> 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.”
Threatening a research mathematician and dangling and $1M payday to dissociate from his research collaborators and to adopt OpenAI's narrative is bad stuff.
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”.
I'm suggesting audits, not suing... if that is the implication.
You realize OpenAI hired Apple employees and covertly had them stay working at Apple to steal from them. You think they're scared of your lawyers lol?
Isn't OpenAI being sued by Apple for their little stunt?
If you're saying "the big bad guys always win anon, just take the black pill," then there are tons of counterexamples. Remember Uber paying Google a sweet Bil for pulling this same trick with LIDAR firmware?
Pretty clear this was rushed: there are no comments from external mathematicians, unlike the Erdős announcement:
https://openai.com/index/model-disproves-discrete-geometry-c...
No one can know if that's correct without proof but I don't know how you're reading it so differently.
Just suggesting to a mathematician to dissociate with their collaborator for a follow-up work, because their collaborator “is inappropriate to author OpenAI’s work”, is completely against the norm of mathematical research. As charm137 puts it in a comment below:
> This is like a researcher from CMU saying to an NYU researcher that their collaborator, being from MIT, is a problem - this is as ridiculous as that!
Progress in humanity's knowledge now has to play second fiddle to narrow corporate interests as IPO timings near (both of which wouldn't exist anyway if generations of mathematicians hadn't paved the way for AIs to become as good as they have).
[0] https://hn.algolia.com/?query=Alpöge
(also https://news.ycombinator.com/item?id=49412947 the Hopf conjecture)
> One option we discussed was that Tristan could be the lead author on a rewrite of OpenAI’s Navier-Stokes proof. It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work.
Why would you offer another researcher the lead authorship on your groundbreaking paper if you thought you had developed it independently?
> but it’s pretty standard to have co-authors from different companies
that's only true for papers that are not millenium problem solutions
Of course, no one understood that presentation so it was Darwin's later book that everyone remembers
“It would be simpler if Levent was not an Anthropic employee” I cannot believe this shit.
It makes a certain amount of sense. The internet data is too polluted with AI usage now to be useful, so the only AI free new data source is the prompts people feed into ChatGPT. The only problem is that its clearly plagiarism
Edit:
OpenAI have admitted to training on prompts at the time the breakthrough was made:
https://mastodon.social/@tristanbuckmaster/11723647135247030...
> Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.
hmmmmmmmmmm
Sociopathic behaviour.
What an admission! "We tried to defraud Alpöge out of sharing the Millenium Prize (that we don't dispute he might actually deserve), for no other reason than he works for our competitor and that inconveniences us".
I thought Tristan Buckmaster's allegations sounded fantastic; and then 'sama just came out (tweet's ~30 minutes old) and admitted to all of them. Wow!
but then they proceed to NOT quote themselves themselves verbatim: "I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey."
The AI-isms are seeping into their speech :)
> Not consistently candid
> "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."
OpenAI (i.e. this OP):
> "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models ."
This is one of the major problems with these enormous closed models, and even most open-weights models, which don't disclose their training process or training data. You can never be sure what went into its training. Did it come up with an idea originally, or is it just plagiarising its training data? Are there malicious inputs being used to train in particular behaviors when given certain trigger phrases? What are the characteristics of the RLHF data and what kind of biases are those embedding in the models?
With proprietary closed models, or even open weights models that don't have open training datasets, you just can't answer these questions.
As a parallel example, can we prove the phase of the moon had no impact on the NS solution? No, not without a bunch experiments run at different phases of the moon.
There's no reason to believe that anything they did in ChatGPT led to our solution; it's just impossible for us to truly prove it. And knowing most of the recipes we use, there's really no reason to think such contamination happened. I've asked the team to make a clearer, less-lawyerly statement here - let's see what happens.
(I work at OpenAI.)
You're right; if the data was used in training, then it gets much trickier; it would be very difficult to show whether some particular data had a significant effect on the outcome.
This is one of the big problems with giant models like these; it becomes nearly impossible to discern what is and isn't plagiarism, or copyright violation.
It would in theory be possible to have things like n-gram databases or rolling hashes of training data, somewhat similar to OLMoTrace (https://arxiv.org/abs/2504.07096), which would allow for detecting whether particular documents ended up in the training data or not (you'd have to keep this for every model used in the whole training chain, as synthetic data generated by earlier models could be influenced by training data that wasn't included in later models). I'm sure there are practical issues with providing such a tool, but I think that it's necessary if you want to be able to categorically say "no, this document has never been present in the training data of this model."
Or look at it the other way: if your model wasn't influenced by things in your training data, why include them in the first place? Clearly, you train on all of these documents because they influence the model. Yes, it's hard to trace the exact influence of each one. But if they're not affecting the output, then why not just stop training on them? You could just not train on any private documents; only train on public, traceable data.
But instead, you choose to train on these private documents, so you have to admit, your model and its outputs are influenced by them.
If prompts were submitted earlier than that and training was not opted out, there's a chance they made their way into our training pipeline in some form. But this would be a droplet in an ocean and unlikely to have made any difference, imo.
See: https://www.nytimes.com/2026/09/10/science/tristan-buckmaste...
That reads as incredibly dismissive and condescending. What makes you think you’re in a position to communicate like that when engaging on such a sensitive topic?
We can judge for ourselves the impact and degree of that wrongdoing, but it seems OpenAI is confirming: yes, that is what happened, but with more words.
Edit: Also, if they opted out of training, then we didn't train on it.
This kind of question is exactly what a company named _Open_AI and founded as a nonprofit is supposed to be doing; open research on AI that helps inform, rather than obscure.
Anyhow, you do have the data available about the documents in the user's accounts, what they opted into (or were forced into via non-negotiable ToS), and whether they pressed a "thumbs up" button. You can answer whether the data entered the training pipeline or not. Yes, how much influence it had is an open question, and one that would be good to have research on and better tools for exploring, but I'll accept that it can't currently be answered precisely.
But whether the data entered the trianing pipeline can be answered. And how to provide better tools for quantifying and tracing this kind of thing is exactly what should be studied.
(1) We'd have to identify their chats. How would we do this? We'd need them to share their chats with us so we could look for matches.
(2) We'd have to prove those chats changed model behavior. How would we do this? We'd need to retrain many models with those specific chats removed, and ask those models to solve the Navier-Stokes problem many times, and keep doing this until reaching the desired level of statistical significance.
#1 requires their cooperation and a bit of work on our side. #2 is extremely expensive and not really feasible.
According to the statement by Tristan Buckmaster, he was in communication by email and calls several times over the past week with you (OpenAI that is, not you personally), asked about whether his chats were trained on, and was declined an answer (https://cims.nyu.edu/~tristanb/statement.pdf).
However, it seems like there was great pressure to hurry the release to compete with Anthropic's recent release, so he was unable to get an answer in time.
The mealy mouthed statement in the release "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 ." is realy not much. If OpenAI had wanted to be transparent about this, you could have worked with him to identify if his data was used in the training of your new model, and actually made a somewhat more certain statement on that basis. But you have chosen not to; it was more important to scoop Anthropic on this than it was to be transparent about your training data.
> (2) We'd have to prove those chats changed model behavior. How would we do this? We'd need to retrain many models with those specific chats removed, and ask those models to solve the Navier-Stokes problem many times, and keep doing this until reaching the desired level of statistical significance.
Just the information from step (1) would improve transparency. Yes, you still can't prove one way or another how much the effect of the training is. But if it's included in the training data, it provided some effect.
Turn off web search and ask a model what a random redditor said about a random topic in 2015. You will only get hallucinations at best, even though that comment is definitely in the training set.
If the internal OpenAI model is as capable as you claim (being able to solve a Millenium problem without using unpublished insights built on years of work from mathematicians), then it should be able to demonstrate this capability again.
How about OpenAI solves another Millenium problem within the next two weeks, that doesn't coincide with the parallel discovery/solution of other teams of mathematicians, using ChatGPT for preliminary proofs & write-ups.
"de-identified" seems more of a euphemism than normal in this context, given the very unique work they were doing.
If OpenAI's answer to this problem is "We can't know," then the rational conclusion may very well be "If I seek to have my reputation attached to the discovery of the solution, it is not sane to use the AI as an assistive tool, lest it scoop me on my own work using my own work. After all, they don't know it doesn't do that..."
You don't need his login information, you just need to identify if anyone was approaching the NS problem using his method. Nobody else on earth (presumably) besides him, his team, and at best OpenAI were approaching the problem this way.
The blog post appears to imply the answer to this is yes, as otherwise I assume it would be impossible for this contamination to have happened.
If you need to do a whole series of extensive experiments to check in that scenario, it implies there are pathways for your conversations to end up in training even though you opted out of that setting.
Of course, this is assuming that the toggle was set to not consent to training. I can't know that of course, but if this is considered a possibility even after using an enterprise account or toggling off data retention, it's a bit concerning.
My comment was about the scenario where they didn't opt out. In that case, it's possible that a droplet of their data went into the ocean of other training data, and it's very difficult to measure what effect that droplet had. My expectation is essentially zero impact, but no one can know for sure.
do you think that the model's proof was unrelated to being fed a solution that was close to completion?
any comment on openai allegedly trying to drop attribution for alpöge and then threatening buckmaster?
The _gall_ to say something like this. Do you perhaps think we are all stupid?? This very blogpost claims not to know if their work was used as input for this model. I don't even understand how that is possible, surely you can know if something is part of the training data, even if you are in the dark about what impact it actually made, qualitatively. The moon....
> Knowing most of the recipes we use, there's really no reason to think such contamination happened.
Yeah sorry but I don't trust you. I don't trust people or companies that have shown themselves to be dishonest before. Especially when the previous paragraph is comparing plagiarism and training data contamination with, _the phases of the moon_.
Might even be you're actually telling the truth, but the boy that cried wolf and all that.
-----
As an aside, I would bet very good money at how most (all?) these companies are flouting their ZDR.
There are hundreds of incredibly strong scientific priors that would have to be disproven for the moon to contribute to the solution.
If a model was trained on this data, even if it was trained using methods that lead you to believe it unlikely to have learned details about the proof (e.g., maybe it was only used to train some kind of reward model, which played a minor role in the overall training and would thus be very unlikely to transfer details of a proof), you wouldn't have to disprove large swathes of known science to be wrong.
The term ruled out is very open ended and gives them significant flexibility of meaning. They may have the information to determine exactly what happened, but they haven't looked so they can't "rule it out".
Probably? I have a few hundred TB of training data for various small scale models and I can attest that I have _no idea_ what's in them. As in, literally zero. Half is scraped from GitHub and other hosting sites, other than that, I couldn't tell you anything else.
At OpenAI's scale their entire pipeline is likely 100% automated.
But that doesn't preclude being able to index and track what the sources of data are. For your data sets, I would hope you are including source information for where the data came frome. And at OpenAI's scale, I would presume they are doing some amount of rolling hashing or similar to weed out duplication, training on too much duplicate data can cause problems.
AllenAI have at least attempted to add some amount of traceability to their models with OLMoTrace (https://arxiv.org/abs/2504.07096), by letting you find n-gram matches from the outputs in their training data. It's not the most useful, there's a reason that LLMs use full fledged attention mechanisms and not just n-grams, a lot of times the n-gram matches it finds aren't all that related to the given output, it might be better to supplement this index with a vector search or other ways of keeping track of what training data would have most influenced particular parts of the output.
But anyhow, this is something that is an important question, and the big labs should be working on to make their products more trustworthy. Instead, they are hiding information about how they train, hiding their reasoning traces, and just producing output with no information on what might have influenced the training.
1. Provide a chain of reasoning from agreed premises. These days LLMs can even do this airtight with proof assistants.
2. Cite data sources for non-agreed premises. I don't care where the model learned a fact. It might not have ever read a document directly from the primary source. I want it to link directly to either widely agreed facts (e.g. standard textbooks, and if necessary school syllabi demonstrating that the text is standard) or primary sources (e.g. datasets).
We wouldn't need a full ablated re-training and solution attempt, contra tedsanders in a sibling comment.
The point of de-identifying data is to ensure you can't trace who it came from. It would be a serious privacy violation if they could.
Which is why, as I said in a recent comment (https://news.ycombinator.com/item?id=49530864) inadvertently leaking ideas to models is a grave risk for Intellectual Property.
> The risk with IP, however, is a lot more grave. You may not even need to memorize the details of the IP verbatim, just the broad idea may be enough. It may lurk encoded in the weights forever, just waiting to be activated by the right prompt to start a chain of thought that unlocks further details. Heck, it may even appear as if the model suggested the idea itself.
However, from a quick skim of the timelines, the specific discoveries, and all the he-said-she-said, so far it seems unlikely that OpenAI's model cribbed from the NYU / Anthropic pair, even if it would be impossible to prove.
Maybe what might help is a timeline of when the other two were using Codex for their work, whether they had opted out, and how long it takes for user data to make it to the training of their internal models. That last bit may be considered sensitive information however, as it could give away a lot about their internal processes.
- was item X in the training data
- did the inclusion of X in the training data lead to Y
I understand why the second is hard, but why is the first one hard?
That’s a bizarre statement. Their website says:
> Services for individuals, such as ChatGPT and Codex
> When you use our services for individuals such as ChatGPT and Codex, we may use your content to train our models.
> You can opt out of training through our privacy portal by clicking on “do not train on my content.”
Are they not sure that the opt-out works?
Oddly, their privacy portal page is not the same page as the one with the checkbox.
I would be surprised if OpenAI isn't doing that. OpenAI will take any advantage they can get. If an employee at their primary adversary is typing useful intelligence into OpenAIs website, a website that does not promise privacy from OpenAI, the only reason they wouldn't weaponize that information against Anthropic is ethics or fair play.
Stories of Apollo’s favor and hallucinogenic gases abound, but I think the late Yale professor of Ancient Greek history, Donald Kagan, explained it best:
“Now, you can bet when these folks came and consulted the priests and said, ‘could you please put us down on the list, we want to consult the oracle’, the priests said ‘sure, have a beer, let's talk about your hometown, what's going on out there’. What I'm suggesting to you is that this was the best information gathering and storing device that existed in the Mediterranean world. These people knew more than anybody else about these things, and so consulting that oracle was a very rational act indeed.”
.. can they really know it didn't do the same inadvertently when they prompted things like "someone is close to solving this problem using our tools, try to beat them", and it then decides to hack and peek at their own chats..?
Yes, wild speculation. But warranted, I feel, given OpenAIs behavior.
The non-Anthropic employee, Tristan Buckmaster, is the one paying for OpenAI models and presumably the one who chose to use them. The Anthropic employee, Levent Alpöge, was collaborating in his personal capacity, and obviously it wouldn't make sense for him to cut off their work together just because his employer's competitor's tool was used.
If this is what they do to academic pure mathematicians, where the stakes are so low (financially)—just imagine the sort of front-running that could be happening in other places.
One of the interesting threads here that is certainly relevant to the OpenAI writeup is the human role in the process. Buckmaster clearly points out that (exceptional!) mathematicians at OpenAI were certainly involved in correcting and guiding the process - and that their path/strategy was no doubt influenced by Alpoge & Buckmaster's work. It is always in OpenAI's interest to de-emphasize the role of people in the process, as is clearly the case here. Indeed, given sufficient compute and resources, I suspect Buckmaster could have also extended their approach to N-S.
> “You are creating your cool streaming platform in your bedroom. Nobody is stopping you, but if you succeed, if you get the signal out, if you are being noticed, the large platform with loads of cash can incorporate your specific innovations simply by throwing compute and capital at the problem. They can generate a variation of your innovation every few days, eventually they will be able to absorb your uniqueness. It’s just cash, and they have more of it than you. So the safest bet again is to stay silent, or at least under the radar. Best bet is to not disrupt - succeed at all … ?”
im still having fun making something
Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.The drama comes from where OpenAI got the idea to use that route to tackle NS, since the authors maintain that no one could have plucked it out of thin air like the OpenAI research claim to have done.
“ There does not seem to be anything in principle preventing the methods from extending all the way to Navier-Stokes, and there is even a non-negligible chance that the forcing term could be eliminated entirely, although there are an enormous number of technical difficulties that would ensue in implementing that program. At this point, I would not be surprised if one could batter out such an extension by pouring an enormous amount of compute and AI assistance at such a task…”
C to C*
[1] - "...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.
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.”..."
Reading Sam Altman's and Sebastien's tweets reads like something written by people who know they did dirty shit and are willing to cross any lines to "win". https://x.com/sama/status/2097385167002415140
OpenAI's leadership just can't help to continue to disappoint everyone with their lack of ethics or integrity.
https://mastodon.social/@tristanbuckmaster/11723647135247030...
Which seems to be very directly accusing OpenAI of plagiarism
This. What is worth a human life's attention? As little as a month ago, mathematics was valuable in part because only a small number of people could possibly make progress on the frontier. We are confronting an existential moment for a 4000+ year-old human cultural endeavor. The assumption that "mathematical thinking is hard" has been built-in at a number of important points in how we support mathematics and mathematicians.
We need a different model, and fast. Already, the research community is feeling unable to digest proofs fast enough to keep up with the output of AI models. The paper is 165 pages, and the discovery was finalized two days ago. What this means is that nobody really understands it. Nobody would accept OpenAI's proof in this amount of time, except that they formalized it in lean. The formalization alone would normally be another years-long (or career-long!) effort if the world was the way it was one year ago.
So, again, what efforts are worth a life's attention today? It's a harrowing change.
woah, this gives some credit to the rumor that openai finetuned a model over the course of a few days for this task, and maybe trained on the Chatgpt/codex history of the authors, including drafts of this research.
https://x.com/SebastienBubeck/status/2097379411691516310
https://x.com/sama/status/2097385167002415140
I tend to believe OpenAI on this. Their stated desires seem rational, and Buckmaster's account makes them sound like cartoon villains. It sounds like there may have been some things lost in translation along with some bruised egos. Seems like the most plausible explanation for what Buckmaster is claiming.
That's not at all what the drama is.
I think the important question which AI made breakthrough, Claude or Codex..
Glad to see this is the top comment. There's also https://news.ycombinator.com/item?id=49605915 which links directly. Corporate talking points where they try to set the narrative are going to get the big press and most discussion elsewhere, which is gross. But inevitably the press will muddle the priority question, and even if they didn't.. as usual OpenAI will even benefit from the accusation of bad behavior. Sigh.