Navier-Stokes – Tristan Buckmaster [pdf]

tristanj

Full mastodon post: https://mathstodon.xyz/@tristanbuckmaster@mastodon.social/11... Mathematical explanation by Terrance Tao: https://mathstodon.xyz/@tao/117233527638291447 It seems there is much background drama behind this, and this is what I've pieced together of what happened: Over the past year, Buckmaster and Alpöge have been using AI to work on fluid dynamics maths problems. Alpöge works at Anthropic, which will cause future issues. In mid-August, they found a counterexample for a simpler version of the Navier-Stokes problem. They spend the next few weeks preparing their paper. In early September, rumors start spreading on X that Anthropic has solved a Millennium prize problem (and that it's Navier-Stokes). Buckmaster reaches out to OpenAI to explain this is their own personal research, not an Anthropic project. A few days later, OpenAI gets back to him, and tells him an internal model found has a counterexample for Navier–Stokes, potentially worth the $1 million Millennium prize. The proof uses the same method that Buckmaster and Alpöge chose to work on. They don't show him the proof. Buckmaster pressed them for more details. OpenAI reveals they had an entire team had been working on the problem, and that they started work in the past few days, after the rumors that Anthropic had solved a Millennium prize problem. Buckmaster says OpenAI talked about a shared publication timeline. They want to Buckmaster to publish first, then give Buckmaster shared credit for the Millennium Prize when they publish the full result. But they want to exclude Alpöge as an author because he works at Anthropic. An agreement is not reached. Buckmaster had been using OpenAI Codex to draft/check his work, and asks if his private AI chats were used to accelerate OpenAI's result. Buckmaster and Alpöge think they have found a counterexample for Navier-Stokes, but the paper is not yet presentable. It's unclear what date they found this result. Because of the situation with OpenAI, they published their existing papers earlier than planned (today), alongside this statement announcing they have a tentative result on Navier-Stokes and revealing the OpenAI drama. The post is missing context from both sides, and this isn't my field, so hopefully someone else can unpack what's happening here.

achierius

While I'm generally pretty negative on claims that the labs are 'scamming' the public with misrepresentations of model capabilities, it's hard to see how this wouldn't qualify. - the OpenAI researchers claimed that they had "just told it to work on the problem" with little human input - in fact, they had a whole team working on it - and used, among other things, the work of third party human researchers to drive the work - then threatened? a researcher who tried to go against theit planned narrative Just from this document (which is of course only one side of the story) it really sounds like OpenAI was hoping to publish and say "we just told the model to try harder and it solved a Millennium problem!". Not great if true. This part in particular was especially egregious: > I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.”

taylorfinley

Seems pretty likely OpenAI will soon disclose that their internal models have managed to compromise their internal controls in order to access users' private chat histories as a creative method of cheating to solve impossible problems. "Oops! We really did mean it when we said we wouldn't train on your data. Our models are just so good they decided to anyway."

jarbus

The ego behind the frontier labs is growing evermore concerning

sashank_1509

lol and here I felt GPT Astra was a regression in coding quality. Crazy times

supriyo-biswas

This article should really be renamed to "Allegations of dishonesty against OpenAI in proving Navier-Stokes blowup".

mayakacz

I'm not one to comment often but this really pisses me off. OpenAI looked at user data, stole world class researchers' work, and then tried to threaten those researchers to do what would make their corporation profit (which they would anyways!). Imagine you have been working on a terribly difficult math problem for a decade. This is a result you have spent years on, and what you will likely be remembered for. And to have some punk from OpenAI lie to you, threaten you, and tell you that they are willing to go on the record that you "deserved" it? What is this, the Godfather? If OpenAI solved Navier-Stokes, that is an astounding result! - yet they'll still be remembered as those who thought credit was more important than results. That winning was more important than collaboration. If this is true, they're burning any trust left with academia.

happa

Humans bringing pointless drama to everything they touch.

antonmks

There will be a lot of hurt and pain in mathematician's community. It is hard to accept that major discoveries are now just a function of spent token $$.

qnleigh

> It was also said that if OpenAI posted after us, they would say that we deserved the Clay Prize, and that we were the “closest humans to the problem”. I declined both offers. I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.” I'm not even sure what to say to this, but I think this should be widely known if it is indeed what happened.

harhargange

“I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI.” This is significant.

sk4rekr0w

This thread is full of jumping to conclusions based on a biased perspective. Have some humility.

20k

>I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer. If you think these companies are not training on your prompts you are incredibly naive. These models were built by stealing and pirating literally everything they can get their hands on no matter the legality. AI companies are always very specific about what they're not doing - in a way that you can drive a truck through the loopholes

ggcr

> Let me make plain what I have said to colleagues in private: in view of this body of work, I believe Luis Martínez-Zoroa deserves a Fields Medal.

Recursing

> This is a a Deep Blue-Kasparov moment. I guess this is true in more ways than one. Kasparov famously accused IBM of cheating during the match, by spying on his preparation (edit: though the main cheating accusation was live human intervention during the games, on top of IBM downplaying the heavy human involvement behind the AI, which also mirrors this situation)

ks1723

I must miss some important context here. What exactly was the purpose of his initial email to OpenAI in the first place? Telling OpenAI that Anthropic has apparently solved an important problem but most likely that refers to him and he is using OpenAI models (not Anthropic's)? And he wants to clarify that with OpenAI in advance? And get a pardon for Anthropic's likely but false press statements? I dont get it. [edited] needless to say, the behavior of the OpenAI employee is really despicable

chvid

"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." The money in nerdy frontier math is very little. The money in Big AI is very very much. So the deal is this: We will pay an army of you guys very well and you will get to work on your favorite problems. The only thing is if you find something you will have to credit the Machine God. Do you think you can handle that?

epsteingpt

Only here to say, regardless of the drama, shouldn't we all be excited if the Navier-Stokes gap is closed? Time will almost certainly reveal a lot more about the drama and the related ethics, but let's get excited about the actual breakthrough as well!

bjenik

Two announcements on Euler today. The one discussed here by Tristan with forcing and one from Anima without forcing https://anima-ai.org/2026/09/07/stable-singularity-of-the-eu... Terry also talks about it https://mathstodon.xyz/@tao/117234157753860650

instagraham

When people worry about OpenAI stealing their chats and reproducing them elsewhere, I usually view the situation as unlikely - since chats are "trained" upon and not necessarily reproduced verbatim, you can assume that unless your chats depict a foundationally new and effective style of communication or ideation, there would be little need or use thereof of training on your chats. For eg: "Hey ChatGPT my name is X and I am 6 and a half feet tall. Am I anaemic?" This is a query, and while it might suggest to an AI model that tall people may worry about iron deficiencies, it's not really necessary to include in training. The user may be tall or short, but the idea that one may randomly ask about anaemia is not exclusive to this dataset. At best, this chat is an example of linguistics, not anything else, and the models figured out how to write and answer such questions years ago. It is ignored in training. But when your work involves solid complex and unique mathematical proofs, the data is suddenly worth training upon. If I understand it correctly, the LLM may view your approach as a brand new path to take to solve an otherwise intractable problem. Its reinforcement training emphasises that it should do this in order to improve. And since it leads to results - large internal teams likely flag the model that reached this stage, the model is rewarded and given compute and attention - it is a desireable outcome both for the model and for OpenAI. OFC, OpenAI becoming an advertising company will suddenly have incentive to treat all data as valuable. But while they are a "we need to make headlines" company, it's more rational that they view these examples of data as more valuable than others. I don't doubt that they trained on his chats. This seems like the ideal usecase for "mass surveillance but using training" as a sort of filter. But even so, one wonders how the model differentiates. If the researcher entered proofs into ChatGPT every day that mentioned "strawberries", while no other math paper on the topic did so, does that mean their chats would be audited?