OpenAI were able to replicate that work in their latest model What we're really looking at is seemingly a massive plagiarism scandal, which especially brings a lot of the past results into question If OpenAI is training mode…

even apart from the plagiarism issue, what sort of slimy company thinks "oh, here's someone using our models to work on a problem, let's throw more compute at it and scoop them"?

Training on prompts I can understand - that's kinda baked into the premise, and they've been explicit about it.

Publication, though? Slimy is right.

But the interesting question to me is: once they had a solution, what should they have done with it? I see two choices: bury it, or contact the mathematicians whose prompts they were listening in on.

Re: On the Navier–Stokes Millennium Prize Problem

#680

Post by futureshock »

I feel like something is being lost in the drama here.

First of all, there has been published work from Diego Cordoba and Luis Martinez-Zoroa that will be in every training set. It was suggestive of the pathway to solve Navier-Stokes.

Then Tristan Buckmaster and Levent Alpoge built on this work using LLMs from OpenAI and Anthropic. Possibly internal models were used from Anthropic. And of course Anthropic wants to credit for solving the first Millennium Problem just as bad as OpenAI. It seems they were getting close and were aware that they might get to Navier-Stokes.

OpenAI swoops in. At a minimum they are aware that Anthropic has either solved a Millennium problem or is close to it. At a maximum they may have Tristan and Levant’s unpublished proofs of related problems.

They then throw a truly staggering amount of compute at Navier-Stokes. They seem to be aware it is the best candidate problem. And they crack it. They are the first with a verified proof.

So the outcome here is that we have a solved Millennium Problem. It’s not the extremely simple narrative that would be easy to understand, “solve Navier-Stokes make no mistakes.” It was a messy race to finish against two unpublished frontier models, a whole bunch of brilliant mathematicians and enough compute to drain a lake. It’s kind of irrelevant which company got there first. They were both within a few months of being capable. I think the thing to remember here is that without LLMs, I don’t think we would have a proof to Navier-Stokes in hand today.

Post reply on HN