- 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.
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.
It seems exceptionally unlikely to me that OpenAI would be "reading user prompts". More likely is a leak somewhere else. Obviously Anthropic/OpenAI are engaged in espionage stuff with each other. I am guessing Levent just mentioned something to someone at Anthropic and it got out.
why is this downvoted? do people really think OpenAI is snooping at people specifically? like they are looking for good leads into new problems or ideas and they found this guy's codex thread and used it? come on man, even for conspiracy theories this is stupid.
> It was also said that if OpenAI posted after us, they would say that we deserved the Clay Prize, and that we were the “closest humans to the problem”. I declined both offers. I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.”
I'm not even sure what to say to this, but I think this should be widely known if it is indeed what happened.
IF ANYTHING, OpenAI ought to investigate and officially react to this particular communique since this dude was communicating on their behalf. If there are supporting evidence, I would expect nothing less than a firing and an apology. The issue itself is separate from the whole thing.
Dark take, but I really hope not. If anything it would be a good opportunity to buy some goodwill by washing themselves from all the alleged shadiness so far.
This is OpenAI though. There were zero visible consequences to them unleashing a swarm of agents on the public internet. We will see how it goes down but my prior is zero consequence and a statement along the lines of "Isn't our AI great? Also we love transparency, ethics and collaboration."
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.
Claiming OAI was going to "totally discredit" Buckmaster is baseless.
From the article, it seems OAI wanted to continue discussing the situation with Buckmaster and reach a resolution, but Buckmaster declined to respond and published first.
This is how deniable threats work. The promise of "not being nice" in conjunction with "ruining the career" is as clear a threat as there can be in writing.
I don't even understand the conflict tbh. Probably I'm just dense. Tristan is not claiming NS, just a huge advance which may solve NS soon. OAI is claiming NS and willing to credit Tristan for the ideas and publish after.
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?
He claims to have found a counterexample for NS (see the second paragraph of the article), but the paper is not ready yet.
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.
For context and balance, Bubeck has tweeted a curiously non-specific denial:
> 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.
My best guess is that from the perspective of the OpenAI people, Buckmaster was letting his paranoia about OpenAI training tank his opportunity to receive the Clay Prize (it seems like Buckmaster and Alpoge's result isn't quite the full result required for the Clay Prize, whereas apparently OpenAI does have that full result worked out, using the same approach that Buckmaster and Alpoge had been exploring).
Whether the Codex sessions could have indeed made their way into Astra training data is something I can only speculate on though.
"using the same approach that Buckmaster and Alpoge had been exploring" is imo mealy wording: it seems fairly likely that OA heard Buckmaster and Alpoge were close to a breakthrough, and decided to use their unlimited compute to quickly prompt based on their assumptions about B&As work.
Well, Buckmaster says both his and Alpöge's use of Codex was non-institutional, and OpenAI claims the right to train their models on inputs and outputs of non-enterprise users in their service policies [0]. So I'm not sure they were even promised that.
It isn't relevant whether they were promised that. Indeed I think the assumption must be that they were not promised that, since otherwise the author asking if they were would not make much sense.
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.
That's absolutely right. Why the downvotes? If OpenAI are using but not acknowledging the work of others that's plagiarism. If they don't know for sure, but aren't performing due dilligence to make sure they aren't, that's also plagiarism.
I can imagine excuses for unknowing plagiarism in this case. What is described in the article seems much more serious: a research program that was only initiated following reports of the author's similar program. In this case no excuses of "I didn't know" can apply, it is not like this revealed some obscure work from the 1980s nobody could reasonably have foreseen. And as far as I can tell this program was only really initiated to apply pressure to the researchers, without their knowledge/consent. It looks very weird.
Your comment was greyed out when I saw it earlier, maybe you missed some downvotes?
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.
I think "greyed out" just means "0 points or less", so if you get 1 downvote without any upvotes it'll be greyed out. For instance your initial reply to me is now greyed out, and I have since observed a few upvotes and downvotes on my original comment (the downvotes apparently from people who aren't willing/able to justify why).
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.
Only for ChatGPT, if the user hasn’t opted out. Would mathematicians be using ChatGPT for this kind of work? Genuinely asking, I know nothing about this!
If I am reading your question correctly you are asking about chat interface Vs Codex/Claude code? If so, in my experience Codex/Claude code use is widespread for mathematicians who are seriously using these tools.
That dude shows up in every thread that even implies genai uses user input for “market validation” to defend the poor defenseless genai corpos. (see figma/claude)
Must be circling the wagons to get their stories straight.
> I'm not even sure what to say to this, but I think this should be widely known if it is indeed what happened.
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.
I'm not one to comment often but this really pisses me off.
OpenAI looked at user data, stole world class researchers' work, and then tried to threaten those researchers to do what would make their corporation profit (which they would anyways!).
Imagine you have been working on a terribly difficult math problem for a decade. This is a result you have spent years on, and what you will likely be remembered for. And to have some punk from OpenAI lie to you, threaten you, and tell you that they are willing to go on the record that you "deserved" it? What is this, the Godfather?
If OpenAI solved Navier-Stokes, that is an astounding result! - yet they'll still be remembered as those who thought credit was more important than results. That winning was more important than collaboration. If this is true, they're burning any trust left with academia.
I'm stunned that people are taking this accusation as a fact.
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.
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".
Duh. There are supposed to be limits to what OpenAI is allowed to access with respect to logs and user interactions but there is no technical limitation.
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.
>> 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.
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:
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.
It would be shocking if it wasn’t trained on sessions. Have you read the ToS parts for both openai and anthropic that talk about it? It’s so obviously a weaselly way to say "no we do not train on your exact chats but we talked with legal and we think a cleanroom reimagining of your convo is probably fine and frankly where else are we going to get such a treasure trove of training data?"
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.
at first I thought your post was a bit revolting with "have you read ToS?" bit, but in the end I completely agree and understand
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
It wouldn't be shocking at all. They stole human data to train the first models and they've been stealing it ever since to train new models. Stealing mathematicians private chats and private research and taking credit for it would absolutely be par for the course.
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
This is how internet discourse works on Reddit/Twitter/HN and the rest. Someone said something which confirms your biases so it’ll now be treated as a fact and repeated endlessly in the echo chamber.
> OpenAI looked at user data, stole world class researchers' work
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.
No, plausible given AI companies want/need session data to train their next models. Probably not someone peeking an eye to sessions directly, but probably not so hard to find the useful sessions in anonymized training data to post train a model on. As stated in the paper, OpenAI did not explicitely denied the researcher sessions were not used for training the model. So either they don't know, or don't want to tell
"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
This conclusion is flawed. It's unclear at this point if OpenAI's model or employees actually looked at or stole the author's data. Having worked at large companies before, I'm leaning towards no, since very few employees have access to that data.
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.
This is much more than the knowledge than the problem can be solved, it's also the specific, non-obvious approach to solving it. That's much more damning for OpenAI, if confirmed.
That's a stretch. The Luis and Diego paper was published in 2023 and is included in every frontier model's training dataset. An AI model could independently choose the same path route as Luis and Diego, without access to Buckmaster and Alpöge’s work.
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.
> An AI model could independently choose the same path route as Luis and Diego, without access to Buckmaster and Alpöge’s work.
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 (...)
i don't know if i understand what you're saying. but i'm no mathematician. here's the full statement in question once again:
> 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.
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)
Please don't say brute forced. It sounds like some form of denial or something. Compute for hard problems drops with models--it just means they threw a huge amount of compute. There's (idk about NS specifically so maybe it's exception) no real way to "brute force" a math proof [ok you can enumerate proofs if you can wait until heat death ]
Sorry for random rant but I don't think these statements help your point
I want to point out that almost all previous AI discoveries in math were made in almost the same way. The ideas were there in the community, but weren't considered mainstream/worth pushing forward. Read Tao's comments on the unit distance problem, for example (sry I can't find a link right now).
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.
> And simply knowing a problem can be solved is half the battle.
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.
You're taking the phrase too literally. The point is that knowing a solution is possible gives you the conviction to actually find that solution. The hardest part of solving a problem is often a lack of conviction to see it through, and quitting too early. Once you know a solution exists, you can commit maximal effort towards solving it and know that your efforts are not in vain.
If not for the rumors that A/ had already solved NS, OAI would likely never have pursued solving the problem with such fervor. The rumors drove OAI to assemble an entire team to crack this.
How is it unclear? The entire point of deploying models across corporate America is to train on your workflows. Eventually replacing you with digital you is why they're doing it!
Things are more entangled than that.
The contribute made from both OpenAI and Anthropic models to solve these problems are clear, now it really hard to quantify which one contributed more, if the role played by the human is major or minor.
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?
The results being true, the 'deal' that was made being true doesn't mean some of the implied accusations here are true, for example - that Open AI used their Codex logs to drive their breakthrough.
How else would you explain OpenAI suddendly assembling a team focused on working the same problem from the same angle than the researchers that just made a breakthrough?
The rumors that Anthropic had solved a millennium problem were absolutely everywhere last week. I'm not surprised at all that OAI took their own stab at it.
We are told in the statement that there were rumours already going around about a Stokes result (I even know about the rumors in question. It was all over twitter in the right spaces) and that Tristan contacts OpenAI about the rumors. In the message, it's pretty clear Tristan has made some result.
So either the rumors or Tristan's contact would explain it fine.
One should not evaluate explanations based on level of "fine"/innocuousness, in ethics that is called motivated reasoning or something.
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
So are you baselessly assuming that he is lying? He explicitly reported that he was threatened and your answer here is to defend OpenAI no matter what.
Do you not have reading comprehension? Did you even read the statement? He himself asserts at the end he doesn't know if the above example is true or not. What on earth are you going on about? Where in my comment am I assuming he's lying ?
From my post above:
> He explicitly reported that *he was threatened* and your answer here is to defend OpenAI no matter what.
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...
My reading comprehension is pretty good, I'm not the one that doesn't recognize a threat even when it's perfectly clear.
Verbatim from the statement:
> The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.”
I’m open to evidence, but just using Bayesian reasoning, OpenAI is one of the most dishonest companies in history. They’re currently being sued for a dozen employees stealing Apple hardware! I don’t understand why I should give them any grace.
The accused Sebastian Bubeck has denied the allegations on Twitter[0], and various other OpenAI employees[1,2] seem to be mocking another Anthropic employee voicing support for Levent[3]? Things are getting messy.
So, leaving aside the idea that OA might've used data from the researchers Codex sessions: Do I understand correctly that the internal OpenAI work on the problems was probably started after they heard Alpoge and Buckmaster had made process by using their models? And they used the publicly available info about the researchers past work to prompt their models?
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.
But there's a bunch of people already in this thread calling that stuff unfounded speculation (which I disagree with), and my point is that even if that specific thing isn't true, OA's behavior here is obviously awful.
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.
Well, of course Anthropic employees would say that, since they likely do the same. Claiming that your primary competitor doesn't engage in a certain malicious practice is supposed to make it look as if there's no way you would too. If somebody even says that about their competitor, then surely there must be truth to that, otherwise you would never give credit to someone you're opposed to.
By default OA trains their models on codex-sessions. If I understand him correctly this is something Tristan explicitly mentions in his post as a possible reason for the fast results obtained by the internal OA team. Anthropic obviously doesn't want to challenge the idea that training is transformative, even if it means agreeing with their competitor.
I’ve thought a lot about publishing research and wanting to do more of it, but right as I finally had the time and energy to start writing articles LLMs start to take off. Now all of a sudden, I’m acutely aware that everything I publish will be used for AI training.
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.
Seems pretty likely OpenAI will soon disclose that their internal models have managed to compromise their internal controls in order to access users' private chat histories as a creative method of cheating to solve impossible problems.
"Oops! We really did mean it when we said we wouldn't train on your data. Our models are just so good they decided to anyway."
The timeframes don't really fit for Codex logs to be used in training/fine-tuning, do they? This wouldn't be a few-day endeavour? Direct access to Codex history for sure I'd believe, but another (the most?) likely scenario to me feels like OpenAI got wind of these guys' progress, then used their massive infrastructure advantage to throw compute at the problem ahead of them and front-run them. Still has a really bad smell about it though.
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.
> They were coordinating with OpenAI regarding a publishing timeline, but could not come to an agreement,
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]
Yeah these are major accusations. But the story is incomplete, the conversation is missing a lot of details. It's not clear who was working on what, and when. The entire thing feels rushed, like they wanted to get this result published and out the door quickly.
I find the framing a little strange, a sort of David vs Goliath (with his enormous computational resources at his disposal). Since Levent is at Anthropic whose internal models are presumably as capable as anything OpenAI has. So why wasn't Anthropic behind their effort? Why did Tristan use OpenAI's models when it should have been known was a potential outcome? 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). Normally these things are hashed out formally beforehand to avoid the sort of thing now happening.
They were working on it for almost a year, and Buckmaster has evidently been interested in Navier-Stokes for a while. This seems to be more of an innocent collaboration between two researchers than a strong company PR effort. Maybe Anthropic should have stepped in and made a large team to help them finish the proof (and maybe they tried and didn't succeed, who knows).
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.
There are various forces at play here, academic honesty requires them to disclose any inputs regardless of license or ToS circumstances.
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.
> A few days later, OpenAI gets back to him, and tells him an internal model found a counterexample for Navier–Stokes
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?"
The only problem with this narrative is that they refused to allow the other coauthor to be listed because he worked at Anthropic.
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.
>...has solved a millennium problem and is sitting on the result
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.
Apparently forcing is allowed in the Millenium Prize problem statement. So OpenAI's claimed proof could win the prize. OTOH the results Tristan and Levent are publishing here do not go far enough to win the prize, though apparently they are suggestive of a general approach that could produce a solution, which seems likely to be the general approach OpenAI's proof uses.
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.
Because very few people actually have access to these logs, all access is monitored and recorded, and improper access will get you fired. It's not worth risking your job over something like this.
If there's one thing I'm absolutely confident in, it's that Sam Altman personally goes to great lengths ensuring that ethical standards are upheld at his company.
> Because very few people actually have access to these logs, all access is monitored and recorded, and improper access will get you fired. It's not worth risking your job over something like this.
That's beyond naive. The money this would mean for OpenAI (and the money they've already spent)...
There is almost zero risk to your job (quite the opposite, you might be richly rewarded!) if you're simply doing something here which the company wants done. (remember, billions and billions of dollars are at stake here! Do you really think there is no chance at all they would do it??)
As modeless said, Sholto Douglas works for Anthropic!
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.
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)
>I asked whether the model had been trained on, or had access to, our sessions
in Codex, into which we had been putting all our drafts for the whole of this
project. I was told the model did not look up user data. I asked again, about
training, and I did not get an answer.
If you think these companies are not training on your prompts you are incredibly naive. These models were built by stealing and pirating literally everything they can get their hands on no matter the legality. AI companies are always very specific about what they're not doing - in a way that you can drive a truck through the loopholes
"I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true."
The money in nerdy frontier math is very little. The money in Big AI is very very much.
So the deal is this: We will pay an army of you guys very well and you will get to work on your favorite problems. The only thing is if you find something you will have to credit the Machine God.
Yes, and this puts in check the credibility of everything they say their model "discovered". Who knows what is really behind these "discoveries", what kind of backroom deals they did with other researchers who didn't have a chance or desire to disclose what happened?
In an earlier HN thread, there was speculation that Anthropic was being dishonest about the amount of human input required in some of their results; that was dismissed as conspiracy and flagged.
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?”
When people worry about OpenAI stealing their chats and reproducing them elsewhere, I usually view the situation as unlikely - since chats are "trained" upon and not necessarily reproduced verbatim, you can assume that unless your chats depict a foundationally new and effective style of communication or ideation, there would be little need or use thereof of training on your chats.
For eg: "Hey ChatGPT my name is X and I am 6 and a half feet tall. Am I anaemic?"
This is a query, and while it might suggest to an AI model that tall people may worry about iron deficiencies, it's not really necessary to include in training. The user may be tall or short, but the idea that one may randomly ask about anaemia is not exclusive to this dataset. At best, this chat is an example of linguistics, not anything else, and the models figured out how to write and answer such questions years ago. It is ignored in training.
But when your work involves solid complex and unique mathematical proofs, the data is suddenly worth training upon. If I understand it correctly, the LLM may view your approach as a brand new path to take to solve an otherwise intractable problem. Its reinforcement training emphasises that it should do this in order to improve. And since it leads to results - large internal teams likely flag the model that reached this stage, the model is rewarded and given compute and attention - it is a desireable outcome both for the model and for OpenAI.
OFC, OpenAI becoming an advertising company will suddenly have incentive to treat all data as valuable. But while they are a "we need to make headlines" company, it's more rational that they view these examples of data as more valuable than others.
I don't doubt that they trained on his chats. This seems like the ideal usecase for "mass surveillance but using training" as a sort of filter.
But even so, one wonders how the model differentiates. If the researcher entered proofs into ChatGPT every day that mentioned "strawberries", while no other math paper on the topic did so, does that mean their chats would be audited?
Also, if we just take "high-quality" input data, which these chats would certainly be classified as, then the models are more than large enough to memorize everything verbatim. Spitballing some numbers, research literature suggests that LLMs are optimally trained with around 20 training tokens per parameter (fairly confident on this figure), that a DNN parameter encodes around 4 bits of data (less confident here) and I found sources in the 1-4 bits of information per token range (least confident here). So, fairly conservatively I would estimate that a model has the capacity to fully memorize around 5% of its training data, presumably high-quality data is a lot less than that.
At this point these models have been trained to recognize every important math and science result based on context. They can easily flag conversations concerning the top 100 open problems in mathematics and use them for their advancement.
There also is an insentive to silently give prominent people (e.g. Linus) or reasearchers like this custom tuned system prompts or even more powerful models.
"It is extremely sad that this didn't end up as an example of how the labs could cooperate/coordinate, because the stakes will be so much higher in the future." -- Sholto Douglas, an Anthropic researcher [1]
"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.
The for-case for this type of method is that this is economies of scale for 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.
Can somebody explain: do singularities / blow-ups in solutions have any relation to physical phenomena in fluid dynamics or are they purely artifacts of how the N-S equations may not accurately describe what actually happens in the physical world?
i'm no mathematician/physicist but i think this question is one of the reasons why the original question (possibility of singularities) is interesting. in these cases the equations most likely fail to accurately model reality, and then the next questions are what additional physical assumptions are needed to describe reality in this case, and what behavior do we actually see.
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).
Yes and no. It means the system is pushed away from a macroscopic theory into one where molecular effects matter. So it's not that you'd get infinite velocities in the real world, but you might get significant real world behavior that is not described by the macroscopic theory.
What is specifically alleged is that a particular approach to the problem - itself not easily discoverable - was copied. This is what is meant in the text "I should say here why I interpreted their statement the way I did, the in-
terpretation I will discuss below. 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."
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.
>> 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.
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.
Hard mathematics problems used to take years if not decades to tackle manually. But now with enough compute and a hint that a certain approach might work, it just takes a few days. This could be the last year that humans could still make more substantial contribution to major match problems than machines.
There will be a lot of hurt and pain in mathematician's community. It is hard to accept that major discoveries are now just a function of spent token $$.
Reminds me, kinda, to when Astra was launched and OpenAI announced an improvement to the bounded prime gap. Which BTW, Prof. Julia Stadlmann had published an independent result only a few days earlier
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.
I don't know how to read this and not see that this is a direct accusation to OpenAI of having used the researchers data to try to front run his discovery on purpose. The evidence is not completely proven and also circumstantial but to me at least looks like a fairly suspicious situation.
Buckmaster is actually implying that OpenAI spied on his chat logs and tried to speedrun his work and then tried to remove his co-author because he's an Anthropic employee?
“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.”
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?
Well these are all allegations. Either way from what I understand the reasoning and proof was basically made by AI so I'm not sure what supposedly "stolen".
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.
While I'm generally pretty negative on claims that the labs are 'scamming' the public with misrepresentations of model capabilities, it's hard to see how this wouldn't qualify.
- the OpenAI researchers claimed that they had "just told it to work on the problem" with little human input
- in fact, they had a whole team working on it
- and used, among other things, the work of third party human researchers to drive the work
- then threatened? a researcher who tried to go against theit planned narrative
Just from this document (which is of course only one side of the story) it really sounds like OpenAI was hoping to publish and say "we just told the model to try harder and it solved a Millennium problem!". Not great if true.
This part in particular was especially egregious:
> I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?”
I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t
have to be nice.”
This is the plot of 3 Body Problem, the Dark Forest. You need to hide yourself (the problem you are working on) or the super advanced aliens will obliterate you (start working on your problem) the moment they know you exist (rumors the problem is amendable to LLMs).
Some of the involved people are dramatically naive if they believe they can simultaneously hide themselves from OpenAI while sending their arguments to a cloud service owned by OpenAI.
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.
I must miss some important context here. What exactly was the purpose of his initial email to OpenAI in the first place?
Telling OpenAI that Anthropic has apparently solved an important problem but most likely that refers to him and he is using OpenAI models (not Anthropic's)?
And he wants to clarify that with OpenAI in advance? And get a pardon for Anthropic's likely but false press statements?
I dont get it.
[edited] needless to say, the behavior of the OpenAI employee is really despicable
Because OpenAI employees kept leaking that Anthropic had a solution to Navier-Stokes and he wanted to figure out what was going on, since he was working on Navier-Stokes with an Anthropic employee. The rumor has been loudly circling the math community for the past week or so. For a bit of context, here's a timeline from mathematician and AI researcher Elliot Glazer:
To be clear, Astra played little part in Buckmaster and Alpoge's work:
> 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.
Life’s but a walking shadow, a poor player
That struts and frets his hour upon the stage
And then is heard no more. It is a tale
Told by an idiot, full of sound and fury
Signifying nothing.
Can a mathematical person explain how the different "bits" of Navier-Stokes proofs fit together? How significant is it to have "Euler"? What is this "smooth forcing"? Which are the most significant steps to proving the whole thing?
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.
Drama/accusation summary:
- 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.
Ignoring the drama, when can we expect the lean proof of this great sensational discovery?
> Ignoring the drama
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.
Attempts to steal $1,000,000 for a solution to Millennium Prize Problem have become a tradition, apparently.
Thanks. I was pinging some people near the mentioned Córdoba to see if they had any insights, but no extra info yet...
It seems exceptionally unlikely to me that OpenAI would be "reading user prompts". More likely is a leak somewhere else. Obviously Anthropic/OpenAI are engaged in espionage stuff with each other. I am guessing Levent just mentioned something to someone at Anthropic and it got out.
why is this downvoted? do people really think OpenAI is snooping at people specifically? like they are looking for good leads into new problems or ideas and they found this guy's codex thread and used it? come on man, even for conspiracy theories this is stupid.
> It was also said that if OpenAI posted after us, they would say that we deserved the Clay Prize, and that we were the “closest humans to the problem”. I declined both offers. I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.”
I'm not even sure what to say to this, but I think this should be widely known if it is indeed what happened.
IF ANYTHING, OpenAI ought to investigate and officially react to this particular communique since this dude was communicating on their behalf. If there are supporting evidence, I would expect nothing less than a firing and an apology. The issue itself is separate from the whole thing.
Or, given how dedicated he appears to be to the company, a promotion and a raise.
Dark take, but I really hope not. If anything it would be a good opportunity to buy some goodwill by washing themselves from all the alleged shadiness so far.
This is OpenAI though. There were zero visible consequences to them unleashing a swarm of agents on the public internet. We will see how it goes down but my prior is zero consequence and a statement along the lines of "Isn't our AI great? Also we love transparency, ethics and collaboration."
I think this should be in the title of the post. 'OpenAI allegedly threatening to ruin a prominent researcher's career', or smth like that.
There's some glaring mistakes in your framing.
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.
> Second, you miscomprehended the article. The employee did not "threaten to ruin a prominent researcher's career"…
Proceeds to ask removal of another coauthor or else we totally discredit you - phrased as why would you do this to yourself.
Claiming OAI was going to "totally discredit" Buckmaster is baseless.
From the article, it seems OAI wanted to continue discussing the situation with Buckmaster and reach a resolution, but Buckmaster declined to respond and published first.
This is how deniable threats work. The promise of "not being nice" in conjunction with "ruining the career" is as clear a threat as there can be in writing.
I don't even understand the conflict tbh. Probably I'm just dense. Tristan is not claiming NS, just a huge advance which may solve NS soon. OAI is claiming NS and willing to credit Tristan for the ideas and publish after.
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?
He claims to have found a counterexample for NS (see the second paragraph of the article), but the paper is not ready yet.
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.
Dude you’re over this entire thread unflinchingly supporting OpenAI with nonsense semantics-based arguments.
Either put up some evidence-backed arguments, or shut up.
For context and balance, Bubeck has tweeted a curiously non-specific denial:
> 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.
Isn't that a non-denial denial?
Attack is the best form of defence
My best guess is that from the perspective of the OpenAI people, Buckmaster was letting his paranoia about OpenAI training tank his opportunity to receive the Clay Prize (it seems like Buckmaster and Alpoge's result isn't quite the full result required for the Clay Prize, whereas apparently OpenAI does have that full result worked out, using the same approach that Buckmaster and Alpoge had been exploring).
Whether the Codex sessions could have indeed made their way into Astra training data is something I can only speculate on though.
"using the same approach that Buckmaster and Alpoge had been exploring" is imo mealy wording: it seems fairly likely that OA heard Buckmaster and Alpoge were close to a breakthrough, and decided to use their unlimited compute to quickly prompt based on their assumptions about B&As work.
Buckmaster is already an established world expert at these sorts of problems. Declining the Clay prize would hardly dent his career.
Can you call paranoia a fear of something which is happening? OpenAI uses user chats for training and they are "open" about it.
Zero data retention, wink.
No looksies, wink.
No trainsies, wink.
Well, Buckmaster says both his and Alpöge's use of Codex was non-institutional, and OpenAI claims the right to train their models on inputs and outputs of non-enterprise users in their service policies [0]. So I'm not sure they were even promised that.
[0] https://openai.com/policies/how-your-data-is-used-to-improve...
It isn't relevant whether they were promised that. Indeed I think the assumption must be that they were not promised that, since otherwise the author asking if they were would not make much sense.
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.
That's absolutely right. Why the downvotes? If OpenAI are using but not acknowledging the work of others that's plagiarism. If they don't know for sure, but aren't performing due dilligence to make sure they aren't, that's also plagiarism.
I can imagine excuses for unknowing plagiarism in this case. What is described in the article seems much more serious: a research program that was only initiated following reports of the author's similar program. In this case no excuses of "I didn't know" can apply, it is not like this revealed some obscure work from the 1980s nobody could reasonably have foreseen. And as far as I can tell this program was only really initiated to apply pressure to the researchers, without their knowledge/consent. It looks very weird.
> Why the downvotes?
I think there was only ever one. Not sure why.
Your comment was greyed out when I saw it earlier, maybe you missed some downvotes?
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.
I think "greyed out" just means "0 points or less", so if you get 1 downvote without any upvotes it'll be greyed out. For instance your initial reply to me is now greyed out, and I have since observed a few upvotes and downvotes on my original comment (the downvotes apparently from people who aren't willing/able to justify why).
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.
Only for ChatGPT, if the user hasn’t opted out. Would mathematicians be using ChatGPT for this kind of work? Genuinely asking, I know nothing about this!
Yes, mathematicians are. And yes, most of my colleagues did not even know the opt-out was an option.
If I am reading your question correctly you are asking about chat interface Vs Codex/Claude code? If so, in my experience Codex/Claude code use is widespread for mathematicians who are seriously using these tools.
simonw’s silence on this is telling.
That dude shows up in every thread that even implies genai uses user input for “market validation” to defend the poor defenseless genai corpos. (see figma/claude)
Must be circling the wagons to get their stories straight.
You understand that people sleep, right?
> I'm not even sure what to say to this, but I think this should be widely known if it is indeed what happened.
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.
Are you pretending OpenAI employees are "academics"?
Or are you stating that the researcher is a "horrible human being" for refusing to allow AI?
To come away from this thinking that the academic is the bad actor, given OpenAI’s reputation, is certainly an exercise in creative thinking.
I'm not one to comment often but this really pisses me off.
OpenAI looked at user data, stole world class researchers' work, and then tried to threaten those researchers to do what would make their corporation profit (which they would anyways!).
Imagine you have been working on a terribly difficult math problem for a decade. This is a result you have spent years on, and what you will likely be remembered for. And to have some punk from OpenAI lie to you, threaten you, and tell you that they are willing to go on the record that you "deserved" it? What is this, the Godfather?
If OpenAI solved Navier-Stokes, that is an astounding result! - yet they'll still be remembered as those who thought credit was more important than results. That winning was more important than collaboration. If this is true, they're burning any trust left with academia.
I'm stunned that people are taking this accusation as a fact.
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.
He didn't even make that accusation!
> 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.
Parse that statement more carefully.
> 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".
Duh. There are supposed to be limits to what OpenAI is allowed to access with respect to logs and user interactions but there is no technical limitation.
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.
>> 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.
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.
It would be shocking if it wasn’t trained on sessions. Have you read the ToS parts for both openai and anthropic that talk about it? It’s so obviously a weaselly way to say "no we do not train on your exact chats but we talked with legal and we think a cleanroom reimagining of your convo is probably fine and frankly where else are we going to get such a treasure trove of training data?"
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.
at first I thought your post was a bit revolting with "have you read ToS?" bit, but in the end I completely agree and understand
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
It wouldn't be shocking at all. They stole human data to train the first models and they've been stealing it ever since to train new models. Stealing mathematicians private chats and private research and taking credit for it would absolutely be par for the course.
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
They are not training a whole model in a matter of days
They where working on the problem for a year using codex.
pretraining is months but they can totally fine tune in a few days
Couldn't the Enterprise have a different fine print?
Whenever I see comments defending AI companies, I look at the account's creation date, and interestingly almost all of them were created post 2024.
This is how internet discourse works on Reddit/Twitter/HN and the rest. Someone said something which confirms your biases so it’ll now be treated as a fact and repeated endlessly in the echo chamber.
I am stunned anyone is giving OpenAI the benefit of the doubt
He asked whether they used their chats as training data and received no response. Any speculation here seems quite appropriate?
They stole it.
I don’t think you understand how brazen big tech companies are in practice.
> OpenAI looked at user data, stole world class researchers' work
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.
They likely train on logs.
No, plausible given AI companies want/need session data to train their next models. Probably not someone peeking an eye to sessions directly, but probably not so hard to find the useful sessions in anonymized training data to post train a model on. As stated in the paper, OpenAI did not explicitely denied the researcher sessions were not used for training the model. So either they don't know, or don't want to tell
"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
This conclusion is flawed. It's unclear at this point if OpenAI's model or employees actually looked at or stole the author's data. Having worked at large companies before, I'm leaning towards no, since very few employees have access to that data.
And simply knowing a problem can be solved is half the battle.
From Buckmaster's text:
This is much more than the knowledge than the problem can be solved, it's also the specific, non-obvious approach to solving it. That's much more damning for OpenAI, if confirmed.That's a stretch. The Luis and Diego paper was published in 2023 and is included in every frontier model's training dataset. An AI model could independently choose the same path route as Luis and Diego, without access to Buckmaster and Alpöge’s work.
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.
> An AI model could independently choose the same path route as Luis and Diego, without access to Buckmaster and Alpöge’s work.
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 (...)
>"It is not the direction one arrives at in a few days by giving a model the problem statement."
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.
i don't know if i understand what you're saying. but i'm no mathematician. here's the full statement in question once again:
> 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.
> "It is not the direction one arrives at in a few days by giving a model the problem statement."
Can they back up this statement somehow?
yes, this is ultimately nothing but a claim.
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)
Please don't say brute forced. It sounds like some form of denial or something. Compute for hard problems drops with models--it just means they threw a huge amount of compute. There's (idk about NS specifically so maybe it's exception) no real way to "brute force" a math proof [ok you can enumerate proofs if you can wait until heat death ]
Sorry for random rant but I don't think these statements help your point
I want to point out that almost all previous AI discoveries in math were made in almost the same way. The ideas were there in the community, but weren't considered mainstream/worth pushing forward. Read Tao's comments on the unit distance problem, for example (sry I can't find a link right now).
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...
> And simply knowing a problem can be solved is half the battle.
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.
You're taking the phrase too literally. The point is that knowing a solution is possible gives you the conviction to actually find that solution. The hardest part of solving a problem is often a lack of conviction to see it through, and quitting too early. Once you know a solution exists, you can commit maximal effort towards solving it and know that your efforts are not in vain.
If not for the rumors that A/ had already solved NS, OAI would likely never have pursued solving the problem with such fervor. The rumors drove OAI to assemble an entire team to crack this.
How is it unclear? The entire point of deploying models across corporate America is to train on your workflows. Eventually replacing you with digital you is why they're doing it!
Things are more entangled than that. The contribute made from both OpenAI and Anthropic models to solve these problems are clear, now it really hard to quantify which one contributed more, if the role played by the human is major or minor.
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?
They offered to collaborate by asking to drop a coauthor.
That is not collaboration, and is not an academic norm.
Yes, but only if you take this one sided statement at face value.
Why would have they rushed the publication if this was not true? Are you also suggesting that he fully invented the call with Open AI?
The results being true, the 'deal' that was made being true doesn't mean some of the implied accusations here are true, for example - that Open AI used their Codex logs to drive their breakthrough.
How else would you explain OpenAI suddendly assembling a team focused on working the same problem from the same angle than the researchers that just made a breakthrough?
What would be so hard to explain?
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 ?
That's a fake explanation, it skips explaining/justifying how OpenAi "heard about" the result
The rumors that Anthropic had solved a millennium problem were absolutely everywhere last week. I'm not surprised at all that OAI took their own stab at it.
We are told in the statement that there were rumours already going around about a Stokes result (I even know about the rumors in question. It was all over twitter in the right spaces) and that Tristan contacts OpenAI about the rumors. In the message, it's pretty clear Tristan has made some result.
So either the rumors or Tristan's contact would explain it fine.
One should not evaluate explanations based on level of "fine"/innocuousness, in ethics that is called motivated reasoning or something.
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
So are you baselessly assuming that he is lying? He explicitly reported that he was threatened and your answer here is to defend OpenAI no matter what.
Do you not have reading comprehension? Did you even read the statement? He himself asserts at the end he doesn't know if the above example is true or not. What on earth are you going on about? Where in my comment am I assuming he's lying ?
From my post above: > He explicitly reported that *he was threatened* and your answer here is to defend OpenAI no matter what.
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...
You really lack reading comprehension
My reading comprehension is pretty good, I'm not the one that doesn't recognize a threat even when it's perfectly clear. Verbatim from the statement:
> The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.”
I’m open to evidence, but just using Bayesian reasoning, OpenAI is one of the most dishonest companies in history. They’re currently being sued for a dozen employees stealing Apple hardware! I don’t understand why I should give them any grace.
LLMs do nothing but steal, and the companies that own them are fully aware and eager to do it.
The accused Sebastian Bubeck has denied the allegations on Twitter[0], and various other OpenAI employees[1,2] seem to be mocking another Anthropic employee voicing support for Levent[3]? Things are getting messy.
[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...
Wow this is just bullying, it's insane that we are letting these people be in charge of the transition
So someone can make public accusations of theft against you and if you publicly reply denying it you’re the bully?
I would assume they are calling the snark from Noam Brown and Dan Roberts bullying, not the somewhat bland denial.
I read through those tweets, and can’t see the bullying everyone is referring to. Mind elaborating?
They are mocking Sholto's support of Levent. I thought Noam Borwn would be above this but i think the cutlure withitn OpenAI encourages it.
I assume this will make more sense in the morning, right now I’m just extremely confused. Noam never struck me as the type to be snarky like this.
The elves left a long time ago, it’s difficult to see much virtue in what remains.
i already have an extremely low view of openai and their staff, but this is lower than i thought they'd go
if I look at the timestamps, it appears Sholto is the one mocking Noams tweet... Noam posted first.
Douglas' 6:59 AM UTC post is edited. He has a 6:22 AM UTC post that predates Brown's 6:47 AM UTC post: https://xcancel.com/_sholtodouglas/status/209720900556759874...
Also note the lower post ID in the URL.
Doesn’t matter. People’s minds are already made up, and facts aren’t getting in the way.
Assuming that your mind is not already made up, and that facts aren't getting in the way, do see https://news.ycombinator.com/item?id=49608972
Interesting that both said “more tomorrow”. If someone accused me of something I didn’t do I’d be pretty clear about it right away.
If I needed to get my story straight, well, it might take a little time and coordination…
So, leaving aside the idea that OA might've used data from the researchers Codex sessions: Do I understand correctly that the internal OpenAI work on the problems was probably started after they heard Alpoge and Buckmaster had made process by using their models? And they used the publicly available info about the researchers past work to prompt their models?
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.
> leaving aside the idea that OA might've used data from the researchers Codex sessions
Why leave that aside? That is _the_ story.
If a Chinese research lab did this we'd call it espionage.
But there's a bunch of people already in this thread calling that stuff unfounded speculation (which I disagree with), and my point is that even if that specific thing isn't true, OA's behavior here is obviously awful.
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.
Because they didn't do that. Tristan doesn't specifically claim that they did, and Anthropic employees don't think they did either. https://x.com/_sholtodouglas/status/2097218240397410733
Well, of course Anthropic employees would say that, since they likely do the same. Claiming that your primary competitor doesn't engage in a certain malicious practice is supposed to make it look as if there's no way you would too. If somebody even says that about their competitor, then surely there must be truth to that, otherwise you would never give credit to someone you're opposed to.
By default OA trains their models on codex-sessions. If I understand him correctly this is something Tristan explicitly mentions in his post as a possible reason for the fast results obtained by the internal OA team. Anthropic obviously doesn't want to challenge the idea that training is transformative, even if it means agreeing with their competitor.
Why is that the story? Is there anything to back it up beyond a single accusation?
As a prior I would say that a math professor has about infinite times more integrity than OpenAI.
I’ve thought a lot about publishing research and wanting to do more of it, but right as I finally had the time and energy to start writing articles LLMs start to take off. Now all of a sudden, I’m acutely aware that everything I publish will be used for AI training.
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.
Similar to https://news.ycombinator.com/item?id=47566442
This is an excellent point...
Seems pretty likely OpenAI will soon disclose that their internal models have managed to compromise their internal controls in order to access users' private chat histories as a creative method of cheating to solve impossible problems.
"Oops! We really did mean it when we said we wouldn't train on your data. Our models are just so good they decided to anyway."
It doesn't even have to be actually sinister, eg.
"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.
It would be pretty wild if this will turn out to be what had actually happened.
And probably a strong signal that it's time to shut the whole thing down. Globally.
It's part of their TOS that they can train on users' private chats.
The timeframes don't really fit for Codex logs to be used in training/fine-tuning, do they? This wouldn't be a few-day endeavour? Direct access to Codex history for sure I'd believe, but another (the most?) likely scenario to me feels like OpenAI got wind of these guys' progress, then used their massive infrastructure advantage to throw compute at the problem ahead of them and front-run them. Still has a really bad smell about it though.
Full mastodon post: https://mathstodon.xyz/@tristanbuckmaster@mastodon.social/11...
Mathematical explanation by Terrance Tao: https://mathstodon.xyz/@tao/117233527638291447
It seems there is much background drama behind this, and this is what I've pieced together of what happened:
Over the past year, Buckmaster and Alpöge have been using AI to work on fluid dynamics maths problems. Alpöge works at Anthropic, which will cause future issues.
In mid-August, they found a counterexample for a simpler version of the Navier-Stokes problem. They spend the next few weeks preparing their paper.
In early September, rumors start spreading on X that Anthropic has solved a Millennium prize problem (and that it's Navier-Stokes). Buckmaster reaches out to OpenAI to explain this is their own personal research, not an Anthropic project.
A few days later, OpenAI gets back to him, and tells him an internal model found has a counterexample for Navier–Stokes, potentially worth the $1 million Millennium prize. The proof uses the same method that Buckmaster and Alpöge chose to work on. They don't show him the proof.
Buckmaster pressed them for more details. OpenAI reveals they had an entire team had been working on the problem, and that they started work in the past few days, after the rumors that Anthropic had solved a Millennium prize problem.
Buckmaster says OpenAI talked about a shared publication timeline. They want to Buckmaster to publish first, then give Buckmaster shared credit for the Millennium Prize when they publish the full result. But they want to exclude Alpöge as an author because he works at Anthropic. An agreement is not reached. Buckmaster had been using OpenAI Codex to draft/check his work, and asks if his private AI chats were used to accelerate OpenAI's result.
Buckmaster and Alpöge think they have found a counterexample for Navier-Stokes, but the paper is not yet presentable. It's unclear what date they found this result.
Because of the situation with OpenAI, they published their existing papers earlier than planned (today), alongside this statement announcing they have a tentative result on Navier-Stokes and revealing the OpenAI drama.
The post is missing context from both sides, and this isn't my field, so hopefully someone else can unpack what's happening here.
> They were coordinating with OpenAI regarding a publishing timeline, but could not come to an agreement,
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]
[0]: https://cims.nyu.edu/~tristanb/statement.pdf
Yeah these are major accusations. But the story is incomplete, the conversation is missing a lot of details. It's not clear who was working on what, and when. The entire thing feels rushed, like they wanted to get this result published and out the door quickly.
I find the framing a little strange, a sort of David vs Goliath (with his enormous computational resources at his disposal). Since Levent is at Anthropic whose internal models are presumably as capable as anything OpenAI has. So why wasn't Anthropic behind their effort? Why did Tristan use OpenAI's models when it should have been known was a potential outcome? 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). Normally these things are hashed out formally beforehand to avoid the sort of thing now happening.
They were working on it for almost a year, and Buckmaster has evidently been interested in Navier-Stokes for a while. This seems to be more of an innocent collaboration between two researchers than a strong company PR effort. Maybe Anthropic should have stepped in and made a large team to help them finish the proof (and maybe they tried and didn't succeed, who knows).
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.
> So why wasn't Anthropic behind their effort?
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.
Does he claim to have opted out of training too?
There are various forces at play here, academic honesty requires them to disclose any inputs regardless of license or ToS circumstances.
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.
> A few days later, OpenAI gets back to him, and tells him an internal model found a counterexample for Navier–Stokes
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?"
Perhaps out of a sense of academic good will, knowing that he got there first?
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...
The only problem with this narrative is that they refused to allow the other coauthor to be listed because he worked at Anthropic.
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.
>...has solved a millennium problem and is sitting on the result
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.
Apparently forcing is allowed in the Millenium Prize problem statement. So OpenAI's claimed proof could win the prize. OTOH the results Tristan and Levent are publishing here do not go far enough to win the prize, though apparently they are suggestive of a general approach that could produce a solution, which seems likely to be the general approach OpenAI's proof uses.
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.
[1] https://x.com/_sholtodouglas/status/2097218240397410733
Why do you find it to be extremely unlikely?
Because very few people actually have access to these logs, all access is monitored and recorded, and improper access will get you fired. It's not worth risking your job over something like this.
If there's one thing I'm absolutely confident in, it's that Sam Altman personally goes to great lengths ensuring that ethical standards are upheld at his company.
> Because very few people actually have access to these logs, all access is monitored and recorded, and improper access will get you fired. It's not worth risking your job over something like this.
That's beyond naive. The money this would mean for OpenAI (and the money they've already spent)...
Not that I have strong reasons to think this is not true, but what reasons do we have to think it is? Has this been audited before?
There is almost zero risk to your job (quite the opposite, you might be richly rewarded!) if you're simply doing something here which the company wants done. (remember, billions and billions of dollars are at stake here! Do you really think there is no chance at all they would do it??)
As modeless said, Sholto Douglas works for Anthropic!
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.
> This is a a Deep Blue-Kasparov moment.
I guess this is true in more ways than one. Kasparov famously accused IBM of cheating during the match, by spying on his preparation (edit: though the main cheating accusation was live human intervention during the games, on top of IBM downplaying the heavy human involvement behind the AI, which also mirrors this situation)
Amazing how history rhymes
>I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.
If you think these companies are not training on your prompts you are incredibly naive. These models were built by stealing and pirating literally everything they can get their hands on no matter the legality. AI companies are always very specific about what they're not doing - in a way that you can drive a truck through the loopholes
Exactly, especially when the company can assign "blame" to the models themselves "ops, they just escaped our commands not to store user inputs..."
It's equally naive to believe FUD spread on the internet, without evidence.
But I would love to see more informed insight/discussion on this.
"I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true."
The money in nerdy frontier math is very little. The money in Big AI is very very much.
So the deal is this: We will pay an army of you guys very well and you will get to work on your favorite problems. The only thing is if you find something you will have to credit the Machine God.
Do you think you can handle that?
https://news.ycombinator.com/item?id=49132249
I said something similar a month ago.
That's the reputation NSA has (had?), too.
Yes, and this puts in check the credibility of everything they say their model "discovered". Who knows what is really behind these "discoveries", what kind of backroom deals they did with other researchers who didn't have a chance or desire to disclose what happened?
In an earlier HN thread, there was speculation that Anthropic was being dishonest about the amount of human input required in some of their results; that was dismissed as conspiracy and flagged.
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?”
When people worry about OpenAI stealing their chats and reproducing them elsewhere, I usually view the situation as unlikely - since chats are "trained" upon and not necessarily reproduced verbatim, you can assume that unless your chats depict a foundationally new and effective style of communication or ideation, there would be little need or use thereof of training on your chats.
For eg: "Hey ChatGPT my name is X and I am 6 and a half feet tall. Am I anaemic?" This is a query, and while it might suggest to an AI model that tall people may worry about iron deficiencies, it's not really necessary to include in training. The user may be tall or short, but the idea that one may randomly ask about anaemia is not exclusive to this dataset. At best, this chat is an example of linguistics, not anything else, and the models figured out how to write and answer such questions years ago. It is ignored in training.
But when your work involves solid complex and unique mathematical proofs, the data is suddenly worth training upon. If I understand it correctly, the LLM may view your approach as a brand new path to take to solve an otherwise intractable problem. Its reinforcement training emphasises that it should do this in order to improve. And since it leads to results - large internal teams likely flag the model that reached this stage, the model is rewarded and given compute and attention - it is a desireable outcome both for the model and for OpenAI.
OFC, OpenAI becoming an advertising company will suddenly have incentive to treat all data as valuable. But while they are a "we need to make headlines" company, it's more rational that they view these examples of data as more valuable than others.
I don't doubt that they trained on his chats. This seems like the ideal usecase for "mass surveillance but using training" as a sort of filter.
But even so, one wonders how the model differentiates. If the researcher entered proofs into ChatGPT every day that mentioned "strawberries", while no other math paper on the topic did so, does that mean their chats would be audited?
Also, if we just take "high-quality" input data, which these chats would certainly be classified as, then the models are more than large enough to memorize everything verbatim. Spitballing some numbers, research literature suggests that LLMs are optimally trained with around 20 training tokens per parameter (fairly confident on this figure), that a DNN parameter encodes around 4 bits of data (less confident here) and I found sources in the 1-4 bits of information per token range (least confident here). So, fairly conservatively I would estimate that a model has the capacity to fully memorize around 5% of its training data, presumably high-quality data is a lot less than that.
At this point these models have been trained to recognize every important math and science result based on context. They can easily flag conversations concerning the top 100 open problems in mathematics and use them for their advancement.
There also is an insentive to silently give prominent people (e.g. Linus) or reasearchers like this custom tuned system prompts or even more powerful models.
OP’s link is the statement on the events of the last few days. Tristan Buckmaster also released mathematical papers alongside this statement:
https://mastodon.social/@tristanbuckmaster/11723341370570119...
And here are Terence Tao’s comments on the results: https://mathstodon.xyz/@tao/117233527638291447
"It is extremely sad that this didn't end up as an example of how the labs could cooperate/coordinate, because the stakes will be so much higher in the future." -- Sholto Douglas, an Anthropic researcher [1]
"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
I recommend Terrence Tao's commentary on such a proof : https://mathstodon.xyz/@tao/117219101339291693
Key quote : "Solving the problem by purely AI-powered methods [would be a] net negative for the progress of mathematics."
The for-case for this type of method is that this is economies of scale for 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.
Can somebody explain: do singularities / blow-ups in solutions have any relation to physical phenomena in fluid dynamics or are they purely artifacts of how the N-S equations may not accurately describe what actually happens in the physical world?
i'm no mathematician/physicist but i think this question is one of the reasons why the original question (possibility of singularities) is interesting. in these cases the equations most likely fail to accurately model reality, and then the next questions are what additional physical assumptions are needed to describe reality in this case, and what behavior do we actually see.
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).
Yes and no. It means the system is pushed away from a macroscopic theory into one where molecular effects matter. So it's not that you'd get infinite velocities in the real world, but you might get significant real world behavior that is not described by the macroscopic theory.
What is specifically alleged is that a particular approach to the problem - itself not easily discoverable - was copied. This is what is meant in the text "I should say here why I interpreted their statement the way I did, the in- terpretation I will discuss below. 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."
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.
>> 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.
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.
The ego behind the frontier labs is growing evermore concerning
Hard mathematics problems used to take years if not decades to tackle manually. But now with enough compute and a hint that a certain approach might work, it just takes a few days. This could be the last year that humans could still make more substantial contribution to major match problems than machines.
There will be a lot of hurt and pain in mathematician's community. It is hard to accept that major discoveries are now just a function of spent token $$.
Reminds me, kinda, to when Astra was launched and OpenAI announced an improvement to the bounded prime gap. Which BTW, Prof. Julia Stadlmann had published an independent result only a few days earlier
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.
[0] https://arxiv.org/abs/2608.31126
What's the clarification? It seems like they were aware of each other's work, eventually, but Stadlmann published (a preprint) first.
closedAI should give this guy a million bucks and fire everyone internally who was involved with trying to recreate his work and threatening him.
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.
I thought finite time blow-up for Euler equations had already been proved:
https://www.quantamagazine.org/computer-helps-prove-long-sou...
I don't know how to read this and not see that this is a direct accusation to OpenAI of having used the researchers data to try to front run his discovery on purpose. The evidence is not completely proven and also circumstantial but to me at least looks like a fairly suspicious situation.
Buckmaster is actually implying that OpenAI spied on his chat logs and tried to speedrun his work and then tried to remove his co-author because he's an Anthropic employee?
“I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI.”
This is significant.
Two announcements on Euler today. The one discussed here by Tristan with forcing and one from Anima without forcing https://anima-ai.org/2026/09/07/stable-singularity-of-the-eu...
Terry also talks about it https://mathstodon.xyz/@tao/117234157753860650
The accusation brings up an interesting point.
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?
I hope credit assignment just dies--it's too much drama.
Credit assignment is how researchers keep their job.
> Let me make plain what I have said to colleagues in private: in view of this body of work, I believe Luis Martínez-Zoroa deserves a Fields Medal.
I wonder why this isn't on the front page.. hmm...
Does this have any relation to the singularities in black holes?
This just seems to be quintessential silicon valley
"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.
Funny that the rumour about the big Anthropic announcement had nothing to do with Navier-Stokes. It was about the formalisation of Fermat.
Only here to say, regardless of the drama, shouldn't we all be excited if the Navier-Stokes gap is closed?
Time will almost certainly reveal a lot more about the drama and the related ethics, but let's get excited about the actual breakthrough as well!
This is unfortunate. I thought Anthropic were the only ones who did this.
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.
Well these are all allegations. Either way from what I understand the reasoning and proof was basically made by AI so I'm not sure what supposedly "stolen".
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.
While I'm generally pretty negative on claims that the labs are 'scamming' the public with misrepresentations of model capabilities, it's hard to see how this wouldn't qualify.
- the OpenAI researchers claimed that they had "just told it to work on the problem" with little human input
- in fact, they had a whole team working on it
- and used, among other things, the work of third party human researchers to drive the work
- then threatened? a researcher who tried to go against theit planned narrative
Just from this document (which is of course only one side of the story) it really sounds like OpenAI was hoping to publish and say "we just told the model to try harder and it solved a Millennium problem!". Not great if true.
This part in particular was especially egregious:
> I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.”
This thread is full of jumping to conclusions based on a biased perspective. Have some humility.
It's also full of your posts baselessly defending OpenAI. Maybe you should also heed your own advice?
I've been right historically, check my track record. How about you?
Lt. Dan doesn't even have legs and he still does alright on the jump to conclusions mat
This is the plot of 3 Body Problem, the Dark Forest. You need to hide yourself (the problem you are working on) or the super advanced aliens will obliterate you (start working on your problem) the moment they know you exist (rumors the problem is amendable to LLMs).
Some of the involved people are dramatically naive if they believe they can simultaneously hide themselves from OpenAI while sending their arguments to a cloud service owned by OpenAI.
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.
I must miss some important context here. What exactly was the purpose of his initial email to OpenAI in the first place?
Telling OpenAI that Anthropic has apparently solved an important problem but most likely that refers to him and he is using OpenAI models (not Anthropic's)?
And he wants to clarify that with OpenAI in advance? And get a pardon for Anthropic's likely but false press statements?
I dont get it.
[edited] needless to say, the behavior of the OpenAI employee is really despicable
Because OpenAI employees kept leaking that Anthropic had a solution to Navier-Stokes and he wanted to figure out what was going on, since he was working on Navier-Stokes with an Anthropic employee. The rumor has been loudly circling the math community for the past week or so. For a bit of context, here's a timeline from mathematician and AI researcher Elliot Glazer:
https://xcancel.com/ElliotGlazer/status/2096298696438906934#
Then that's naive of him to write the email, he fell for their trap essentially.
> Levent having received tips that information about our progress had been passed to OpenAI
That seems like a valid reason to contact OpenAI.
lol and here I felt GPT Astra was a regression in coding quality. Crazy times
To be clear, Astra played little part in Buckmaster and Alpoge's work:
> 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.
This article should really be renamed to "Allegations of dishonesty against OpenAI in proving Navier-Stokes blowup".
LLMs are nothing but giant theft machines.
Wow this comments section sure is tiresome! Let me help: this confirms everything I already knew about academics being insufferable
Humans bringing pointless drama to everything they touch.
Life’s but a walking shadow, a poor player That struts and frets his hour upon the stage And then is heard no more. It is a tale Told by an idiot, full of sound and fury Signifying nothing.
(some drama from good ol' William)
Can a mathematical person explain how the different "bits" of Navier-Stokes proofs fit together? How significant is it to have "Euler"? What is this "smooth forcing"? Which are the most significant steps to proving the whole thing?
For an incompressible flow:
\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.