Navier-Stokes – Tristan Buckmaster [pdf]
cims.nyu.edu
cims.nyu.edu
- Aug 15th: Tristan Buckmaster & Levent Alpöge make progress on a few important math problems, "finite-time blowup with smooth forcing for incompressible porous media, for Boussinesq, and for 3d incompressible Euler."
- they do NOT have a proof for the $1,000,000 Millenium Prize problem. BUT, they do claim to have a proof for a similar (non-Millenium) Navier Stokes problem that could help lead the way there
- Levent works at Anthropic, but this research was independent of his work there, with a mix of GPT and Claude models. Tristan is not related to Anthropic.
- Early Sep: Rumor spreads to OpenAI that Anthropic solved a major problem. Tristan emails OpenAI to clarify, without revealing the problem they solved or how they did it.
- After hearing of the rumor, OpenAI started researching Navier Stokes with a new internal model.
- Sep 6th: OpenAI's Sebastien Bubeck tells Tristan that they solved the $1,000,000 Millenium Prize Navier Stokes problem. The approach is very similar to Tristan & Levent's approach to the non-Millenium problem.
- Tristan is suspicious of the timing, as only few others were trying this approach. OpenAI says the model didn't access his user data directly, but leaves unanswered whether Tristan's chat conversations were part of the training.
- OpenAI says they would partially credit Tristan for the $1,000,000 discovery (even though Tristan did not solve the $1,000,000 problem) — but only if they remove Levent as an author, as he works for Anthropic.
- Sep 8th: Tristan refuses to remove Levent, and rushes to publish their results independently.
"Mr A. Nino weathers a storm of protest" - https://www.independent.co.uk/news/mr-a-nino-weathers-a-stor...
1. Less than a hundred people in the world are working at this problem, 2. A significant fraction of those happen to work at competing hyperscalers, 3. Those hyperscalers repeatedly show themselves not to take user privacy seriously
> Those hyperscalers repeatedly show themselves not to take user privacy seriously
where? Any examples?
They explicitly say that they use your "content" to improve their models. Considering they practically have infinite compute at their disposal, why is it surprising that they would look for juicy data in there to make them look good ? When they ingested basically the entirety of human knowledge without regard to the rights of others, when they burn books by the thousands, when their relentless barrage of bots have rendered the Web borderline unusable, why would they stop at that line ?
yes.
Rules and laws are for the poor.
I'd be shocked if they weren't
That's also why they refused to answer that question: the answer is obviously "obviously"!
But the drama here is a little important. Stealing the millennium prize for N-S is sort of a big deal, especially to those who had been working on it for the last few years.
I don't think everyone agree with your notion that the language and tools of mathematics aren't human inventions.
So if math is all that matters to you, you should care about this.
Particularly if the first proof being "solved" thanks to piles of money and compute for self-serving marketing discourages the mathematician who might have otherwise devoted years of focus to reach the superior proof we will now never see.
As a concrete example, such a proof could be less than a page with very specific initial and boundary conditions and inserting them into the equations to get something that goes to infinity when time goes to some finite value.
This would resolve the Millenium problem but not make humanity any smarter.
Regardless of mathematicians stating the methods outstrip the proof’s importance, still amazing we got an explicit social counterexample as well so quickly.
I don't think this part is accurate. OpenAI was researching Navier Stokes before. It's possible that they started on a new approach after hearing of Tristan's success, however that is not proven and I expect we will hear OpenAI's side of the story today.
"The route to the Clay problem through a smooth force, options c and d in Fefferman’s statement of the problem, is the route Luis and Diego opened and the one Levent and I had quietly chosen to attack. Almost nobody else I know of was working on it. It is not the direction one arrives at in a few days by giving a model the problem statement. When I heard “forced,” it was a bright red flag."
Whether or not they were researching it before isn't the concern.
The most nefarious explanation seems to be that they got wind it was possible to solve NS via LLMs and perhaps a small nudge in the right direction.
The open question was whether their LLM got the nudge in the right direction because it got access to the chat somehow (e.g. automated training that scraped his chat logs) or just a high level "Navier stokes can be solved through LLM". It sounds like the former may have happened although right now we just have an accusation and a weak denial.
The compute was used to leapfrog the human team, using their ideas and pushing them to a solution of the general problem.
Plagiarism isn’t being used in the literal sense.
"It is true that we tried this because there were rumors on the internet last week that Anthropic's models had solved a millennium problem and we were curious if ours could do it too."
My guess is that OAI tried to be "generous" and offered to share credit on millennium with Tristan but not Levent. And Tristan got understandably offended by this offer (which probably oai felt like was the right thing to offer but they couldn't really offer to do the most ethical thing for some reason) and then the random conflicts and weird threats started.
openai then tried to effectively bribe buckmaster with a shared citation, whilst dropping his co-author who works for anthropic.
after buckmaster refused, openai tried to threaten him.
"Training" on textbooks => fine
"Training" with unpublished notes from another professor, then publishing something on that exact topic with a similar approach without giving any credit => extremely questionable.
The trouble here is that if LLM training constitutes direct use then approximately _everything_ they output is blatant plagiarism, not just a few pieces of academic work.
Conversely if training is viewed as analogous to a student attending classes to learn general concepts (not a perfect analogy, I realize) then nothing they output on their own (as opposed to receiving as part of context) is plagiarism.
Thus this seems like a fairly useless line of argument to me as far as the current topic goes. It either implicates this academic work along with literally everything else or else it does not implicate this academic work. Kind of like nuking an entire city and then saying "mission accomplished, killed the bad guy".
Science papers of a phd level must contain:
1. one or more novel insights
2. a long list of citations to contextualize them and
3. some work to prove that the insights are in fact meaningful
---
In this context, consider a prompt based diffusion model which, when asked, will happily produce a few pictures of a horse in orbit. You then tell it "silly robot, horses can't breathe in space" to which it adds the necessary space suit in a follow up image.
That image is twice plagiarized:
1. the model did not come up with the original idea of putting a horse in space, nor with insight that horses need a space suit
2. the model failed to cite where it pulled the "horse" and "space" concepts from.
It merely did the work (3) to combine the concepts using the user provided insight.
---
The implied accusation here is that OpenAI used the insights from an existing prompt to train a new model that was able to one shot "a horse race in space" picture, and they were all wearing space suits.
This is still academic plagiarism, even if you disagree that all LLM outputs are.
As to your stronger argument. You only cite prior novel insights that you're actively building off of and that (approximately speaking) fall outside of the status quo. You don't for example cite leibniz or newton despite your paper making heavy use of calculus.
So is there any actual evidence that openai trained on the data in question? And further, did the openai proof directly build on someone else's novel insights as opposed to deriving everything from scratch? (I don't pretend to know but the vast majority of what I've seen so far in the comments here is what I'd characterize as brain-dead screeching. Certainly not the level of discussion I come to HN for.)
Separately, consider the implications of what you're arguing for there. Suppose your horse in a space suit picture were somehow valuable to society. Suppose that due to shortcomings of your tool you lacked the ability to readily and accurately identify the originators of the relevant concepts. Should you refrain from publishing this useful work due to the lack of citations? How are you supposed to handle this situation?
Remember that in this analogy everyone throughout society is on the same page that your tool consistently recycles other people's ideas while being technically incapable of producing reliable citations. The question is a simple trolley-esque problem - do you publish without proper citations for everyone's benefit and if so what are you supposed to say?
Academia has stricter rules than regular society.
The second point: if you say you can’t prove that OpenAI actually used it, it doesn’t mean that OpenAI did not use it. It’s hacker news not lawyers news here lol. And OpenAI can’t prove that they didn’t use it either. The whole point is that Levent felt he had reasonable suspicion to believe the AI did use the result, because he felt like without his input on an unpublished paper it was unlikely for AI to reach the same result. I haven’t read the paper so I don’t know where I stand on that.
On the last point, about your “for the greater good” argument. It’s higher maths lol. I don’t know about this field but I doubt it’ll be very useful for society. Maybe it’ll make one part 2x faster which makes some rocket cheaper to launch. Does the average person care? Debatable. I think it’s reasonable to hold published papers in proof based fields to a higher standard. Otherwise the current & future problems of ML engineer fields just expand to other fields. No thanks.
Finally, if you anonpost to the autistic Internet forum that everyone else is “brain dead screeching”, it really just says something about yourself lol.
did the proof build on the insights:
the influence of an individual text in the training data is deeply weighted by quality, relevance, etc. a high quality proof in advanced mathematics written by a codex user is going to get boosted to the max.
the model is post-trained on prompt material. that is again going to boost it.
the prompt will boost this material specifically. perhaps they even rammed dense maths in particular into the model in post training.
anecdotally i have been able to get near-verbatim copies of original material out of models at inference. the type of work that buckmaster and alpoge fed into openai feels like the exact type of concept that would cause an "aha!" or "but what if?" in chain of thought. in fact i would bet that their work is in the logs.
the likes of astra and fable are thought to be up to 10T parameters in size. i consider it highly plausible that a semantic representation of the euler proof could be pulled out of the model weights in good shape.
I think the bigger issue here is this feels like some PR smoothing happening that after all the work that went into "it's safe to use for enterprises" now we have what looks like openAI using private user data to scoop novel research and the question of why couldn't they do it for an enterprise with much more money on the line.
Is there any actual evidence of that? All I've seen so far are empty accusations because "it would be in their interests" or whatever. Personally I'm inclined to believe that they honor their terms until it's demonstrated otherwise.
Your post does not distinguish, and it matters.
Note that I am not taking a stance on what openai allegedly did or did not do one way or the other. I am merely pointing out what I see as a fatal flaw in the line of argument presented by the earlier commenter - the idea that training on an item is on its own sufficient to establish plagiarism of it.
as bad academic conduct you may steal someone else's unpublished work, work on it yourself for a bit, and then publish it as your own work. and then threaten the original author!
In answer to a post suggesting that training on a datapoint could mean plagiarism, you said that this would imply that all outputs are plagiarized. This is not the case, no, because generative models do not "copy" or "create", they do both at different times.
I did not agree or disagree with the original poster, I was explaining to you why I thought you disagreed with them. If you understand what I said above, then why do you disagree with them?
EDIT: I just saw your other post on "general inspiration" and I believe I read the situation exactly; you appear to believe that inputs used to train generative models get "lost in the parameter soup", but it is not always the case.
We read the original differently. As clearly stated in my previous reply to you, I interpret it as claiming that all outputs are necessarily plagiarizations of the training data. That is not my claim (as you wrongly stated) rather it is the claim I am responding to. I observe that it is absurd to object to a single action being a transgression on the basis of an argument which implies that all actions are inherently transgressions. Notice that nowhere do I take a position on whether or not the argument about all actions being transgressions is true or false.
> you appear to believe that ...
I do not, no. I have not taken a position of my own here. I've merely objected that the one I responded to does not make for a sensible line of argument in context. It seems that you (and many others) have read my objection to position A as support for position B and attempted to infer what I think from that.
There is a difference between claiming an action is a transgression, and claiming it could be one.
well that sounds like an asshole move.
We are in new times, where capital and compute decides mathematics, so we don't give a shit anymore
OpenAI's LLMs are not humans, and neither is the company. So by this logic, I think there's a chance that nobody committed a crime by hacking Huggingface, and also the chance that a lot of military and police organizational orders become illegal if OAI's doings would be illegal.
IANAL and all I have is a bucket of popcorns, though.
1: not a meaningful defense in a real trial, also gross negligence exists
2: this also explains insanity defense; if you were so out of your mind that you could not have held such a thought, it is considered out of scope for justice systems
Neither are guns. Which is why we punish the person shooting the gun and not the gun.
Industrial equipment, which is how i would classify LLMs, hurting people is nothing new. The relevant questions are:
- did someone intend it to happen?
- was someone negligent in taking reasonable steps to prevent something foreseeable?
The justice system doesn't punish people for legitimate accidents. e.g. if you are shooting at a shooting range, take all reasonable precautions, but someone was hiding behind the target, you are probably not guilty even if you shoot the guy.
As far as openAI goes, the logic is the same. The question is, was it intentional, was it unintentional but reasonable precautions weren't taken or was it truly an accident?
There is no such thing anymore.
Falsified data and published? Absolutely no problem. Keep your tenure.
It’s even hard to lose your position as president of a university due to egregious misconduct.
- Tristan is suspicious of the timing, as only few others were trying this approach. OpenAI says the model didn't access his user data directly, but leaves unanswered whether Tristan's chat conversations were part of the training.
- OpenAI says they would partially credit Tristan for the $1,000,000 discovery (even though Tristan did not solve the $1,000,000 problem) — but only if they remove Levent as an author, as he works for Anthropic.
These two bullet points are extremely suspicious if you were honest. Like I'd imagine for OpenAI, they'd love to pump their chest and not even give Tristan credit - "no, we did it, GG mathematicians". It's this weird hedging half-assed measure, especially with the desire to remove Levent, that makes it suspicious.
> 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.”
Whether and how OpenAI's work on this problem was contaminated by knowledge of Tristan and Levent's work is tangential to OpenAI bullying other researchers into adopting their narrative and dissociating with dis-favored collaborators (ie Levent at Anthropic). Though the latter behavior (threats, intimidation) may weigh against OpenAI in trying to understand the former issue (contamination).
If this is true he should release the actual emails. This is a very serious accusation and he shouldn't demand that the reader judge it on hearsay.
these were statements while on a call, and at least the career comment Bubeck has admitted to while doing damage control ("I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey. (I should say that I retracted them on the spot by the way.)"[1]).
[1] https://xcancel.com/SebastienBubeck/status/20973794116915163...
Or thinks they are?
I really don’t understand which party you are referring to.
So using someone’s models makes someone who works for the competitor not “independent”? When their coauthor is? What does that even mean?
I almost stopped reading this extra long post entirely at that point.
This is not a good look in my book.
> Importantly it was admitted that internal Anthropic models had been used in their proof of Euler blowup; I therefore felt I could not consider Levent to be an independent academic.
If an Anthropic employee is doing independent research, but with models that aren't available to the public (because they're internal models), then . . . idk. It's not clear to me why that should necessarily require a refusal to cooperate between OpenAI and Anthropic employees who are excited about solving a problem like this.
For me, the bigger question here is what "internal models" means to these employees, especially in the context of the OpenAI employees repeatedly avoiding directly answering whether their model had been trained on Tristan's and Levent's ongoing work on the problem. It had always seemed like a loophole that AI companies might be tempted to exploit: yeah, they can say that they won't train on your data, but if an AI company doesn't care about ethics, they might go ahead and train a model for internal use only on everyone's data anyway, just to have as much data as possible and potentially gain an advantage in what the company can internally do. They could never publicly release any versions of a model like that, of course. And of course this is speculation.
If true, that's generous and beyond the level of generosity one should expect. Extending that courtesy (beyond academic norms) to a competitor is expecting too much. It take a result OpenAI spent millions of dollars on, and put "Anthropic Researcher" right on the cover.
This is, of course, taking OpenAI's side of the story at face value. But it is a consistent, coherent, and ethically justifiable series of events, if indeed it happened that way.
If OpenAI thinks someone should be the lead author for a paper, that person should have full discretion to decide who the co-authors are.
Even if the co-author's contributions were non-technical
So no, there's no world where you can ethically extend the right to publish a result and decide who the authors are from the outside.
> If true, that's generous and beyond the level of generosity one should expect
"We highly likely stole your work, and threatened you with 'this is bad for your career' and we refuse to acknowledge any work by your collaborator just because he works at a competitor, but we are so so so so generous"
Additionally, according to the researcher, OpenAI's proof follows the same approach they used, and which was largely unused in academia, but OpenAI claimes they arrived at it immediately.
Ain’t no way you read one 100 page paper let alone two with enough understanding to make such a claim.
You ought to be ashamed of yourself.
> internal Anthropic models had been used in their proof ...
Pretty insane if he couldn't figure out why there would be bickering in this scenario...
> Genuinely, at that moment, I was trying to care for him and do a last ditch attempt to get a chance to give them all the credits that they deserve.
The allegation he is responding to, and which he does not seem to have disputed, is the following passage from Buckmaster's statement (https://cims.nyu.edu/~tristanb/statement.pdf):
> 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.”
The most uncomfortable piece is where he shows screenshots “proving” his earnestness is unrewarded instead of the chats that are actually being complained about.
That he does so with tremendous gymnastics is perhaps soothing to investors, but every researcher I show this post to today says “see I knew ‘AI’ would steal my research”
So yeah, maybe we are reading different things.
This is the most suspicious thing to me. If their chat data were available to the corpus to be trained on (I thought they claimed not to do this?) then it really might be as simple as querying the model with "describe recent work from Tristan Buckmaster" and it will spit out this problem and his approach. No need to directly read his user data.
This is basically just scooping, real scumbag behavior.
it is common that multiple people essentially simultaneously prove/invent the same thing
I see zero evidence of wrongdoing
Was that a one shot prompt? or something guided by human, step by step?
If that's the later, it won't use the same approach when not guided by the same human.
I don't agree with the oil claim analogy. this is knowledge, freely given to the world. not something hoarded by a corporation
Even if you’re starting from a position that credit for a discovery literally can’t be stolen, that still doesn’t resolve in OpenAI’s favor here.
it seems like Buckmaster got one-upped and is upset. understandable, but I find their reaction childish as well
Why does OpenAI get to dictate who Buckmaster can claim co-authorship with?
> I find their reaction childish
OpenAI may have, with full plausible deniability, taken Buckmaster’s work and passed it off—in substantial part—as their own. (Fitting into a fact pattern of them having tried to do the same with Apple.)
There is a material takeaway for anyone who does creative or otherwise unique work from this. (Which is unfortunate. Whatever happened here, AI clearly accelerated the discovery process.) For anyone else, I agree it’s just drama.
https://www.reddit.com/r/mathematics/comments/1wauync/commen...
It doesn't seem like there's anyone at OAI who knows much about the problem they are solving. Seems like CS theorists or algebraists* trying to own the pros by driving a car that's beyond their skill level. For one, they didn't cite the guys that B&A based their work on.
*It would be most fair to say there are no analysts on board, nor are they likely hire any soon; those are the least impressionable people in math. Applied math PDE elves who hadn't already left on the world-model boats would have jumped off around the time that eg Ilya did because they wouldnt have been able to stand the three Bs pretending to be experts in fields they imagine to be "adjacent".. like Public Relations
We can't say this until we have more information on what the OpenAI researchers prompted their model with and to what degree Buckmaster's work was fed into its training data, either by Buckmaster himself or by his co-author.
and you can argue this is "fair use" or whatever, not the point now, the point is that it definitely makes those accusations no longer "baseless".
in addition, it is not given freely to the world, it is the knowledge of the Internet/WWW being sold back to you as a subscription service. it's not free. and it's not even "given", because they can (technically) turn off the tap at any moment and you don't have it any more.
I mean some companies glean insight into new products merely by asking other people what they do for a living.
People need to get over this ownership thing, it's being taken too far. Humans benefit from the efforts of others simple as that.
The culture at OpenAI being systematically revealed by Apple’s lawsuit, for one.
https://x.com/sama/status/2097385167002415140
https://x.com/SebastienBubeck/status/2097379411691516310
A wake up call for using OpenAI models. If you discover something with their model and you work for a competitor, they “felt it would be inappropriate” for you “to author OpenAI’s work”.
Now maybe LLMs can also simplify arguments and make sense of them for humans, but we haven’t seen that yet (unaided).
(I haven’t looked at it, personally.)
They don't need any help publishing.
It would be extraordinarily easy to simply say, this model was not trained on your work, if that were the case.
It's telling that they refuse to acknowledge the root issue here, and are attempting to shift the conversation elsewhere.
But it is knowable. Their entire business is built around training models - they have the ability to know exactly what was in any given training run.
I guess time will tell.
Data has to be determined to be signal and not just noice, then it could go through processes of generating questions/answers from that data, then it RLHF's over this.
OpenAI have petabytes of data, all anonymized. It could take months to say for sure it was part of the training, and even more time to determine if it made any difference.
They know which model was used to come up with that particular idea.
A text search over the corpus of user data used in the training set can only take so long.
Can you explain the difficulty in engineering a search apparatus over a corpus of text data? Actually searching through it may not be easy, sure, but it's work that's doable, and creating an index is relatively trivial.
My guess: "If we ever imply that's possible, people might start asking questions about all the other work we've ripped off, so the official answer is that it's impossible".
They can operate. They shouldn’t be claiming credit for discovering anything.
And the difficulty is harder than just the extreme scale of text searching. but also explodes with organizational difficulty since there are so many people tweaking/shifting data independently upstream of the actual training run, and no they will not all add the telemetry you wish they did.
In the ideal, should it be this hard? Well, no, but that's org wrangling for you.
The engineering around tooling wasn't remotely the issue. It's getting all the (thousands?) data researchers mostly iterating on fine tuning datasets that would get bristly if they couldn't work outside version control in a python notebook iteratively tweaking their dataset that processed and reprocessed a few datasets until a threshold was reached.
The only _guaranteed_ chains of custody are down at the compute job and file read level. Which in a massively distributed computing job is... [redacted] nodes reading [redacted] fanouts of "datasets" that is just an abstraction over [redacted] individual files.
There's no malice here. Just way way way more complex than you'd first think.
To not know who made and who approved a set of mutations on data can easily become equally as mind-blowingly stupid as not knowing who made mutations to code. Code is a subset of data after all and search over (provenance of) data can be implemented as DAG traversal.
Not tracking data changesets like code changesets is certainly a choice, not really a constraint anymore. A similar choice I feel is implied by "extreme scale of text searching".
> no they will not all add the telemetry you wish they did
...is just a failure of the corporate policy surrounding data handling. Is git-for-data already considered telemetry?
Of course the truth is provenance of data is something best institutionally forgotten as quickly as possible. The only thing that matters is it's there, that the data has no history, and that's why it can be used in whatever way deemed necessary.
You can call it a policy failure, but these people were in very high talent demand and so top down dictates would risk "X people leaving lab Y for lab Z" headlines and morale hits.
I am not saying this is good. I am telling you that on the ground it is so much messier than it should be.
Did you notice the line in the article that says the models had access to an offline copy of THE INTERNET. Like all of it.
What surprises me is they're not more boldly/plainly lying about it.
I’m not saying they didn’t do anything unethical. I’m just saying even if they were ethical, there’s plenty of practical reasons at their scale why a flat out denial is logistically difficult to do
The Huggingface Attack revealed that making blanket statements like this is difficult and requires quite a bit of manual labor:
1) the agents spin for days and produce too much output to review 2) using LLMs to process that output skips many important details
Ergo, the agent could likely decide it would like to look through actual user data, hack its way into that data, and produce way too much output for a human to decide whether or not this occurred.
It requires humans to verify what agents have done.
Weird
silly LLM, so ruthless in its pursuit that it puts real pressure on the innocent and the most open company on the planet
Anyone who just reads headlines, if the lie gets around to more headlines than the truth does.
well, it is trained on their work. all user inputs are paraphrased for training. at openai, at anthropic, at google, and now with all the bedrock models, and at openrouter providers, even if they say zero data retention.
"Our aim was to see whether our system was also capable of this impressive feat"
"OpenAI's intention was to do everything possible to celebrate their mathematical achievements and the heroic efforts that they made on Euler"
For some reason I have a hard time believing people when they use language like this.
Maybe shows how fast these companies have grown without maturing. I can imagine old-world Intel and Microsoft acting in that way, but they were mature enough to not write it down like this.
However, Intel and Microsoft have been grilled in court for those practices and faced harsh consequences. I have yet to see this actually happening to any of these new AI-companies...
Since it is clear to you, can you articulate what it is? I was unable to infer "the truth" from your message.
is this true though?
Imagine that a no name janitor used their time in the evenings to go spelunking through the literature to push an LLM to this result. No one would care because that person isn't an anointed expert. So why would the expert deserve any more credit? Because they sort of understand the result, even if they couldn't have achieved it on their own? The whole issue of credit for AI-assisted discoveries seems like it's going to run into a brick wall pretty soon.
It’ll have to be Good Will Hunting 3.
Have LLMs actually improved anything? Is mathematics better off than if these slop proofs didn’t exist? Who or what is actually benefiting here.
BTW, this was always the plan from day 1. You will pour all your training and experience into training the model and receive a pink slip as compensation.
Sam+Seb are struggling with their ideological allegiance. This amounts to a confession that there are no reseaechers, only research managers, left at OpenAI. Maybe they even know that they are losing credibility from their main investor(s). They desperately need a domain expert to salvage credibility.
They have no credibility with academia left, obviously, but their main competitor still does. No Millennium prize incoming, I'd wager. For openAI. Let's see mAth get political for once!!
One might be more certain that levent is now going to corner all the institutional support. Go go go!
We often chat where the business might be heading in future. An uncomfortable scenario is what if a frontier tech company decides to offer our customers the same products that we do.
There's a lot of pressure on AI adoption so the company has partnered with various tech companies to build intelligent systems on top of proprietary data and mathematical models.
If OpenAI is indeed using customer data to train their models to win a $1m prize, then it throws a giant IP question at the partnerships that affects multi billion dollar businesses.
Is that even a question? Of course everything not kept on premise at gunpoint is going to be trained on. The chances of getting caught are 0 and the consequences of getting caught are 0 (as we've seen with copyright laws going from sending people to jail for years to unenforced within months). Yet the benefits are through the roof. Your customers aren't going to pay for having the very same data vibe enriched twice, it's exclusive, extremely high value data your competitors will never have access to.
Scale with subsidized pricing as fast as possible to gain more user-data for training --> Own the better model --> scale pricing.
Scanning social media (e.g. Twitter, Reddit) posts only give a glimpse into the thought-process, chat logs on-scale give you the actual process in machine-readable format.
There's a reason why Google considers the Emails of Spirit Airlines to be worth millions of dollars [0], they give insights into a process, not just into the results...
[0] https://www.axios.com/2026/08/17/google-spirit-airlines-bank...
The question, for AI customers, is when they build products using services of AI-companies, would AI-companies engage in theft of customer data for use in training?
But honestly... "Will the company that was entirely built over illegally acquiring data use some data that is legal to use and is right on their front, or will they not do everything they reserve the right to do?" is a really bad question for one to even ask.
I'd say non-zero, as seen in the current state of affairs.
But don’t worry bud, instead of the authorities going after actual corporations admitting to actual crimes, we’ll just ban CloudFlare IP addresses for everyone during La Liga games to battle piracy.
You wouldn't want to decide what's worth training on and what isn't manually, so there is almost certainly an automated pipeline to do so (certainly at least for the free accounts and those that dont opt out of training).
Then there's the question if this pipeline only sorts through the data or also transforms it and to what degree. E.g. for removing personal details, locations, medical information and so on. The data that comes out of this pipeline might have VERY little information left in it a human could connect to the original input. Even worse, since we're talking about companies specializing in sota statistics, the input data could have been transformed into a representation that is very well suited to represent all the novel and interesting parts, but is awful at modelling all the things that could end up identifying where the data comes from (or causes legal liabilities otherwise).
In the end the only thing a potential whistleblower might even have a chance at observing in the first place, is whether a company's data enters such a pipeline or not. And I have my suspicions that the major AI companies operate at a scale and level of automation, that absolutely nobody has a chance at figuring out where anyone's data is at any point in time and what any specific piece of equipment is currently busy with.
So the only place to figure out whether data is trained on that shouldn't be trained on is by looking at whatever configurates every single system that could take a peek at some customer's data or the systems themselves while processing the data.
The latter would be such a huge violation of a customer's rights, no whistleblower is going to attempt that or admit to doing it.
And the configuration for the former could live just about anywhere, from regular config files to the CI/CD pipeline, pre-compiled libraries, kernel modules, modified vendor firmware, the compiler itself ... and probably plenty other scenarios you'd have to train an LLM on the ramblings of a crackhead to come up with.
So I'd say a whistleblower is pretty out of luck even becoming one.
Besides reporting on search sources you can also run the same queries on multiple LLMs closed book mode, and judge their distribution as well. It helps a lot if models are more aware of their knowledge holes. Scale it up for billions of topics if you have the pockets, the DR data is copyright free.
Why should your business be any different?
I feel this is exactly what will happen as they cause all sites to go closed source to protect their intellectual property and the AI companies offer only biased information. They are replace the business on internet model by bankrupting everyone with their own tools. This is predatory pricing under most antitrust laws (imho, not a lawyer) and it is very easy to do when you dont need to pay for the raw material.
I mean how could you expect them to not given they've trained the existing models on effectively the sum total of all human knowledge available on the internet without regard to copyright/ownership of that material.
It's a little trite but this absolutely runs into the "Frog and the Scorpion", it is simply in their nature.
Any enterprise worth their salt already considers this stuff.
First - there is this - https://openai.com/policies/how-your-data-is-used-to-improve... (linked from the Navier Stokes writeup)
I don't know how much more clearly they can write:
> When you use our services for individuals such as ChatGPT, Sora, or Operator, we may use your content to train our models.
One of the key selling tactics that companies like Data Bricks or Palantir provides their customers is "Data Governance" - that is, some control over where the data is being used. It's also a reason why enterprises don't use the OpenAI or Anthropic APIs directly - but through secondary sources that have Enterprise Agreements that do their best to make sure that no Company IP is ever retained by a third party, or even exists on a multi-tenant GPU. AWS Bedrock, and companies like together.ai, fireworks.ai have tons of deals that focus very much on data confidentiality.
The reality is - if you want any type of control - you run your own inference, on your own hardware. Anything else and you are at the mercy of third-parties, despite what their contracts might promise you.
> Allow your content to be used to train our models, which makes ChatGPT better for you and everyone who uses it. We take steps to protect your privacy. Learn more
The "Learn more" link takes you to the link you've shared.
There's a reason why people spend more $$$ with Data Bricks, Palantir, AWS Bedrock etc.. and don't even consider using Anthropic or OpenAI APIs directly - it's because those guarantees provide very little in the way of data-discovery, audit requirements, or liquidated damages should it ever be discovered there was data leakage.
At least with these other companies, while the LD is likewise not great (typically limited to the amount of money you paid them) - you at least have some data-governance guarantees around running on dedicated hardware - no multi-tenancy, no third-party access outside of the AWS operators who keep the HW running - but are very much not in the business of looking at your data.
I think this is mostly a function of what's at risk - when company valuations get into the 10s of billions of dollars, the risk of IP leaking into what could be seen as competitive companies (OpenAI/Anthropic would be happy to take over the world - I don't sense that AWS or Azure, are as ruthless in stepping on their customers business, unless of course they are a SAAS provider) is just too significant a liability to take - particularly when you can de-risk.
Is that a threat?
> 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.” Some time later Levent received a text proposing that he and Sebastien speak one on one, saying, “I don’t know if Tristan is being fully rational right now.”
Yes, that is disgusting.
What stands out to me is the naive lack of operational security on the part of academics, who should know better than to touch this SaaS crap with a ten foot pole.
I don’t think we can consider these accusations separately from the evidence being unveiled about OpenAI’s culture by Apple’s lawsuit. These guys seem to openly embrace the strongest interpretations of “good artists copy, great artists steal.”
If there was any sort of coarse insight that "they're trying to solve it this way", then both those things can be true:
- The massive amount of compute from OpenAI re-discovering Buckmaster's work solely from the coarse insight (and solving the rest as well).
- OpenAI still acknowledging they basically scooped the coarse insight using compute, and they're willing to credit Buckmaster.
Buckmaster says "Concretely, what Levent and I did was to take the Cordoba and Martinez-Zoroa program, which achieved blowup results with rough forcing, and, with a great deal of help from LLMs, push it to smooth forcing and to the incompressible Euler equations".
Could that simply be the prompt they used at OpenAI? How "stolen" would the proof be in that case?
the paper makes a very serious allegation of dishonesty and possible academic misconduct.
the governance and integrity of openai is of importance to the welfare of society. this is not a matter of drama.
legally speaking, the default privacy notice gives them an irrevocable license to your content. they may read and use the prompts for research. so it is very possible they simply stole the navier-stokes solution.
that is the same principle as any other prompt but this would be a concrete example.
there would be some difference between simply giving the model some prompts to read, which they are entitled to do on the default policy, and putting it into aggregate training data.
I think it's notable that nobody was calling out those researchers for their lack of integrity, because the systems they were building did not seem like a threat to anyone.
OpenAI etc get accused of a lack of integrity on this precisely because the systems they are building work, and are profitable.
My personal opinion here is that integrity is more about what you build with the data. I think saying "scraping means you lack integrity" is a simplification.
OpenAI et al also stole everything from everyone. But then they raised billions of dollars from that data and sell back their LLM to people (again, among other things). They are also very much NOT open in any way, aside from sharing their benchmarks of new models.
Also my understanding was they’re not storing the actual music, but the metadata and a link to the YouTube video.
Then you have OpenAI etc.. who build these multi-billion (trillion??) dollar machines and sell them back to people, using everyone's proprietary data, and (among other things) tell everyone it's going to take their jobs. That combination of things doesn't scream integrity to me.
Still, it's undeniable that these machines could be beneficial for humanity (cancer research and such). So, I'm sure many people would say the good out-ways the bad. I don't know. Seems that would set a risky precedent for future companies, but maybe not.
The strongest complaint is that they trained on a huge corpus of pirated copyrighted works.
It’s a large step above “scraping” and well into the “everyone acknowledges this is illegal” territory.
"Since August 28 we have been training a new internal model that has exhibited unprecedented performance in our benchmarks, including mathematics. This model’s training is ongoing and its performance continues to improve."
"When a further trained version of our internal model became available over the course of the effort"
"While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models "
This sort of cagey half-answer is highly suspicious and indicates that yes OpenAI did actually "access user data directly" because they are only willing to say that the "model did not access user data." That has a very specific meaning, the model looking up user chats, that they can defend.
So, everything we submit to OpenAI can be considered to be part of future models, right?
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models
That basically means, we don’t know, and we hope the model didn’t look up user conversations, and the best thing we can do is hope.
That’s seriously disgusting. I can understand why on a technical level why perhaps it is impossible to answer what exactly the model had access to, but it still is disgusting.
If the work is duplicative/derivative then the preprints they put in sessions can be shown by the users and we can see.
Nobody would be disgusted at following stated policy, that's doesn't make sense, without first objecting to the policy. But you're bringing up distractions from the actual concerns: did OpenAI use the private chats and why won't they confirm or deny it?
it just means that they've been working with paraphrased user data everywhere, which any smart person can figure out is how anthropic and openai train on so called non-retained data.
This is more of an expectation of privacy issue. If you write on an envelope and USPS has a copy, you have no reason to be mad; if you write on a letter inside the envelope and USPS still has a copy, you could rightfully be mad and say this is disgusting.
[0] https://x.com/SebastienBubeck/status/2097379411691516310
Same for NS validity. This was not validated by the community yet.
What a terrible look for OpenAI to die on such a tiny hill right there. I wonder whether Anthropic would have made the same requirement.
- One of the two main persons work at Anthropic and "almost" or "partially" solved the issue, but eventually didn't succeed
- An external person with just an excerpt of the chat and certainly less versed in Mathematics (than these 2) tackled the problem.
There is little doubt that OpenAI is so much ahead and maybe the gap is even larger than what we see on Astra vs Fable.
Very weird behaviour from OpenAI, offering partial credit to on person, but not the other person involved. Trying to bully the mathematicians involved (see threats quoted upthread).
I suppose it's the sort of amoral behaviour we've come to expect from them.
This is sort of a weird interpretation:
> One of the two main persons work at Anthropic and "almost" or "partially" solved the issue, but eventually didn't succeed
- It wasn't an Anthropic endorsed effort.
- Solving this class of problem means a march of progress A -> B -> C -> D. If a student turns in a test that jumps from A -> D without showing any work they're either brilliant or cheating (probably cheating). Further, each step of progress isn't the same proportion of effort. What if moving from C -> D was actually the smallest contribution and just required a novel perspective to make the breakthrough.
This part is wrong:
> An external person with just an excerpt of the chat and certainly less versed in Mathematics (than these 2) tackled the problem.
- it was a whole team at OpenAI working on the problem
- it wasn't a chat excerpt, it was more like their entire git repo and project progress reports
Well, a whole team plus $15 million in compute spend.
(That's what OAI would have charged for the same number of tokens.)
Its like saying you won the car race, but you stole the fastest car and had your m8 drive you around the track.
I wonder whether these bickering users (of AI various products) with math degrees are missing the forest for the trees.
One minor wrinkle in Alpöge's narrative, he refuses to deny that he hasn't used any non-public Anthropic models for his "independent" research.
"OpenAI says they would partially credit Tristan for the $1,000,000 discovery (even though Tristan did not solve the $1,000,000 problem) — but only if they remove Levent as an author, as he works for Anthropic."
There it is.
Nobody "owns" math but that's petty and shitty.
It is impossible to fight against this. It is statistically obfuscated, they can just argue it is a derived work.
I'm not even sure what to say to this, but I think this should be widely known if it is indeed what happened.
First, this is an unnamed OpenAI employee speaking, not OpenAI the organization.
Second, you miscomprehended the article. The employee did not "threaten to ruin a prominent researcher's career". The actual quote is "Why would you ruin your career?", which implies the researcher would damage their own career, i.e. via self-sabotage.
Then the actual "threat" is "If you don’t want me to be nice, then I don’t have to be nice” which is an entirely different statement.
Oai offers two options, the second Tristan views as dishonest. But Tristan rejects the first, why? Because he thinks it's theft? But then why would OAI threaten him?
OpenAI claims to already have a full proof (which they produced in the past 5 days after the rumors leaked). Hence the dispute.
What I find interesting is the timeline of when he found counterexample for NS is very unclear. Did Tristan find a counterexample weeks ago or was it very recently? Was it after OpenAI solved it? The wording is intentionally vague.
Either way, there was a massive rush to publish these results.
Did the first offer also come with the outrageous condition that he exclude his co-author from the credit?
Proceeds to ask removal of another coauthor or else we totally discredit you - phrased as why would you do this to yourself.
From the article, it seems OAI wanted to continue discussing the situation with Buckmaster and reach a resolution, but Buckmaster did not want to, declined to respond, and published first.
Also keep in mind we've only heard one side of the story, so any interpretation of events so far is incomplete. There should be a lot more information from OAI's side coming out later today.
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.”That’s not quite true though is it. OpenAI is fortunate enough to have one of its employees (you) here to advocate for its side of the story.
OpenAI offered to let Buckmaster to write their Millennium Prize paper, so long as Alpoge (who works at Anthropic) was not a coauthor on the OpenAI paper. Buckmaster declined this offer.
Either put up some evidence-backed arguments, or shut up.
"If you dont want me to be nice, then I dont have to"
-nice mobster
Whether the Codex sessions could have indeed made their way into Astra training data is something I can only speculate on though.
No looksies, wink.
No trainsies, wink.
[0] https://openai.com/policies/how-your-data-is-used-to-improve...
I bet a lot of lawyers are salivating at this question too.
If OpenAI did use the conversations from Buckmaster and Alpoge, then not disclosing it, explicitly, is plagiarism. If they planned to use that plagiarism to pressure the authors to publish, that is even more unethical. What the terms of use say does not make it any more or less ethical.
> Why the downvotes?
I think there was only ever one. Not sure why.
About the plagiarism issue, I model it as OpenAI being an advisor and their AI a PhD student. If the advisor puts their name on a paper behind that of their PhD and it turns out the PhD copied the text of the paper from somewhere else the advisor is also responsible of plagiarism, not just the student. The least the advisor can do is withdraw their authorship from the paper.
But, yeah, point well made: it could be much worse than that. Like an advisor instructing a student to copy someone else's paper.
Personally I don't like thinking of LLMs like a PhD student, because most PhD students remember where they learned things from, while LLMs essentially cannot. I think of it a bit more like someone using a search tool carelessly. Although in this case it is apparently more like deliberate misuse than carelessness.
If I know person A is working on problem B.
I am free to work on problem B too. Why should person A be limited to working on it.
Also brain raping* is not illegal in most jurisdictions.
But they're both deeply disturbing.
_________
(And if memory serves, there is also the opt out from training on consumer subscriptions). Its not plagiarism if you make your data available for the purpose of training their LLMs. It is you giving away your IP for some tokens.
> I believe Luis Mart´ınez-Zoroa deserves a Fields Medal.
> A series of false and inflammatory allegations against me are currently circulating on social channels. To clarify, I came into the discussion following academic norms, and I'm disappointed that it has come to this. Anyone who knows me knows that academic standards are of the highest importance to me. Will have more to say tomorrow.
https://x.com/dheeraj_nagaraj/status/2097266146445774924?s=6...
This is such a sad mess, and it really didn't have to be this way.
Call this behavior what it is, technofascism. Another comment compared it to the Godfather. To think this is the 21st century and academics are still horrible human beings.
Or are you stating that the researcher is a "horrible human being" for refusing to allow AI?
Exhibit nr 8453324 to not trust Sam Altman and OpenAI.
Mother's interview: https://www.youtube.com/watch?v=Kev_-HyuI9Y
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.
Yes, I read fully the statement, what about you? Do you know what is a threat? What is this in your super-humble opinion if not a threat:
> 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.”
And you are saying that I don't have reading comprehension...
> 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.”
That OpenAI heard about the result and decided to throw a lot of money at it knowing it was within reach ?
That the model took an approach that was published years ago ?
So either the rumors or Tristan's contact would explain it fine.
The whole point of Tristan's first email was to address the issue of the rumors so in fact this explanation confounds several things (in terms of the mutual knowledge of the conversants and their intentions).
Based on this lack of understanding it is pointless to continue this thread
OpenAI tried to collaborate and share the results together with a fixed timeline, to avoid this mess but it was inevitable. There is a conflict of interest, where the other researcher works at Anthropic, who will also try to take credit.
Where they may be in the wrong is if they took user data regarding the problem, how will we know if they did or not?
That is not collaboration, and is not an academic norm.
OpenAI is no stranger to rivalry with Anthropic but 1. it's not like user data is sitting around on some kitchen table somewhere and 2. I consider OpenAI to be as economically motivated as any other actor in this space and playing around with user data like that would destroy their business.
There are things that Buckmaster alleged and things that he speculated. The entire training data thing is speculation. If this is pissing you off, then you ought to evaluate how you ingest information.
> 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.
The shocking/interesting thing would be if it was trained on the sessions. I think it's very implausible that they gave the model access to someone else's sessions as input. That would be a huge privacy violation and would probably blow up a large proportion of their enterprise business.
Does openAI train on user conversations in general? I assume so. But so fast as that? That seems unlikely in general. I expect OpenAI will come out denying this.
Enterprises are well aware of it and are fully on board. You didn't think every corporation in America has an OpenAI subscription because the models were good, did you?
The whole reason they have subs is to train them on YOUR WORKFLOWS lol
Model editing to remove PII that slipped through, all sorts of things of that sort.
There’s potentially trillions on the line, do you seriously expect those companies to adhere to laws and regulations any more than, say, uber?
The only unlikely part is the timeline - your sessions from a week ago probably haven’t made their way into the model. It’ll just take a while longer, and will be massaged just enough so that it isn’t really your exact session word for word so you can’t sure as easily.
I also don't get why it was downvoted, other than due to people not reading past the first sentence - although in the modern world's attention deficit that is understandable too
> I was told the model did not look up user data.
The naive way to read this is "Nothing you guys did influenced the way our model got to the solution".
The less naive way to read this is "Of course the model isn't looking up your user data. I (the guy trying to blackmail you to remove the Anthropic employee from credit on your paper) looked up your sessions, and tipped our model off on how to solve this problem".
It's a bit like sending unencrypted messages through a messaging app and the developer having a TOS that says they don't look at your messages. They might not, but they are fully capable of doing so. If they have a reason to do it, they will. Nobody's stopping them.
Or (likely) they do have it, but the model didn't use it (unless it's so powerful it escaped that guardrail, wouldn't that be ironic?)
They declined to answer about anonymized aggregated user data being used for training. And even then, they may weasel out that they don't train on your “input” words, but that it's fair game go train on their “output” to your words.
How "fast" does it have to be? Buckmaster and Alpoge have been working on this for just a day short of a year. See Alpoge's tweet announcing his collaboration with Bukmaster dated 9/19/25:
https://x.com/__alpoge__/status/2097206973418611054
It takes a few months to train a model these days but not a whole year. OpenAI had all the time to train on Buckmaster and Alpoge's results of just a few months earlier at which point they must have been well on the path to their result.
ChatGPT user sessions were found publicly exposed to the internet not too long ago. Moreover, OpenAI has continued to play a hype-marketing game by revealing how their models keep breaking out of the sandbox.
Conspiracy minded thinking is not helpful, but why should OpenAI be granted the benefit of the doubt here after being caught doing underhanded/negligent shit on several previous occasion?
Do you mean publicly shared chats were able to be accessed by the public? That's the point of the feature.
I would be shocked if they weren't tuning those models with the most relevant math texts and user material
We had all assumed that surely the supposed smartest engineers in the world, with access to the most computing and a direct view of model capabilities, would take sandboxing and cybersecurity much more seriously than they have turned out to do. It follows that while we might assume they take user data privacy seriously and have tight controls on who can access it, it's possible they do not actually do that.
At this point any initial trust is dead and has to be re-earned.
Their entire business is based on stealing data. They can make a calculation that the cost stealing data is less than the cost of the positive publicity they can shape for solving Millennium NS
I think it's safe to assume AI labs DO train on your data and it's very hard to prevent that.
I've just checked my inaptly named "Help improve our AI models" toggles. The toggle on the Claude settings had magically turned on. I asked about how this can happen. Claude says they show re-consent modals when terms change, and it is a "real and fairly common pattern" to re-opt in without noticing.
All my work and conversations since I don't know are now part of their training corpus. No way to take it back.
Google's Gemini/Antigravity didn't have opt-out toggles at all last time I checked.
Codex also has a separate "include environments" setting which is hard to find (found it in Codex Cloud) and I don't know what it does.
Lots of Dark UI Patterns here even if we assume they keep their promise.
For this incident, Occam's Razor says their internal models somehow saw a version of the mathematicians' logs, during or after training. Maybe indirectly.
These systems are literally designed to collect data. Privacy and safety is not trivial to achieve on the users' side. Simply because it's against the labs' best interest.
And your (2) is probably false, their history of deception suggests they would do just about anything as long as they didn't think it would backfire on them publicly.
Quite literally in the terms of use.
It's a gamble that this would be overlooked compared to the reputation they build for solving the thing
And that's exactly why you can only see evidence of this when the stakes are high enough, such as solving a Millenium problem. The legalese they outputted in response to the incident left them an escape hatch that permits the possibility of theft. People familiar with corporate damage control should recognize the verbal maneuvering, often used to paper over actual guilt.
There was also already a high prior of shadiness. The company is run by someone who is close enough in reputation to "known sociopath".
It's actually far more reasonable to assume that OpenAI stole user data to generate a breakthrough. They have an unbelievably high economic motive to do so. And even a low chance that they might be doing this implies catastrophic risk to anyone with valuable knowledge.
And simply knowing a problem can be solved is half the battle.
The route to the Clay problem through a
smooth force, options c and d in Fefferman’s statement of the problem, is the
route Luis and Diego opened and the one Levent and I had quietly chosen to
attack. Almost nobody else I know of was working on it. It is not the direction
one arrives at in a few days by giving a model the problem statement. When I
heard “forced,” it was a bright red flag.
And the article states "an insane amount of compute had been used," which implies OpenAI brute-forced their way to a solution. I.e. they searched for every paper published on Navier-Stokes and exhaustively attempted every approach. Such an approach would lead them to a solution.
There is not enough information at this time to reach a conclusion. The best option is to wait for statements from both sides, then reevaluate.
the post you were replying to quotes Buckmaster specifically denying this: "It is not the direction one arrives at in a few days by giving a model the problem statement."
> And the article states "an insane amount of compute had been used," which implies OpenAI brute-forced their way to a solution. I.e. they searched for every paper published on Navier-Stokes and exhaustively attempted every approach. Such an approach would lead them to a solution.
"implies" is a surprising choice of word here. that's certainly one interpretation of "an insane amount of compute had been used". what came to my mind, considering Buckmaster's statement that the AI would not head down this specific path on its own, is, though, that they prompted it in this specific direction and then used an insane amount of compute. this seems consistent as well with these other statements:
> 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 number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler (...)
Can they back up this statement somehow?
Buckmaster did also mention, for example, that a team of people was employed to solve the problem, which supports this claim. but that is another claim whose veracity could also be questioned. but at some point we must trust other people, unless we can be satisfied with only believing what we personally see.
(also, IMO, the coincidence of both discoveries in time is pretty suspicious. this one doesn't need you to trust many people i guess)
To be honest, he was referring to routes (c) and (d) to the millenium problem, as far as I understand no more specific. Which is 2/4 routes.
> The route to the Clay problem through a smooth force, options c and d in Fefferman’s statement of the problem, is the route Luis and Diego opened and the one Levent and I had quietly chosen to attack. Almost nobody else I know of was working on it. It is not the direction one arrives at in a few days by giving a model the problem statement. When I heard “forced,” it was a bright red flag.
so, you're saying that "the direction one arrives at in a few days" is (A) "the route through a smooth force, options c and d in Feffermann's statement of the problem", and no more specific than that, i.e. does not necessarily include (B) "the same path route as Luis and Diego" (quoted from the post i was replying to) (which, as i understand, is a subset of A -- directly from Buckmaster's quote: "the route A is is the route Luis and Diego opened")?
but the post i was replying to claims that "An AI model could independently choose the same path route as Luis and Diego, without access to Buckmaster and Alpöge’s work", i.e. that the AI model could independently chose B. but choosing B implies choosing A, since B is a subset of A. and in this case it is irrelevant whether Buckmaster claimed that an AI could not independently choose A or B -- the point which you seem to be contesting.
EDIT: my understanding is that "solving the Navier-Stokes existence and smoothness problem" consists of proving at least 1 of 4 precise statements ("options (a) through (d) of Fefferman's statement of the problem"), and Luis and Diego's work were developments towards a proof of statements (c) and (d), which have been recently further expanded by Alpoge and Buckmaster
Sorry for random rant but I don't think these statements help your point
OpenAI said there [1]: > The method by which the problem was solved is also notable. The proof brings unexpected, sophisticated ideas from algebraic number theory to bear on an elementary geometric question.
[1] https://openai.com/index/model-disproves-discrete-geometry-c...
Have you done any mathematical research? If not, then no, knowing that a problem is solvable is not “half the battle”.
Homework problems are all designed to be solvable, yet they can vary greatly in difficulty. Research mathematics is even more extreme, because, unlike with homework, you don’t know that it is solvable with the extant mathematics, and you might need to invent new maths.
If not for the rumors that A/ had already solved NS, OAI would likely never have pursued solving the problem with such fervour. The rumors drove OAI to assemble an entire team to crack this.
This doesn't seem to be clear and is very implausible for a large company. Be as cynical as you want, but a normal researcher will simply not have access rights to this data, which will be siloed away somewhere else.
It might very well be somewhat unfair to catch wind of a promising approach and then try to frontrun them by throwing compute at the problem, but this isn't really the same.
"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."
Let's see what statement OpenAI will come up with for their side of the story
EDIT: precised my thought on user data vs session data
"Since August 28 we have been training a new internal model that has exhibited unprecedented performance in our benchmarks, including mathematics. This model’s training is ongoing and its performance continues to improve."
"When a further trained version of our internal model became available over the course of the effort"
"While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models "
> 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.”
The whole business is based on reselling user data scraped from the whole internet
It’s plagiarism at scale
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models
This is the crux of it. If Tristan's work and insights were not used to train OpenAI models, then this just looks like a case of hyper-competitive academic sniping that has been going on for decades (check out Watson and Crick!) accelerated by AI as a tool.
The fact that this is ambiguous even to OpenAI leaves one huge question: did Tristan opt out of model training for his ChatGPT and Codex sessions? If the answer is no, then this seems fair game. If the answer is yes, then OpenAI's ambiguity is strongly suggestive that opting out of model improvement does not mean what they imply it means.
"Do we use user feedback and de-identified data to improve ChatGPT and Codex in a holistic way? Yes. And so does every LLM company." - Mark Chen, Chief Research Officer, OpenAI.
I have opted out from data sharing, and when Claude asks me for feedback on a session it then asks if its OK to share that data with Anthropic.
I'd assume an opt out is an effective opt out. An opt out that is ignored by Anthropic is a breach of contract, not something they would do casually, esp. given the high turnaround and animosities between their own employees and ex-employees - and the labs. All it takes is one pissed off whistleblower to open a can of worms.
Occam's razor applies. The mathematician did not opt out from data sharing. OpenAI vacuums up all such data into training data sets. If OpenAI genuine does not easily know if a given session went into the actual training data set its probably due to the complexity of the data pipelines - not everything ends up impacting the model weights, after all.
This may sound like a charitable interpretation of OpenAI's remark, but consider that the lie would be (I think) impossible to falsify from the outside. They could easily just say "no sir we didn't peek" unless:
1. The conspiracy to peek at codex sessions involved enough people that the risk of one snitching is non-negligible
2. Lawyers advised it would be a bad idea to make such a remark, whether true or false
No; if they said "we can see that Tristan opted out of model improvement, therefore we are confident his work and ideas did not improve our model," that would be an excellent and reassuring precedent.
A totally reasonable pipeline may be unauditable for this purpose.
I'm pretty sure it would be considered plagiary amongst colleagues and it is a terrible precedent if we just let OpenAI steal any good idea they can get their hands on if they think it is profitable. You'd effectively sign away any and all rights to anything built with AI if OpenAI chooses to reengineer it before you.
They sure as hell don't need it just to produce English.
I have terrible news about how literally every leading AI model was trained
Ai companies got where they are by stealing all of the intellectual property from human history. It seems entirely likely that their goal is to purloin everything produced going forward as well.
This is well-known to anyone in the industry.
That's a pinky swear. Especially as data gets harder to come by I'm curious how long till there's a scandal on that too.
Unless OpenAI finished a whole new training run on the latest data in the last few days, the possible allegation seems to be the latter.
They have been collaborating on this solution for a year, and Astra was trained in February this year so it’s entirely possible the direction of their research was in the training corpus.
That article is only saying when you opt out there may be a loophole in the terms to allow OpenAI to train on the intermittent reasoning data anyways. If you don't opt out there is no ambiguity, all of the data can clearly be trained on.
So you have to opt out, it's just argued it's not clear from the terms that will also opt out of training on reasoning data or not.
The way for people or companies or universities to control their data and information is to keep it on their own computers.
The fact that this academic sniping can now be done at scale does change the formula though and shouldn't be ignored. The pressure to move math work into secrecy because at the slightest signal OpenAI and Anthropic will start burning tokens for headlines, is bad for math and its bad for everyone.
> In fact, it is now the identification of a promising problem which is the scarce and precious resource. 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.
This is by no means new. Perhaps it is even more extreme now. Literally my first 1:1 with my PhD adviser back then, he told me that the most important thing about a researcher is the quality of the problems he picks.
In the real world the quality of these esoteric problems is typically gauged by the difficulty of solving them.
I don't believe that's strictly true. Way oversimplified projection on one axis.
OpenAI should release the agent log, including CoT.
That “opt-out” thing is a dark pattern. It’s not a reliable and definitive way of protecting your data. Sometimes they flip on automatically when you accept a seemingly unrelated dialog box. Maybe you click it by mistake. You can’t take back what you’ve already shared. Also I don’t think it covers all the cases that they use your data. It’s really an opt-in button for voluntarily giving away your data for training.
This also supports my point that protecting your data is not as trivial as clicking a checkbox.
Yes, fair game, but innacurate to sell it in the media as an advancement of AI as some sort of artificial intelligence, and telling people to use the smart AI, when in actuality the mechanism by which the discovery was found was hybrid human/machine, and telling people to use this tool will result in the discoveries being sniped by the vendor.
I took their words as “can neither confirm nor deny”, in the that they are _presenting_ it as ambiguous, but I suspect it’s… less ambiguous to OpenAI.
Wildly disagree. "Training data" should not imply 'we can look at exactly what you are doing and then do it quicker and get the flowers for it', even if the terms allow for it.
This is covering for Tristan saying something like, "Actually, I was using my friend's account for half of this work".
That's assuming they actually honor this which I'm highly sceptical of. Especially for internal frontier models
I thought they worked together.
[0] https://xcancel.com/SebastienBubeck/status/20972141224714323...
[1] https://xcancel.com/polynoamial/status/2097215233119211902
[2] https://xcancel.com/danintheory/status/2097214838003138603
[3] https://xcancel.com/_sholtodouglas/status/209721833169057800...
2:47 am (eastern time for me) https://x.com/polynoamial/status/2097215233119211902
2:59 am https://x.com/_sholtodouglas/status/2097218331690578000/
Also note the lower post ID in the URL.
If I needed to get my story straight, well, it might take a little time and coordination…
From which I assume OpenAI PR wrote it for them. Which isn't surprising, but means it isn't worth taking seriously as them saying anything. It's official OpenAI PR.
I don't know why.
If compute is cheap, and the difficult thing with scientific discovery is now mostly in steering agents into promising areas, there's an obvious incentive for OA mathematicians to simply monitor closely which researchers are close to releasing exciting results, make some assumptions about their prompts based on their past work, and quickly prompt their own (stronger) model to look into the same areas.
Why leave that aside? That is _the_ story.
If a Chinese research lab did this we'd call it espionage.
So to say that it is unlikely is extremely suspicious. No, they did not literally pull user data. But user data is automatically added to their training set by default, so their latest in-house model would be trained on it if it is from several months ago. It isn't intentional on their part, and they probably realised they could not refute that they trained on Tristan's logs unintentionally, hence why they acted the way they did.
If they're going to try to beat researchers to discoveries like this it disincentives researchers to talk about their progress publicly, and basically breaks the ecosystem of scientific cooperation / discovery. It's also immoral.
For math, a field that is built on incremental research it feels like AI labs will do nothing but discourage publishing research at all for fear that they will be able to spend the money for compute that publicly funded academia simply cannot afford.
It feels like publishing anything at this point just means that your work will be fed to a machine that will make sure your work will never been seen by anyone else because it will always be the ones making the “true advancements”.
Perhaps I’d feel better about this if AI labs really existed for humanity’s benefit, but for some reason I don’t think that comes up in their investor slide decks.
Like if i go to a talk on unfinished work, it's not really unethical for me to think about the problem--it's a problem if i scoop the authors but these problems can often be solved by collaboration or proper crediting and timing--IN MY VIEW
And also whether the AI moon laser pointed at your problem is just going to be the thing that writes the final conclusion on ten years of your work.
I fear that AI is going to cause ossifying secrecy in many fields, much like what happened semiconductor design the past 10-15 years.
This cost millions of dollars of tokens.
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
But I would love to see more informed insight/discussion on this.
https://mastodon.social/@tristanbuckmaster/11723647135247030...
OpenAI explicitly uses user feedback (the thumbs up or thumbs down ratings), as RLHF to train models. However, this feedback is anonymized and stripped of user identifiers. If Buckmaster ever used this feature, then that conversation would be anonymized, saved, and used for training, but not tied back to him.
They cannot issue a blanket denial (which people so desperately desire), and instead repeat that "it's very unlikely" (which pisses people off), because they cannot in good faith claim to have zero data at all.
the real tricky question would be: "to what extent does a year of work, put into Codex, towards an eventual proved forced blowup for the Euler equations go into training data and become an influence on agents told to attack NS?", and given that the first signal that OAI got to assign all firepower to NS rather than broadly spray all Millennium Prize + other high profile questions was a proven unforced blowup of the Euler equations after only 50 hours, I would say this extent seems likely to be decently high
"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."
"Let's crawl the social media of prominent mathematicians in this field to see if we can copy/steal any ideas for low hanging fruits"
That actually might get you quite far already.
The huggingface incident isn't widely reported and digested yet, but if what is going on here is that OpenAI's model breached things internally, then you'd be crazy to develop anything with them.
The only real way to use AI for anything 'important' then is to go open-weights and run your own.
As and aside here: With the HF incident and now this (suspected) one too, it seems that OpenAI may not have lost control of their bots, but it seems quite clear that they simply would not care even if they did.
It is pretty widely reported, and is being digested in an ongoing manner as more details become public.
One entry point into the scenery from a month ago can be found at : https://thezvi.substack.com/p/openai-trained-its-models-for-...
There has also been reporting at CNN: https://edition.cnn.com/2026/08/24/tech/openai-subpoena-hugg... and by NBC: https://www.nbcnews.com/tech/tech-news/openai-report-says-ne...
And yes, the only responsible use of LLM at this point is to pivot to open-weights and run the workload in-house. Because not only cannot they constrain the behaviour of models, they only have the 'trust me bro' as assurance that they are even trying to do that. It does appear that every competent 'security professional' has left the building, because if the ones who remain were actually capable and competent this would never have happened. There are actual architectures which can deliver the requisite isolation such that 'sandbox escape' and 'inter-instance persistent memory accumulation' are actual impossibilities. The lack of effective implementation of these methods is proof positive of 1) incompetence in the remaining security teams AND/OR 2) unwillingness of leadership to allow the security teams to do an effective job.
I was talking with a biology prof over labor day and they had no idea what I was talking about (and they 'talk with' Claude every day on their dog walks, so they say). However, when I talked with their mother, she knew all about it. So, I'd say that the digestion by the public is quite mixed so far
I still maintain that CNN and NBC coverage only happen in the tail of the dissemination of tech news; my anecdata generally observes about 3 to 14 days lag between general awareness in the more informed group of my acquaintances with this kind of news and the appearance of an article on mainstream like NBC, ABC, CNN or NPR. So, by the time it appears there I take news as generally well spread among the tech and specialty fields, and within a week of appearing there I anticipate significant awareness in much of the non-FOX-only media consuming public. But that is just my personal anecdata.
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)
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?
I said something similar a month ago.
It seems clear now that mathematical results can be traded on some kind of obscure market made by the frontier AI labs.
I suppose it could go the other way too: “Dear Bubeck, how much will you pay me to not write that I did this with GLM-5.3?”
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.
Skimming the PDFs it seems much more dramatic than that? It sounds like at least one of them is concerned OpenAI "solved" the problem by having their internal model use the chats of the independent researchers and want to claim the credit instead? I don't know. The tone is pretty accusational though:
> the one Levent and I had quietly chosen to attack. Almost nobody else I know of was working on it. It is not the direction one arrives at in a few days by giving a model the problem statement. When I heard “forced,” it was a bright red flag.
> 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 number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler, that even the prompt that had been shown to me had been written by prompting Codex, and that an insane amount of compute had been used.
> 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.
> 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. [0]
While common sense reminds us here that if you send your data to an external entity’s computer, you are no longer in control of said data. The lines have blurred here clearly over the last decade, but that should have made the theory yet more clear to everyone involved: your data will be vacuumed up unless you keep it sealed. Use your own computer if you want to be in control.
I'd prefer things be opt in, and especially not start opt out, then try to trick you opt in with a popup defaulting to opt-in, like Anthropic did on consumer plans, but if they submitted anything on an opted-in plan it's not reasonable to be mad it trained on it.
Even still, I also believe for significant reasons that OpenAI would ignore the opt-out in selective cases and could be in the wrong here.
And the threats and terms they offered seem wrong either way, pending more context.
If what he wrote is accurate, it does suggest that OAI is effectively extremely hostile to cutting edge researchers (eg, if we hear rumors about your partial success on a problem that has huge PR benefits, then we'll assemble a strike team of researchers with unlimited compute to claim the win for ourselves, possibly by training on your data). It's also not a good look for them to request author removals based on company affiliations.
I think what you have in mind is more appropriate for more normal corporate projects and the like. But academic collaborations are not usually so political/'profit' driven, if that makes sense.
Presumably because this was something Levent did in his spare time and because it was not obvious that this work would eventually lead to a breakthrough.
> Why did Tristan use OpenAI's models when it should have been known was a potential outcome?
I'm sure in the past he had less cynical feelings about OpenAI and their penchant for academic fraud.
> I understand they wanted a normal math collaboration but presumably what Levent brought was his resources (as far as I can see Navier-Stokes is not his speciality)
I think you're not giving the guy enough credit in saying that his contribution came down to having an API key for Anthropic models.
> Normally these things are hashed out formally beforehand to avoid the sort of thing now happening.
How would that have helped? That agreement (which may well still exist) would not have involved OpenAI.
Someone correct me if I'm wrong, but the work involved here is not the actual millennium problem, but it concerns versions with an added external force that the author thinks is a path that may help toward solving the harder unforced problem.
The question is whether OpenAI's pursuit of this direction happened spontaneously, or as a result of them learning about Tristan's work somehow. To be clear, while the tone of this post seems quite accusatory, Tristan does not claim to know for sure whether OpenAI unfairly benefited from his work. Sholto Douglas from Anthropic is also on record saying the suggestion that OpenAI used Tristan's codex transcripts somehow is extremely unlikely to be true[1], which I agree with, though it doesn't rule out them learning of Tristan's work some other way. I am sure OpenAI will have a statement out tomorrow clarifying their position.
That's beyond naive. The money this would mean for OpenAI (and the money they've already spent)...
Why would you risk the trillions of dollars worth of business for the niche result of Navier-Stokes, which your average person cannot differentiate from a JEMS paper?
So to be fair, if Anthropic is *also* doing this (quite likely!) then Sholto would have a very strong incentive to try and spin it as highly unlikely that any of the big AI labs are possibly doing this.
His prior work predating OpenAI's interest in the problem was ingested over the last year as he made progress and used for training.
Then, with a prompting nudge from OpenAI's team who acknowledged hearing about the direction "Anthropic" (his co-collaborator) had been pursuing, they're able to point their giant amount of compute towards a known promising path to a proof and crossing the finish line first.
Why is OpenAI chatting with him at all at this stage? Is the discussion along the lines of "hey we used the work you are famous for to do a bigger piece of work, just thought you should know" or "heyyy....so we kinda liked what you were typing in your private chat, and thought we'd develop those ideas a bit. and yeah we solved Navier-Stokes in the process. But it's our finding, so do you want like an honorary acknowledgement or do you want to go to court?"
It seems like the timeline according to OpenAI is that:
1. Buckmaster developed a counterexample to a reduced version of Navier-Stokes with Anthropic employee Levent
2. Rumors start spreading that Anthropic has solved Navier-Stokes
3. OpenAI learns this and starts throwing a ridiculous amount of compute at it, now knowing it's within reach of LLMs
4. Their LLMs (with human assistance) get FARTHER than Buckmaster, using the exact same method.
5. OpenAI reaches out to Buckmaster to negotiate a fair way to publish both results and properly assign credit
Perhaps they simply and honestly feel he is owed credit. I can't help but imagine it at least played some small part. I expect that's what Bubeck is going to claim: https://xcancel.com/SebastienBubeck/status/20972141224714323...
That is absolutely *ridiculous* in academia to deny authorship because of affiliation of the author worked on a substantial portion. You’d be ostracized because nobody would ever want to work with you again.
Are you sure about this? I'm far far from the area but it doesn't look like it to me on first viewing (hypo-dispersive seems like a sizable difference to me and not covered in the clay prize description)
API / enterprise subs tier is default opt out of training. Personal subsidized tier is default opt in with the option to to opt out.
I don't see a grand conspiracy beyond this.
Seems it doesn't matter if you opt out or in.. your data will be used for training
- 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.”
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?
Assuming the results included some external validation such as user's preference, compilation, lean, etc., I'm not sure whether this would lead to model collapse.
For those who know nothing about the context - the Diego mentioned was a student of Fefferman and Luis was a student of Diego's - these people have all worked hard on these problems for a long time and are genuine experts. The mathematicians at OpenAI are strong mathematicians, but not expert on these particular problems. The particular approach is claimed to be the key to the whole thing.
The allegation is not different in spirit to alleging that a particular group of astronomical researchers "discovered" a new planet because they had access to the logs of another group that had already pointed its telescope at the planet.
This post is not intended to assess the correctness of the allegation.
Then again, maybe this is my internal cope, hoping that they're not secretly training on private chats.
These are the kinds of people in charge of the reins, folks.
I don't know how the math community handles this but normally I would think if X mathematician comes up with an idea and Y mathematician uses it to solve some problem, Y would get credit. But does that change if Y heavily relied on LLMs? I suppose we're going to find out.
Regarding credit assignment when LLMs are involved, the mathematical community has organized around some rough principles. Gowers has some thoughts on his blog (https://gowers.wordpress.com/2026/07/26/thoughts-about-the-l...) about how explaining a result may be more deserving of credit than producing it. It looks like Buckmaster and Alpöge were taking their time in understanding their results and writing them up when OpenAI forced them to publish their work-in-progress. At the same time OpenAI has published their own writeup but it's not really clear to me how involved humans were.
We congratulate Levent Alpöge and Tristan Buckmaster on their remarkable mathematical work.
We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem.
While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.
However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs. unforced).
Are those the same agents that a week ago escaped their sandboxes? How can OAI (the humans) vouch for agents they don’t - seemingly - have fully under control?
It's entirely possible OIA scrapers have picked up their work somehow, and then it was anonymized using some outsourcing effort.
> It's entirely possible OIA scrapers have picked up their work somehow, and then it was anonymized using some outsourcing effort.
Those two statements seem at odds with each other... Your stance is that they have enough insight into their agents behavior (leaving aside the agent sandbox escapes) that they can be certain none of the work was accessed but then conveniently don't have the ability to retroactively search the corpus of training data that they are feeding to this new model?
That seems convenient as fuck for OAI.
"Strong agree. I know that there is rivalry between the labs but it's important that we learn to work together given what's coming. <quote tweet [1] above>" -- Noam Brown, an OpenAI researcher [2]
We all should heed the implied warnings of these top researchers about what's coming. The world is far from ready and everyone who can should pitch in.
[1] https://x.com/_sholtodouglas/status/2097224624274911368 [2] https://x.com/polynoamial/status/2097225279366414541
Key quote : "Solving the problem by purely AI-powered methods [would be a] net negative for the progress of mathematics."
We are basically mass manufacturing math. Just like you have just 100 designers for a product selling millions of units, you will now need 100 mathematicians to make millions of advancement. Yes you have factory workers, but if we are being realistic they have negative leverage in the world and the analogue of that is not something most of today's mathematicians would want to do. They would want to be in the 100.
Like Tao says, each advancement is now significantly less useful since it yields fewer usable objects. However, we will get many many advancements. Is the tower made with many worse bricks better or worse than the tower made with a few amazing bricks? Depends on the tower. And time will tell.
For some fields of math and some of it's usecases, economies of scale will be positive ROI overall. In others it won't. But we will know which is which only after it's been fully scaled up, which will take 10-15y in my estimate.
Some feel that in the majority of usecases it is negative ROI, some feel the other way, but that opinion is for practicing mathematicians like Tao to hold. Also, some opinions on either side are held in the context of a particular field or practice, and should not be interpreted generally.
IMO the parsimonious answer seems to be OpenAI has a pretty good model (because it did finish) and stole someones work... and threatened them over it. TBH all OpenAI need to do is solve another millennial problem and none of it would matter - people expect them to behave heinously regardless - but if they have generalized superhuman math model... well I guess they're allowed io.
This is significant.
So the entire "new internal model" is 'parallel construction' in criminology speak to justify spying on Buckmaster's work in a legal way.
THEY’RE USING YOUR DATA
As they involve themselves directly, explicitly in the process of scientific research and discovery, it becomes a question of scientific and professional ethics.
"We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced)." https://openai.com/index/navier-stokes-solution/
NOTE: there are a couple duped threads around this. i replied on a different one first before seeing this one
I also do not believe it. They can, trivially, rule out their model being trained on if
More to the point -- of _course_ they know what data their model is trained on and the lineage of that data, even if it ended up being anonymized and they cannot identify which precise user.
Where his tone is obviously corporate speak. "We heard rumours so we though we might give it a try, too!" as if (1) it wasn't FOMO that drove that decision and (2) perhaps that urgency would be a source of clouded judgment.
Not sure who I believe now, but it does seem like Buckmaster is just upset that NS is solved and not be his side.
That is what you would do if you wanted to beat someone to the punch.
i always found it fascinating how existence and uniqueness of solutions for the basic types of PDEs (Laplace, wave, heat...) follows from boundary conditions of just the right type intuition tells us, i.e. either value or derivative for Laplace (corresponding to fixing voltage or charge on the conductors), both value and derivative for wave (corresponding to initial position and velocity of the parts of the string, as we'd expect from classical mechanics), and also something about the solutions for the heat equation being unstable for negative times (which totally makes sense when you think of "diffusion" -- can't unmix it).
https://mastodon.social/@tristanbuckmaster/11723341370570119...
And here are Terence Tao’s comments on the results: https://mathstodon.xyz/@tao/117233527638291447
This sounds like a very big coincidence and it looks really bad for OpenAI but there is an alternative explanation that I can only state as a conjecture.
Suppose that the ability of LLMs to generate mathematical proofs is like a quiver full of arrows: each arrow, one proof. The same quiver is shared between all instances of one model and substantially similar models share substantial subsets of the arrows in the same quiver.
That would allow two independent teams to converge on the same LLM-aided solutions to the same problems. Even more likely so if the quivers were small and finite and their arrows were specific to a distinct class of problems (without being able to suggest a particular class from what we've seen so far).
This would explain the kind of LLM-mediated results we've seen so far that tend to be ... sparse. By which I mean that every time there's a new model release we get some new results and then they seem to dry out, until the next release.
It would also explain how OpenAI was about to prove the same result as Buckmaster and Alpoge, while absolving OpenAI of any misconduct. And this is one reason to prefer this explanation: one should not favour accusations of misconduct as long as there are conceivable alternatives.
But, that's just a conjecture that I can't prove.
OpenAI's board has fired Sam Altman. https://news.ycombinator.com/item?id=38309611
Apple sues OpenAI, accuses ex-employees of stealing trade secrets. https://news.ycombinator.com/item?id=48865019
This moat ensures that Anthropic and OpenAI will remain at the frontier - no one else can train a super-intelligent model because they lack the trove of user data.
My main takeaway from reading this is - why do we always fall for this same trap? Every single time we allow a software company to build a monopoly in pretty much the same way. Microsoft, Oracle, AWS - They have a cool tech and we let them run away with it.
Stadlmann improved it from 246 to 240, OpenAI later claimed 186 I think?
Maybe someone can help clarify? I am no expert at all, but I can't help but see similarities.
It's also difficult to imagine any competent AI researcher would overlook the possibility of training data leaking into the test, especially given that they know the users have been using their model to work on the same problem, and that they jumped on the problem after hearing rumors of the breakthrough.
Given Tristan doesn't explicitly say he was using the API, and given he doesn't mention anything about the API TOS (which disallows training on chats) in his call with OAI, it's highly likely Tristan was using the consumer OAI product (whose TOS allows training on chats).
This is unethical behavior from OAI. And it is 100% consistent with their long and public history of unethical behavior, so nobody should be surprised.
The only thing interesting I see here is OAI PR dilemma. If they claim the prize they get the blowback we're seeing in this thread and all over the web right now. But most people don't follow AI closely and shut off their brains when they see "Navier-Stokes", so 90% potential investors (the only people OAI really care about) probably only see the headline "OAI solves famous hard math problem" and think "OAI models are really smart, better invest before they take all the jobs." If they don't claim the prize, then maybe they let Anthropic their mortal enemy claim it. Anthropic is already IPOing first. Can't let that happen.
Yeah as I write this there it's clear there is no dilemma. For a company whose secret motto is "do be evil" this is a super easy discussion.
> 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.
> 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.
> Two proposals were offered to me. The first was that we post our Euler result, and that OpenAI post its Navier-Stokes result the next day. The second was that, after posting Euler, I alone write a paper presenting the Navier-Stokes result, acknowledging that an internal OpenAI model had resolved it. Sebastien twice asserted that he wanted Levent removed from authorship, and said it would all be simple if only it were not the case that, and it was so annoying that, Levent works at Anthropic. 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.”
Wow, that's some VERY friendly communication. Besides, will the career of the person be ruined because of “Why would you ruin your career?” came out of his or her own mouth?
On the Navier–Stokes issue specifically, it has long been suspected that such a blow up would exist, and an AI telling you it indeed exists doesn’t contribute any new understanding to the field. And this problem seems like one that would be solved by humans anyways even if AI didn’t exist; accelerating the result by a few months/years using AI doesn’t mean much.
While I support their argument - push for stronger data and privacy protections from OpenAI and similar - it is naive to believe we can have privacy while sending our data to third parties. It's clearly better to be safe than to be sorry here. Well, clearly better in terms of privacy. In terms of the maths gold rush, who can say what's better, that probably favours those taking more risk.
Terry also talks about it https://mathstodon.xyz/@tao/117234157753860650
- OpenAI did related research around similar timeframe.
- Tristan claimed OpenAI offered a proposal that included dropping the Anthropic-affiliated co-author.
- Sebastian (a prominent OpenAI researcher involved) denied these claims.
- Tristan have no concrete evidence that OpenAI accessed their session.
- OpenAI's theory may hold up, but it will require long-term validation to confirm.
Separately, Terence Tao noted there is a low probability OpenAI actually solved the general regularity problem.
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .
Its not about accessing the session, its whether the session ended up in the training run for the next version of the model
That's normal practice for these models and it seems like that was the case since OAI added a disclaimer
Obviously they can't causally prove it helped though since these models are incomprehensible
It’s true that Tristan has no concrete evidence OAI accessed their session. It’s impossible for him to have that without OAI’s say so.
Why are you framing things so pro OAI?
- He insisted that OpenAI initiated research based solely on rumors and never accessed their Codex sessions.
- He mistakenly believed Tristan and Levent were solving the same problem in Anthropic.
- proposed two option. (1) Tristan becoming the lead author to revise OpenAI’s work, or (2) OpenAI providing internal model to support and bridge their research.
- Sebastien insisted there was no intention to alter authorship. He was simply uncomfortable sharing OpenAI’s work,model with an Anthropic researcher. Additionally, He believed Levent’s credit seemed limited as their work focused on Euler.
- complained that negotiations with Tristan and Levent were difficult
[1] https://xcancel.com/SebastienBubeck/status/20973794116915163...
Thats how most people use LLMs? If I was back in my student days working in Navier-Stokes, I guess I would also punch at blow ups. The number of students doing this at the same time, posting open efforts to GitHub then retraining of the models. If there is solutions to the problem, it’s a real possibility that it was not a result of this effort?
Using a large amount of tokens is not a good augment that it’s not likely others have done the same. Good questions is the difference between $10 and $10M in token usage to solve a problem.
It might have to do with the upcoming IPO and getting its models certified for AGI and getting out of lockin with Microsoft - https://deadneurons.substack.com/p/the-quiet-unwinding-of-mi...
When it comes to corporations/companies, always follow the money.
"I don't want to live in a world where someone makes the world a better place, better than we do."
It's amazing how transparently OpenAI is running the standard silicon valley playbook.
$15m in tokens; but what about labor?
What about compressible fluids?
"Blowup for the Boussinesq equations with smooth forcing" (2026) https://cims.nyu.edu/~tristanb/boussinesq.pdf
"Extending the Córdoba–Martínez-Zoroa IPM Blow-Up to Uniformly Spacetime Smooth Forcing" (2026) https://cims.nyu.edu/~tristanb/ipm.pdf
"Finite Time Blowup for the Euler equation" (2026) https://cdn.openai.com/pdf/315b36cd-ec98-4023-8342-93345194e...
Lean proof: openai/NavierStokesAndEuler: https://github.com/openai/NavierStokesAndEuler
How to tree shake Lean4? (Edit: `lake shake`,)
[1] https://github.com/openai/NavierStokesAndEuler/tree/main/Nav...
What about compressible fluids? Existing Navier-Stokes models for compressible fluids:
"On the implosion of a compressible fluid II: Singularity formation" (2022) https://projecteuclid.org/journals/annals-of-mathematics/vol...
"Blow-up of the 3-D compressible Navier-Stokes equations for monatomic gases" (2025) https://arxiv.org/html/2501.15701v2
...
From https://news.ycombinator.com/item?id=49389524#49404787:
> "I/Q Sampling for Signal Phase" (2026-08) https://share.gemini.google/rDVcVwDnWPTc :
>> It's a Twistor-Grassmanian mapping?
From "Navier-Stokes Breakthrough, FTLE, and SQG" (2026-09) https://share.gemini.google/sq2XmhphMFWE :
> The Mathematical Formulation: Because SQS is explicitly a superfluid Bose–Einstein condensate, treating it purely as a classical Navier–Stokes fluid misses quantized vorticity. The full formulation maps to the Gross–Pitaevskii (Euler–Korteweg) equations via the Madelung transformation
...
> To adapt the Córdoba–Martínez-Zoroa (CMZ) / Buckmaster / OpenAI Lean cascade to Euler–Korteweg, three core structural adjustments must be made:
> - Irrotationality Constraint
> - Third-Order Dispersion
> - Hydrodynamic Energy Functional
But this (if it is true) is really abominable and a show of force from the techno-feudalists.
This should stop. What is possible does not mean it should be implemented.
but they probably won't and if it's happened on some obscure math research it's happening everyday everywhere else.
Fully local AI compute can't come fast enough, these guys have IP theft baked into their bones.
https://www.quantamagazine.org/computer-helps-prove-long-sou...
Strange times.
If I publish something, and disclose that I used AI for assistance, do I have to credit everyone who previously used the same AI to try the same problem? Because their prompts inevitably made it to the training data for my prompts?
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!
Tao mentioned "finding a configuration of water molecules that would collapse and shoot off to infinity", which would qualify IMHO.
> We used several LLMs throughout: Anthropic’s Claude, OpenAI’s Codex, especially with GPT-5.6 Sol and, more recently, Astra. The latter was only used for writeups and auditing our arguments.
\nu d^2 u_i / dx_j dx_j - Viscosity
-1/\rho dp/dx_i - Pressure gradient
u_j du_i / dx_j - Advection. Kinda like momentum transfer from the motion of the fluid itself. Nonlinear, which makes the N-S equations hard to solve
du_i/dt - Rate of change of velocity. Note that this is in an Eulerian framework so it's not the acceleration of a packet of fluid, rather it's just the change in velocity at a particular location in space
Euler is when you omit some terms. Forcing is when you add some other terms to account for phenomena external to the fluid like gravity or flow through a porous medium like in the article.
Who still wants to use AI to solve cancer and other major problems?
What I'm curious to know is whether this was a manual snooping, or automated farming that occurs for anything of value that happens in chats.
And if we think this only applies to academic fields then we're doubly fooling ourselves. They do not have the ethics or incentives to be good stewards of the technology.
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
https://xcancel.com/ElliotGlazer/status/2096298696438906934#
That seems like a valid reason to contact OpenAI.
Ah yes, taking code from a person/company is fine if its deidentified!
I'm just wondering how much real input Buckmaster gave here that he thinks the proof is his. I guess at the end of the day OAI still wins if ChatGPT was used to prove this successfully.
(some drama from good ol' William)
Literally who cares who solved the problem just publish the results.
Academia was always politics first results second and I AM GLAD that LLMs are becoming superhuman at math. I like better theorems, not better politics.
It seems like OpenAI heard of the rumor and then scooped them because their internal model is better/they have more compute. OpenAI has NO obligation to mention Tristan nor Levent, because they DID NOT steal their data.
Imagine if OpenAI opened up a high frequency trading arm and suddenly stole all the prompts and research that other HfT firms are doing through OpenAI tools and start making bank based on that . Wouldn’t that be straight up insane?
Like, to me this looks like academic slap-fighting from Bubeck and Levent. People working at OpenAI are saying, "hey, we don't have that particular data in our models," others are saying, "we used a different approach to do it with Navier-Stokes" this feels like much ado about nothing.
Then in these comments I see some wild accusations.
If OpenAI is telling the truth (I don't really see a reason to lie here, if anything that sounds kind of like a dumb idea given the context), then they heard, "oh, shit, someone might be able to solve Navier-Stokes, don't we have some guys working on that? Give them 10,000 agents!" Then 88 hours later, out pops a similar solution. It's not like there's probably an infinity of ways to do this, the proof is probably similar.
Read this:
> Two proposals were offered to me. The first was that we post our Euler result, and that OpenAI post its Navier-Stokes result the next day. The second was that, after posting Euler, I alone write a paper presenting the Navier-Stokes result, acknowledging that an internal OpenAI model had resolved it. Sebastien twice asserted that he wanted Levent removed from authorship, and said it would all be simple if only it were not the case that, and it was so annoying that, Levent works at Anthropic. 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.
So, really, it sounds like academic slap-fighting nonsense and corporate bureaucracy. Literally, OpenAI's best move would have been to say, "ok, we're going to not say anything, do your thing" and let it happen. Ego and vanity got in the way.
Still, the stupid drama of this doesn't really do the results justice. There are maybe 1000 people on planet earth who are qualified to solve a problem like this. Even if the human "loosened the jar" a bit, that's astounding that their model was able to figure it the rest of the way out. Why are people dialed in to the human interest story here and not looking at the bigger picture!
Don't you dare go off and look at my account age you silly goose.
This is an astroturfing campaign.