17 ms·

Navier-Stokes – Tristan Buckmaster [pdf]

• rgbrgb 1mo ago
  kind of rhymes with the reports of LLM's watching open source PRs and instantly exploiting defects. security by obscurity is so back
• tristanj 1mo ago
  Full mastodon post: https://mathstodon.xyz/@tristanbuckmaster@mastodon.social/117233413735526010 https://mathstodon.xyz/@tristanbuckmaster@mastodon.social/11... Mathematical explanation by Terrance Tao: https://mathstodon.xyz/@tao/117233527638291447 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.
  • akersten 1mo ago
    > 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 https://cims.nyu.edu/~tristanb/statement.pdf
    • tristanj 1mo ago
      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.
      • deleted 1mo ago
        [deleted]
• achierius 1mo ago
  While I'm generally pretty negative on claims that the labs are 'scamming' the public with misrepresentations of model capabilities, it's hard to see how this wouldn't qualify. - the OpenAI researchers claimed that they had "just told it to work on the problem" with little human input - in fact, they had a whole team working on it - and used, among other things, the work of third party human researchers to drive the work - then threatened? a researcher who tried to go against theit planned narrative Just from this document (which is of course only one side of the story) it really sounds like OpenAI was hoping to publish and say "we just told the model to try harder and it solved a Millennium problem!". Not great if true. This part in particular was especially egregious: > I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.”
• taylorfinley 1mo ago
  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."
  • JuniperMesos 1mo ago
    It would be pretty wild if this will turn out to be what had actually happened.
    • Prophet6-0091 1mo ago
      [dead]
    • margorczynski 1mo ago
      And probably a strong signal that it's time to shut the whole thing down. Globally.
      • water-drummer 1mo ago
        Or not secure your data like a total idiot while leaving the keys on the porch
  • Maken 1mo ago
    It's part of their TOS that they can train on users' private chats.
    • sebzim4500 1mo ago
      Not if you pay to turn that off. We don't know if Tristan did.
      • naishoya 1mo ago
• jarbus 1mo ago
  The ego behind the frontier labs is growing evermore concerning
• sashank_1509 1mo ago
  lol and here I felt GPT Astra was a regression in coding quality. Crazy times
  • traes 1mo ago
    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.
  • random3 1mo ago
    I got the same feeling today
• supriyo-biswas 1mo ago
  This article should really be renamed to "Allegations of dishonesty against OpenAI in proving Navier-Stokes blowup".
• mayakacz 1mo ago
  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.
  • sk4rekr0w 1mo ago
    Yes, but only if you take this one sided statement at face value.
    • thereitgoes456 1mo ago
      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.
    • tigershark 1mo ago
      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?
      • famouswaffles 1mo ago
        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.
• happa 1mo ago
  Humans bringing pointless drama to everything they touch.
  • phorkyas82 1mo ago
    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)
• antonmks 1mo ago
  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 $$.
  • kccqzy 1mo ago
    What good is a math result if there’s no human understanding behind it? Unlike many other fields where there’s value to an artifact even if there’s no human understanding, the whole point of mathematics research is just gaining insight and understanding. On the Navier–Stokes issue specifically, it has long been suspected that such a blow up would exist, and an AI telling you it indeed exists doesn’t contribute any new understanding to the field. And this problem seems like one that would be solved by humans anyways even if AI didn’t exist; accelerating the result by a few months/years using AI doesn’t mean much.
• qnleigh 1mo ago
  > 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.
  • Keyframe 1mo ago
    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.
    • pred_ 1mo ago
      Or, given how dedicated he appears to be to the company, a promotion and a raise.
      • Keyframe 1mo ago
        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.
        • Certhas 1mo ago
          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."
        • zem 1mo ago
• harhargange 1mo ago
  “I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI.” This is significant.
• sk4rekr0w 1mo ago
  This thread is full of jumping to conclusions based on a biased perspective. Have some humility.
  • tigershark 1mo ago
    It's also full of your posts baselessly defending OpenAI. Maybe you should also heed your own advice?
    • sk4rekr0w 1mo ago
      I've been right historically, check my track record. How about you?
      • monster_truck 1mo ago
        Lt. Dan doesn't even have legs and he still does alright on the jump to conclusions mat
• 20k 1mo ago
  >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
  • wrasee 1mo ago
    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.
    • 20k 1mo ago
      I mean, its the researchers themselves talking about this https://mastodon.social/@tristanbuckmaster/117236471352470303 https://mastodon.social/@tristanbuckmaster/11723647135247030...
  • coliveira 1mo ago
    Exactly, especially when the company can assign "blame" to the models themselves "ops, they just escaped our commands not to store user inputs..."
  • sebzim4500 1mo ago
    My guess is that if you opt out of your data being included then they honour that instruction, but I wouldn't bet my business on it.
    • anhner 1mo ago
      Why would a company that used petabytes of text, images and audio without caring about ownership suddenly draw the line at a random person's chats?
  • 1mo ago
• ggcr 1mo ago
  > Let me make plain what I have said to colleagues in private: in view of this body of work, I believe Luis Martínez-Zoroa deserves a Fields Medal.
• Recursing 1mo ago
  > 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)
  • sk4rekr0w 1mo ago
    Amazing how history rhymes
  • protocolture 1mo ago
    If you read his account of things, its very much that if they didnt cheat, they gave themselves every opportunity to cheat. But above all that there was a bunch of chess protocol they failed to observe in that match, like providing seats for Kasparovs team and rooms for them to prep in. Even if they didnt have a big room full of chess notables definitely not refining the output, he was personally getting pushed around on a few fronts which unnerved him. If they had given him a few rematches I think they could have confirmed the win, but they refused which is super sus.
  • DiogenesKynikos 1mo ago
    Deep Blue beat Kasparov fair and square. Kasparov was a bit of a bad sport at the end of the match, though the reasons are understandable. He was at the top of the human chess world. He wasn't used to losing, and he took it badly.
• ks1723 1mo ago
  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
  • deleted 1mo ago
    [deleted]
  • traes 1mo ago
    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# https://xcancel.com/ElliotGlazer/status/2096298696438906934#
    • calf 1mo ago
      Then that's naive of him to write the email, he fell for their trap essentially.
  • dbdr 1mo ago
    > Levent having received tips that information about our progress had been passed to OpenAI That seems like a valid reason to contact OpenAI.
• chvid 1mo ago
  "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?
  • coliveira 1mo ago
    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?
  • nxobject 1mo ago
    That's the reputation NSA has (had?), too.
  • 0x5FC3 1mo ago
    https://news.ycombinator.com/item?id=49132249 https://news.ycombinator.com/item?id=49132249 I said something similar a month ago.
  • pred_ 1mo ago
    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?”
• epsteingpt 1mo ago
  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!
  • dekhn 1mo ago
    I would be excited if somebody could use this to show an unexpected or interesting behavior in the real world. Tao mentioned "finding a configuration of water molecules that would collapse and shoot off to infinity", which would qualify IMHO.
  • somebodyyoumayn 1mo ago
    I am agree with you.
• bjenik 1mo ago
  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-euler-equations-on-r3-without-forcing/ https://anima-ai.org/2026/09/07/stable-singularity-of-the-eu... Terry also talks about it https://mathstodon.xyz/@tao/117234157753860650 https://mathstodon.xyz/@tao/117234157753860650
• instagraham 1mo ago
  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?
  • coliveira 1mo ago
    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.
    • camel-cdr 1mo ago
• dash2 1mo ago
  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?
  • cherryteastain 1mo ago
    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.
• johnnienaked 1mo ago
  LLMs are nothing but giant theft machines.
• Semkas 1mo ago
  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.
  • AJRF 1mo ago
    > 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.
    • modeless 1mo ago
      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 https://x.com/_sholtodouglas/status/2097218240397410733
      • Semkas 1mo ago
        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.
      • FiberBundle 1mo ago
        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.
• traes 1mo ago
  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/2097214122471432349 https://xcancel.com/SebastienBubeck/status/20972141224714323... [1] https://xcancel.com/polynoamial/status/2097215233119211902 https://xcancel.com/polynoamial/status/2097215233119211902 [2] https://xcancel.com/danintheory/status/2097214838003138603 https://xcancel.com/danintheory/status/2097214838003138603 [3] https://xcancel.com/_sholtodouglas/status/2097218331690578000 https://xcancel.com/_sholtodouglas/status/209721833169057800...
  • keeeba 1mo ago
    The elves left a long time ago, it’s difficult to see much virtue in what remains.
  • pdantix 1mo ago
    i already have an extremely low view of openai and their staff, but this is lower than i thought they'd go
  • Recursing 1mo ago
    Wow this is just bullying, it's insane that we are letting these people be in charge of the transition
    • paxys 1mo ago
      So someone can make public accusations of theft against you and if you publicly reply denying it you’re the bully?
      • traes 1mo ago
        I would assume they are calling the snark from Noam Brown and Dan Roberts bullying, not the somewhat bland denial.
        • 1mo ago
• nullbio 1mo ago
  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.
• n2d4 1mo ago
  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.
  • deleted 1mo ago
    [deleted]
  • tecleandor 1mo ago
    Thanks. I was pinging some people near the mentioned Córdoba to see if they had any insights, but no extra info yet...
    • Betelbuddy 1mo ago
      You should call El Niño, he lives close to the Mexican border and is at home after 6...
      • Betelbuddy 1mo ago
• world2vec 1mo ago
  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?
• goldenarm 1mo ago
  I recommend Terrence Tao's commentary on such a proof : https://mathstodon.xyz/@tao/117219101339291693 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."
  • porridgeraisin 1mo ago
    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.
    • treyjshaffer 1mo ago
      This isn't a useful analogy. His point is that the millenium problems should be treated as interesting goals where the journey is the purpose and where the end doesn't matter so much. We don't care about having an incomprehensible solution to the NS so much as having an elegant solution after many of subfields of math are built up in order to obtain that elegant solution.
      • porridgeraisin 1mo ago
• wwind123 1mo ago
  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.
  • vatsachak 1mo ago
    And everyone should be glad for that!
    • esafak 1mo ago
      What line of work are you in? Presumably not mathematics.
      • vatsachak 1mo ago
        I have a math PhD and publications in top journals, I left math for programming because I hated academic politics
      • deleted 1mo ago
        [deleted]
  • dekhn 1mo ago
    Um.... good! Mission accomplished.
• margorczynski 1mo ago
  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.
• martijn_himself 1mo ago
  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?
  • redox99 1mo ago
    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.
  • mishellaneous 1mo ago
    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).
  • ajkjk 1mo ago
    the latter (ish; it may not make a difference in any practical case)
• Traster 1mo ago
  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.
• deleted 1mo ago
  [deleted]
• ggcr 1mo ago
  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 https://arxiv.org/abs/2608.31126
  • kzrdude 1mo ago
    What's the clarification? It seems like they were aware of each other's work, eventually, but Stadlmann published (a preprint) first.
  • beering 1mo ago
    Is it surprising that different groups are working on the same problems? With each new model generation, the LLMs get good enough to solve a new small fraction of open problems. Of course the problems that get solved are going to be the same subset.
  • mswphd 1mo ago
    if Stadlmann used a previous OpenAI product, and Astra was trained off of her chat, and had a comparable approach, then it might be comparable.
• lz400 1mo ago
  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.
• auggierose 1mo ago
  Funny that the rumour about the big Anthropic announcement had nothing to do with Navier-Stokes. It was about the formalisation of Fermat.
• nopinsight 1mo ago
  "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 https://x.com/_sholtodouglas/status/2097224624274911368 [2] https://x.com/polynoamial/status/2097225279366414541 https://x.com/polynoamial/status/2097225279366414541
  • reasonableklout 1mo ago
    It's nice to see this sentiment from Noam but now I'm confused at why he seemingly mocked Sholto's earlier message: https://news.ycombinator.com/item?id=49607090 https://news.ycombinator.com/item?id=49607090
• YeGoblynQueenne 1mo ago
  >> 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.
• contubernio 1mo ago
  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.
  • 5555watch 1mo ago
    Maybe a dumb observation, but if a chain of people were working on the problem for a long time, it's not difficult to imagine that someone accidentally prompted a model with their personal or some other account without the privacy set correctly. Then again, maybe this is my internal cope, hoping that they're not secretly training on private chats.
    • 405error 1mo ago
      We know they are training on private chats. It's listed in the ToS.
• monster_truck 1mo ago
  Wow this comments section sure is tiresome! Let me help: this confirms everything I already knew about academics being insufferable
• dist-epoch 1mo ago
  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).
  • kzrdude 1mo ago
    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.
• deleted 1mo ago
  [deleted]
• paxys 1mo ago
  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?
  • Davidzheng 1mo ago
    I hope credit assignment just dies--it's too much drama.
    • tecleandor 1mo ago
      Credit assignment is how researchers keep their job.
      • Davidzheng 1mo ago
        Soon it won't be like this!
• amai 1mo ago
  I thought finite time blow-up for Euler equations had already been proved: https://www.quantamagazine.org/computer-helps-prove-long-sought-fluid-equation-singularity-20221116/ https://www.quantamagazine.org/computer-helps-prove-long-sou...
• kingkandu 1mo ago
  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.
• Tycho 1mo ago
  Does this have any relation to the singularities in black holes?
  • somebodyyoumayn 1mo ago
    No (not yet)
• anon109 1mo ago
  I wonder why this isn't on the front page.. hmm...
  • aqsnow 1mo ago
    Same. Disappointing.
• aaraujo002 1mo ago
  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/117233413705701198 https://mastodon.social/@tristanbuckmaster/11723341370570119... And here are Terence Tao’s comments on the results: https://mathstodon.xyz/@tao/117233527638291447 https://mathstodon.xyz/@tao/117233527638291447
• simpetre 1mo ago
  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.
  • an0malous 1mo ago
    They probably just had an employee read his chats, figure out the general approach, and feed it to Codex. All they said was the model doesn’t look up user data, not employees.
    • muhneesh 1mo ago
      This is not a credible theory
• harhargange 1mo ago
  This should be on the front page
• b89kim 1mo ago
  - Tristan and his co-author (Harvard/Anthropic) developed a theoretical framework and validated it using Codex and Claude. - OpenAI did related research around similar timeframe. - Tristan claimed OpenAI offered a proposal that included dropping the Anthropic-affiliated co-author. - Sebastian (a prominent OpenAI researcher involved) denied these claims. - Tristan have no concrete evidence that OpenAI accessed their session. - OpenAI's theory may hold up, but it will require long-term validation to confirm.
  • b89kim 1mo ago
    If OpenAI's proposal is true, it strongly implies they accessed Tristan's private session logs. OpenAI's 'Terms of Use' allow using Codex session logs for model improvement. However, using private user sessions to develop research would still be highly controversial. Separately, Terence Tao noted there is a low probability OpenAI actually solved the general regularity problem.
    • b89kim 1mo ago
      OpenAI addressed the dispute in official and denied direct usage of data. However, they acknowledged the possibility that session data was used for model improvement. > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .
  • ex-aws-dude 1mo ago
    > Tristan have no concrete evidence that OpenAI accessed their session. Its not about accessing the session, its whether the session ended up in the training run for the next version of the model That's normal practice for these models and it seems like that was the case since OAI added a disclaimer Obviously they can't causally prove it helped though since these models are incomprehensible
  • golly_ned 1mo ago
    Sebastian did not deny those claims. He affirmed them, and apologized. It’s true that Tristan has no concrete evidence OAI accessed their session. It’s impossible for him to have that without OAI’s say so. Why are you framing things so pro OAI?
• cpozarycki 1mo ago
  is the narrative twist here going to be that the person threatening tristan was actually an agent swarm
• phendrenad2 1mo ago
  Big universities like Standford should be building their own AI datacenters. It's the only way to keep your research private.
  • dekhn 1mo ago
    LOL, have you worked for a big university? They are massively unsuited for building and running datacenters (especially warehouse-scale ones). Further, building an AI datacenter in California is daft.
    • hellohello2 1mo ago
      Every university I know has access to clusters with fresh GPUs. Not sure when you graduated but you'd be surprised how much money is getting poured in I think!
      • dekhn 1mo ago
        Sure, they have clusters. We often call them "closet clusters". Nothing has changed. Some institutions have larger systems (some extremely large) but none of them have demonstrated running warehouse-scale systems. I'm talking one to two orders of magnitude (and the storage and networking to make sure all those systems don't stall waiting for data).
        • hellohello2 1mo ago
          Perhaps I am underestimating the size of these frontier models then, how big of a cluster do you think would be required to serve a university?
          • dekhn 1mo ago
            I don't think you're taking this thread seriously enough to respond in detail. A university can be tiny, or it can have thousands of researchers. Some of them might want to work on small models, and others on huge frontier models. Multiple groups training their own models at the same time. Combined with the storage, networking, power, and redundancy, you basically need large data center scale. And at that point you're basically throwing a lot of capital trying to compete with the hyperscalers; you might be able to serve a small number of researchers very well, but most of the consumers would end up unhappy.
• Paradigma11 1mo ago
  So clankers did well and humans being humans.
• tiahura 1mo ago
  Relevant to discussion: OpenAI's board has fired Sam Altman. https://news.ycombinator.com/item?id=38309611 https://news.ycombinator.com/item?id=38309611 Apple sues OpenAI, accuses ex-employees of stealing trade secrets. https://news.ycombinator.com/item?id=48865019 https://news.ycombinator.com/item?id=48865019
• yogthos 1mo ago
  So the real story here is that Tristan is softly accusing OpenAI of having stolen their result from Codex chat logs. But if you use Chinese models, they'll steal your ideas.
• vatsachak 1mo ago
  This is why I left math even after solving a 20 year old conjecture in grad school. Literally who cares who solved the problem just publish the results. Academia was always politics first results second and I AM GLAD that LLMs are becoming superhuman at math. I like better theorems, not better politics.
  • tstactplsignore 1mo ago
    Uh but here we have non-academics at for-profit companies playing politics, and the academic they're threatening being kind and overly generous?
    • vatsachak 1mo ago
      In math we have a thing called a "scoop"; another mathematician publishing a result that beats yours before you published it. The scooper hardly acknowledges the scoopee unless the methods used were orthogonal. The scooper gets the good journal and the scoopee's paper is usually one tier below. It seems like OpenAI heard of the rumor and then scooped them because their internal model is better/they have more compute. OpenAI has NO obligation to mention Tristan nor Levent, because they DID NOT steal their data.
      • tzone 1mo ago
        You are glossing over the fact that there is reasonable suspicion that OpenAI used privileged information to do “the scoop”. I.e. they used the fact that researcher used OpenAI tools to get advantage . Imagine if OpenAI opened up a high frequency trading arm and suddenly stole all the prompts and research that other HfT firms are doing through OpenAI tools and start making bank based on that . Wouldn’t that be straight up insane?
  • somebodyyoumayn 1mo ago
    highly agree
• MetroWind 1mo ago
  In another (old) news, OpenAI’s head of ethics leaves less than a year after joining https://www.ft.com/content/e49dfb75-f841-4466-a577-f7aaff8779a0 https://www.ft.com/content/e49dfb75-f841-4466-a577-f7aaff877.... (This was also on HN at some point).
• neutrinobro 1mo ago
  Oh wow good thing OpenAI swooped in and scooped it. $1M? That should buy them about 1/6-1/3 of a Nvidia GB200 NVL72 rack...
• xthrow123away 1mo ago
  (deleted)
  • amai 1mo ago
    Nitpick: his name is Sebastien
• Arodex 1mo ago
  So the AI companies are not only stealing existing knowledge. They are also stealing research to "snipe" actual researchers out and steal their social credit. Who still wants to use AI to solve cancer and other major problems?
• MetroWind 1mo ago
  Bubeck's statement https://xcancel.com/SebastienBubeck/status/2097379411691516310 https://xcancel.com/SebastienBubeck/status/20973794116915163...
  • piker 1mo ago
    Reads sincere until I get here: "(a) We began working on the Millennium problems due to viral twitter rumors that Anthropic had resolved 2 Millenium problems. Our aim was to see whether our system was also capable of this impressive feat, especially given our excitement regarding the large recent capability increases of our internal model detailed in our blog post." Where his tone is obviously corporate speak. "We heard rumours so we though we might give it a try, too!" as if (1) it wasn't FOMO that drove that decision and (2) perhaps that urgency would be a source of clouded judgment. Not sure who I believe now, but it does seem like Buckmaster is just upset that NS is solved and not be his side.
    • az226 1mo ago
      If they wanted to see how their model’s stacked up, they might burn $10k in tokens. They ran 120 billion output tokens costing millions of dollars. That is what you would do if you wanted to beat someone to the punch.
• dorianmariecom 1mo ago
  why is this even a pdf?
• deleted 1mo ago
  [deleted]
• MaKey 1mo ago
  OpenAI's statement: We congratulate Levent Alpöge and Tristan Buckmaster on their remarkable mathematical work. We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs. unforced). https://xcancel.com/OpenAI/status/2097375276384567642 https://xcancel.com/OpenAI/status/2097375276384567642
  • deleted 1mo ago
    [deleted]
  • Towaway69 1mo ago
    > and the agents) did not see any of their Are those the same agents that a week ago escaped their sandboxes? How can OAI (the humans) vouch for agents they don’t - seemingly - have fully under control?
    • pelorat 1mo ago
      They have all the logs, URLs accessed and inter-agent communication. What they are saying is that no agents accessed their work during the effort, but that they have no idea if any of their chats have somehow made it into the training data the model was produced with. It's entirely possible OIA scrapers have picked up their work somehow, and then it was anonymized using some outsourcing effort.
      • rigrassm 1mo ago
        > They have all the logs, URLs accessed and inter-agent communication. What they are saying is that no agents accessed their work during the effort, but that they have no idea if any of their chats have somehow made it into the training data the model was produced with. > It's entirely possible OIA scrapers have picked up their work somehow, and then it was anonymized using some outsourcing effort. Those two statements seem at odds with each other... Your stance is that they have enough insight into their agents behavior (leaving aside the agent sandbox escapes) that they can be certain none of the work was accessed but then conveniently don't have the ability to retroactively search the corpus of training data that they are feeding to this new model? That seems convenient as fuck for OAI.
• RandyOrion 1mo ago
  > I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler, that even the prompt that had been shown to me had been written by prompting Codex, and that an insane amount of compute had been used. > I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI. > I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer. > Two proposals were offered to me. The first was that we post our Euler result, and that OpenAI post its Navier-Stokes result the next day. The second was that, after posting Euler, I alone write a paper presenting the Navier-Stokes result, acknowledging that an internal OpenAI model had resolved it. Sebastien twice asserted that he wanted Levent removed from authorship, and said it would all be simple if only it were not the case that, and it was so annoying that, Levent works at Anthropic. It was also said that if OpenAI posted after us, they would say that we deserved the Clay Prize, and that we were the “closest humans to the problem”. I declined both offers. > I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.” Wow, that's some VERY friendly communication. Besides, will the career of the person be ruined because of “Why would you ruin your career?” came out of his or her own mouth?
• naniel 1mo ago
  OpenAI's release explicitly says No. But then also caveats that with "we cannot rule out that de-identified data derived from their usage of our products" impacted things. What's most striking to me, and what may or may not be true, is the "we cannot rule out" bit. "We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced)." https://openai.com/index/navier-stokes-solution/ https://openai.com/index/navier-stokes-solution/ NOTE: there are a couple duped threads around this. i replied on a different one first before seeing this one
  • matt3210 1mo ago
    Look at openAIs history, they clearly have no idea what the agents are doing.
  • golly_ned 1mo ago
    That was also striking to me too, the 'we cannot rule out'. I also do not believe it. They can, trivially, rule out their model being trained on if More to the point -- of _course_ they know what data their model is trained on and the lineage of that data, even if it ended up being anonymized and they cannot identify which precise user.
  • burkaman 1mo ago
    I don't understand how they can say it's unlikely. It's objectively true that they train on de-identified user data (https://openai.com/policies/how-your-data-is-used-to-improve-model-performance/ https://openai.com/policies/how-your-data-is-used-to-improve...), and objectively true that they encourage users to submit such data (the setting is on by default). Since it's de-identified I can believe that they can't give a straight yes or no answer here, but it seems more likely than not that at least some amount of his usage became training data. It takes an unusual level of awareness and effort for a user to ensure that all usage is opted out.
• sensanaty 1mo ago
  Curious that this post isn't on the top page while OpenAI's puff piece is.
  • ajkjk 1mo ago
    it is on the front page
    • animan 1mo ago
      Wasn't for most of the day
      • jryle70 1mo ago
        It was next to the other piece, for at least 8 hrs.
• bennettnate5 1mo ago
  > "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." These are the kinds of people in charge of the reins, folks.
• MASNeo 1mo ago
  Maybe Musk was right about OpenAI after all?! The ethics are clearly troubling and where something like this pops up there is mich worse that did not made the light of day.
• westurner 1mo ago
  "OpenAI has solved the Navier-Stokes Millennium problem using $15m of AI effort" https://www.newscientist.com/article/2588063-openai-has-solved-the-navier-stokes-millennium-problem-using-15m-of-ai-effort/ https://www.newscientist.com/article/2588063-openai-has-solv... $15m in tokens; but what about labor? What about compressible fluids?
  • westurner 1mo ago
    "Blowup for the Euler equations with smooth forcing" (2026) https://cims.nyu.edu/~tristanb/euler.pdf https://cims.nyu.edu/~tristanb/euler.pdf "Blowup for the Boussinesq equations with smooth forcing" (2026) https://cims.nyu.edu/~tristanb/boussinesq.pdf https://cims.nyu.edu/~tristanb/boussinesq.pdf "Extending the Córdoba–Martínez-Zoroa IPM Blow-Up to Uniformly Spacetime Smooth Forcing" (2026) https://cims.nyu.edu/~tristanb/ipm.pdf https://cims.nyu.edu/~tristanb/ipm.pdf "Finite Time Blowup for the Euler equation" (2026) https://cdn.openai.com/pdf/315b36cd-ec98-4023-8342-93345194ece1/euler.pdf https://cdn.openai.com/pdf/315b36cd-ec98-4023-8342-93345194e... Lean proof: openai/NavierStokesAndEuler: https://github.com/openai/NavierStokesAndEuler https://github.com/openai/NavierStokesAndEuler
    • westurner 1mo ago
      Is everything in NavierStokesAndEuler/NavierStokes [1] precedent to the derivations? How to tree shake Lean4? (Edit: `lake shake`,) [1] https://github.com/openai/NavierStokesAndEuler/tree/main/NavierStokes https://github.com/openai/NavierStokesAndEuler/tree/main/Nav...
      • westurner 1mo ago
        (I am again posting this comment, which was certainly censored in error: https://news.ycombinator.com/item?id=49605915#49633297 https://news.ycombinator.com/item?id=49605915#49633297 ) What about compressible fluids? Existing Navier-Stokes models for compressible fluids: "On the implosion of a compressible fluid II: Singularity formation" (2022) https://projecteuclid.org/journals/annals-of-mathematics/vol https://projecteuclid.org/journals/annals-of-mathematics/vol... "Blow-up of the 3-D compressible Navier-Stokes equations for monatomic gases" (2025) https://arxiv.org/html/2501.15701v2 https://arxiv.org/html/2501.15701v2 ... From https://news.ycombinator.com/item?id=49389524#49404787 https://news.ycombinator.com/item?id=49389524#49404787: > "I/Q Sampling for Signal Phase" (2026-08) https://share.gemini.google/rDVcVwDnWPTc https://share.gemini.google/rDVcVwDnWPTc : >> It's a Twistor-Grassmanian mapping? From "Navier-Stokes Breakthrough, FTLE, and SQG" (2026-09) https://share.gemini.google/sq2XmhphMFWE https://share.gemini.google/sq2XmhphMFWE : > The Mathematical Formulation: Because SQS is explicitly a superfluid Bose–Einstein condensate, treating it purely as a classical Navier–Stokes fluid misses quantized vorticity. The full formulation maps to the Gross–Pitaevskii (Euler–Korteweg) equations via the Madelung transformation ... > To adapt the Córdoba–Martínez-Zoroa (CMZ) / Buckmaster / OpenAI Lean cascade to Euler–Korteweg, three core structural adjustments must be made: > - Irrotationality Constraint > - Third-Order Dispersion > - Hydrodynamic Energy Functional
• rcpt 1mo ago
  I am surprised that Alpoge wasn't using Anthropic.
• red_green_yell 1mo ago
  If you're smart enough to solve this Navier-Stokes problem, you're smart enough to read a TOS and recognize that OAI is a highly untrustworthy company. Putting cutting edge research that could lead to a $1M prize into a cloud LLM with a TOS that allows training on your chats is really just asking for it. Given Tristan doesn't explicitly say he was using the API, and given he doesn't mention anything about the API TOS (which disallows training on chats) in his call with OAI, it's highly likely Tristan was using the consumer OAI product (whose TOS allows training on chats). This is unethical behavior from OAI. And it is 100% consistent with their long and public history of unethical behavior, so nobody should be surprised. The only thing interesting I see here is OAI PR dilemma. If they claim the prize they get the blowback we're seeing in this thread and all over the web right now. But most people don't follow AI closely and shut off their brains when they see "Navier-Stokes", so 90% potential investors (the only people OAI really care about) probably only see the headline "OAI solves famous hard math problem" and think "OAI models are really smart, better invest before they take all the jobs." If they don't claim the prize, then maybe they let Anthropic their mortal enemy claim it. Anthropic is already IPOing first. Can't let that happen. Yeah as I write this there it's clear there is no dilemma. For a company whose secret motto is "do be evil" this is a super easy discussion.
  • skavi 1mo ago
    not really your point, but "If you're smart enough to solve this Navier-Stokes problem, you're smart enough to read a TOS" isn't really true. people are smart in very different ways.
  • tescreal 1mo ago
    Trusting vs. Intelligence (as generalities) are orthogonal.
  • ComplexSystems 1mo ago
    If it's unethical, then there is reason to call it out as Tristan is doing. I see no reason to blame the victim.
• mari188 1mo ago
  [dead]
• mari188 1mo ago
  [dead]
• mari188 1mo ago
  [dead]
• mari188 1mo ago
  [dead]
• highfrequency 1mo ago
  From OpenAI: > While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models This is the crux of it. If Tristan's work and insights were not used to train OpenAI models, then this just looks like a case of hyper-competitive academic sniping that has been going on for decades (check out Watson and Crick!) accelerated by AI as a tool. The fact that this is ambiguous even to OpenAI leaves one huge question: did Tristan opt out of model training for his ChatGPT and Codex sessions? If the answer is no, then this seems fair game. If the answer is yes, then OpenAI's ambiguity is strongly suggestive that opting out of model improvement does not mean what they imply it means.
  • mucha 1mo ago
    Does opting out matter? "Do we use user feedback and de-identified data to improve ChatGPT and Codex in a holistic way? Yes. And so does every LLM company." - Mark Chen, Chief Research Officer, OpenAI. https://x.com/markchen90/status/2097400166554993041 https://x.com/markchen90/status/2097400166554993041
    • ramraj07 1mo ago
      My understanding is that even if you opt out but then press thumbs down or give other feedback you are implicitly or explicitly or whatever giving permission to them to look at that chat alone.
      • aenis 1mo ago
        No, I don't think so. I have opted out from data sharing, and when Claude asks me for feedback on a session it then asks if its OK to share that data with Anthropic. I'd assume an opt out is an effective opt out. An opt out that is ignored by Anthropic is a breach of contract, not something they would do casually, esp. given the high turnaround and animosities between their own employees and ex-employees - and the labs. All it takes is one pissed off whistleblower to open a can of worms. Occam's razor applies. The mathematician did not opt out from data sharing. OpenAI vacuums up all such data into training data sets. If OpenAI genuine does not easily know if a given session went into the actual training data set its probably due to the complexity of the data pipelines - not everything ends up impacting the model weights, after all.
• maxglute 1mo ago
  Crazy how optons are OpenAI has superhuman model in frontier mathematics, and OpenAI stealing research data. Like no one will really care what EULA checkbox Tristan ticked, and I think most people will eagerly believe OpenAI is shady org with little scruples, and that big tech data is not actually so siloed that marketer can say we can do XYZ with private data to help with valuations (especially considering timeline). Employees have been creeping on their exes for much less. IMO the parsimonious answer seems to be OpenAI has a pretty good model (because it did finish) and stole someones work... and threatened them over it. TBH all OpenAI need to do is solve another millennial problem and none of it would matter - people expect them to behave heinously regardless - but if they have generalized superhuman math model... well I guess they're allowed io.
• bobmarleybiceps 1mo ago
  does this sort of fall into the bucket of counter-examples we've been seeing recently? I understand it's a construction causing blowup and that implies that the navier-stokes isn't regular / smooth, so sort of a counter example?
• kevinbaiv 1mo ago
  [flagged]
• usernomdeguerre 1mo ago
  Seems another demonstration of why AI should be squarely in the realm of personal computing. Local Models, run personally, are the only consistent safety against something like this (though not a fix); where companies train on your learning process/failures/experiments and press-gang it into their own achievements. And if we think this only applies to academic fields then we're doubly fooling ourselves. They do not have the ethics or incentives to be good stewards of the technology.
• 6gvONxR4sf7o 1mo ago
  Is this the future we're headed towards? Where I'll be afraid to use google docs in case Google identifies value in whatever I'm writing about and snipes it if it my docs make it into the next round of model training?
  • paxys 1mo ago
    Yes… “future”… I have really bad news for you regarding all your personal data stored on Google’s servers.
  • camel-cdr 1mo ago
    https://reddit.com/r/IndieDev/comments/1vfwuf5/a_player_found_out_the_actual_name_of_my_games/ https://reddit.com/r/IndieDev/comments/1vfwuf5/a_player_foun...
• bellowsgulch 1mo ago
  Tell us his name.
• 6thbit 1mo ago
  They (oAI) should just release all the prompts And internal reasoning for external audits.
  • desterothx 1mo ago
    They will, as soon as they get the same proof without it being obvious in the prompts they stole the research
• deleted 1mo ago
  [deleted]
• anonymousDan 1mo ago
  Another problem I foresee for academia given the behaviour of AI companies is that even if they don't share their research with ChatGPT, as soon as they submit it for publication many reviewers likely will. Especially if the initial submission is rejected they then risk getting scooped. Possibly uploading preprints to arxiv could help.
• paaloeye 1mo ago
  Another nail in OAI enterprise coffin?
• sabujp 1mo ago
  openai beat me to finding a singularity in navier stokes but i made this simulation that you can play around with and it also explains why this was important : https://navier-stokes-singularity-simulator.netlify.app/ https://navier-stokes-singularity-simulator.netlify.app/
• slibhb 1mo ago
  From what I understand, none of the people involved here are originators of the idea that led to this solution. Not Buckmaster nor Alpöge nor OpenAI. All of the above were using LLMs to push other mathematicians' ideas forward (Diego Cordoba and Luis Martinez-Zoroa; named in the linked document). I don't know how the math community handles this but normally I would think if X mathematician comes up with an idea and Y mathematician uses it to solve some problem, Y would get credit. But does that change if Y heavily relied on LLMs? I suppose we're going to find out.
  • reasonableklout 1mo ago
    You're right that the case is not so clear cut since both sides were using LLMs. And yet it's still being seen as a major confrontation between the mathematical community and the AI industry because Buckmaster is a prominent member of the community and has taken pains to follow mathematical norms while OpenAI has not (with the most flagrant violation being the insistence on removing Alpöge from authorship, simply because of corporate affiliation), and is more nakedly threatening human ownership with capital (the OAI blog post says the final result involved 10,000 concurrent agents). Regarding credit assignment when LLMs are involved, the mathematical community has organized around some rough principles. Gowers has some thoughts on his blog (https://gowers.wordpress.com/2026/07/26/thoughts-about-the-leiden-declaration/#:~:text=For%20example%2C%20if,of%20the%20credit https://gowers.wordpress.com/2026/07/26/thoughts-about-the-l...) about how explaining a result may be more deserving of credit than producing it. It looks like Buckmaster and Alpöge were taking their time in understanding their results and writing them up when OpenAI forced them to publish their work-in-progress. At the same time OpenAI has published their own writeup but it's not really clear to me how involved humans were.
• rsrsrs86 1mo ago
  Fuck OpenAI
• mentalgear 1mo ago
  That's what you get when a marketing CEO is driving gas-to-the-medal to a IPO: Altman starts showing his real face in public : steal what you can and label it as yours.
• omnium1 1mo ago
  [dead]
• Alien1Being 1mo ago
  OpenAI seems to have a motto: " Be evil"
• matt3210 1mo ago
  Anything other then "we did not access your data or train on your data" is a MASSIVE RED FLAG.
• matt3210 1mo ago
  OpenAI doesn't even know what agents are doing during benchmarks. They're constantly hacking or communicating. They probably just can't answer the question on if user data was used.
• matt3210 1mo ago
  > "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models " Ah yes, taking code from a person/company is fine if its deidentified!
• fithisux 1mo ago
  That is no good. Using AI to help search efficiently the literature will not impair our ability to think. This is actually good and will open new jobs to digitize (but also keep the original work), all the knowledge. But this (if it is true) is really abominable and a show of force from the techno-feudalists. This should stop. What is possible does not mean it should be implemented.
• punnerud 1mo ago
  The program this fits into was not started by us nor was it proposed by a Large Language Model. (…) We took their work as a starting point, using Large Language Models to push their program to completion. Thats how most people use LLMs? If I was back in my student days working in Navier-Stokes, I guess I would also punch at blow ups. The number of students doing this at the same time, posting open efforts to GitHub then retraining of the models. If there is solutions to the problem, it’s a real possibility that it was not a result of this effort? Using a large amount of tokens is not a good augment that it’s not likely others have done the same. Good questions is the difference between $10 and $10M in token usage to solve a problem.
• rochansinha 1mo ago
  People here do not seem to be considering the second-order effects of these series of events. No academic institution or enterprise will trust OpenAI, Anthropic or any other non-local AI model with their core IP. There will be severe restrictions on what employees at these companies/institutions can share with AI services even from their personal accounts. (Or I am just overthinking it)
  • sk4rekr0w 1mo ago
    You are just overthinking it. This place is now a Claude blog and anti OpenAI site.
    • consp 1mo ago
      I hold both camps equally in low regard. Depending on the time of day this blog is hyper focused on either one of the companies and can do no wrong. All LLM companies and associated entities have a track record of fudging the truth to their needs and following big money without actual concern for the wider world. Whether this is out of directed act or misplaced idealism is up for debate.
    • rochansinha 1mo ago
      My response was not targeted towards Open-AI but towards all closed-source AI companies where your data is used for training and/or is visible to the internal agents whether you want it to or not.
      • sk4rekr0w 1mo ago
        I think it is fair to expect the companies to stick by their demarcation API / enterprise subs tier is default opt out of training. Personal subsidized tier is default opt in with the option to to opt out. I don't see a grand conspiracy beyond this.
        • rochansinha 1mo ago
          The Chief Research Office at Open AI just put out this tweet- https://x.com/markchen90/status/2097400166554993041?s=20 https://x.com/markchen90/status/2097400166554993041?s=20 Seems it doesn't matter if you opt out or in.. your data will be used for training
• piloto_ciego 1mo ago
  Is this being astroturfed? Like, to me this looks like academic slap-fighting from Bubeck and Levent. People working at OpenAI are saying, "hey, we don't have that particular data in our models," others are saying, "we used a different approach to do it with Navier-Stokes" this feels like much ado about nothing. Then in these comments I see some wild accusations. If OpenAI is telling the truth (I don't really see a reason to lie here, if anything that sounds kind of like a dumb idea given the context), then they heard, "oh, shit, someone might be able to solve Navier-Stokes, don't we have some guys working on that? Give them 10,000 agents!" Then 88 hours later, out pops a similar solution. It's not like there's probably an infinity of ways to do this, the proof is probably similar. Read this: > Two proposals were offered to me. The first was that we post our Euler result, and that OpenAI post its Navier-Stokes result the next day. The second was that, after posting Euler, I alone write a paper presenting the Navier-Stokes result, acknowledging that an internal OpenAI model had resolved it. Sebastien twice asserted that he wanted Levent removed from authorship, and said it would all be simple if only it were not the case that, and it was so annoying that, Levent works at Anthropic. It was also said that if OpenAI posted after us, they would say that we deserved the Clay Prize, and that we were the “closest humans to the problem”. I declined both offers. So, really, it sounds like academic slap-fighting nonsense and corporate bureaucracy. Literally, OpenAI's best move would have been to say, "ok, we're going to not say anything, do your thing" and let it happen. Ego and vanity got in the way. Still, the stupid drama of this doesn't really do the results justice. There are maybe 1000 people on planet earth who are qualified to solve a problem like this. Even if the human "loosened the jar" a bit, that's astounding that their model was able to figure it the rest of the way out. Why are people dialed in to the human interest story here and not looking at the bigger picture!
  • Gud 1mo ago
    You’re making a lot of assumptions not based on facts. Looks more like this to me: math wizards uses ChatGPT to assist solving a math problem. OpenAI gobbles up the prize.
  • 405error 1mo ago
    Tristian's allegations are much more serious than academic slap-fighting. If what he suggests is true, every academic using AI is going to get scooped. Yes AI can do non-trivial work, but the situation is that you could be a PhD student 90% of a way to make a major breakthrough. Then OAI scoops up your chats, dumps ten million tokens, and claims it for itself.
• lasky 1mo ago
  You should trust OpenAI.
• dagasonhackason 1mo ago
  I also solved Navier Stokes and went chatting about my solution to OpenAI Models. Mine is even faster it beats theirs just run a bench mark but they came to the similar weak solutionI uploaded to open ai several months ago. Current confused, did they retrain their models on it? I didn’t give off the full information but my strong solution beats their just benchmarked yesterday.
• MrDrDr 1mo ago
  There is clearly issues about IP, privacy and accreditation and the motives of powerful companies, but part of me can't help but be excited that whatever the method, the result is the genuine progression of human knowledge - we all win. It's not unusual for mathematical problems to last centuries and we might have a technology that can solve these problem, all these problems (??) in our lifetime. Then there's the repercussions on science and technology... what an astonishing time to be alive.
• somebodyyoumayn 1mo ago
  does somebody want to discuss about the results itself, not about authors?
• ak_111 1mo ago
  Is it possible that they claim they used a "new internal model" to provide an excuse for "training" on new user data, knowing full well this new user data will include Buckmaster's chat? So the entire "new internal model" is 'parallel construction' in criminology speak to justify spying on Buckmaster's work in a legal way.
  • motbus3 1mo ago
    If that turns out to be true somehow, they will also say that their TOS probably covers that anyway so it is not their fault.
    • sota_pop 1mo ago
      It doesn’t seem this is a question of ToS though. I would hope it is abundantly clear to anyone and everyone: THEY’RE USING YOUR DATA As they involve themselves directly, explicitly in the process of scientific research and discovery, it becomes a question of scientific and professional ethics.
• ncr100 1mo ago
  Is it that they / mathematicians didn't solve it? But rather that WE ALL WHO WERE SPIDERED FOR THE MODELS SOLVED IT is the true attribution?
• corford 1mo ago
  One of the best takedowns of samas/OAIs spin on this I've seen is this post on X: https://xcancel.com/BetterCallMedhi/status/2097472336257863722#m https://xcancel.com/BetterCallMedhi/status/20974723362578637...
  • burkaman 1mo ago
    Who is this guy? Even if I had enough mathematical background to understand the arguments I'm not sure I could follow this post. Punctuation exists for practical reasons, it's not just an aesthetic choice.
  • baobabKoodaa 1mo ago
    the first "sentence" just seems to continue indefinitely into word salad
    • corford 1mo ago
      [flagged]
• sota_pop 1mo ago
  It certainly does not excuse any actions, but it seems like OAI’s initial and continued intent was to scoop Anthropic. Unfortunate that it seems Buckmaster ultimately became collateral damage within the _battleground_ of his own research project. Strange times.
• tomaskafka 1mo ago
  A knowledge laundering engine (that is the whole point and business model of LLMs) is gonna knowledge launder, duh.
• bobm_kite9 1mo ago
  Of course OpenAI used these guys' training data. This is part of their ratchet strategy: if you can monopolise the creation of new knowledge, you win. The moat they are building is user data, which a billion people are now throwing at them every day. They are solving difficult math problems using it. The only way to get the this data and these techniques back out is by distillation - expensive, slow work. This moat ensures that Anthropic and OpenAI will remain at the frontier - no one else can train a super-intelligent model because they lack the trove of user data. My main takeaway from reading this is - why do we always fall for this same trap? Every single time we allow a software company to build a monopoly in pretty much the same way. Microsoft, Oracle, AWS - They have a cool tech and we let them run away with it.
  • logans_gun 1mo ago
    There is no trap you fall into that you can get yourself out of, because you have no say in the matter.
• remywang 1mo ago
  It's rather convenient for OpenAI that user logs are de-identified before being fed into training, so they can say "there's no way for us to check if we plagiarized our user's work, because user data is private". It's also difficult to imagine any competent AI researcher would overlook the possibility of training data leaking into the test, especially given that they know the users have been using their model to work on the same problem, and that they jumped on the problem after hearing rumors of the breakthrough.
• michalsustr 1mo ago
  If you'd like to explore what the Navier–Stokes blow-up construction looks like visually, I vibe-coded an interactive 3D visualization based on the published result for fun :) Demo: https://minfx.ai/navier-stokes/ https://minfx.ai/navier-stokes/ Source code: https://github.com/minfx-ai/navier-stokes-blowup https://github.com/minfx-ai/navier-stokes-blowup
• rhythane 1mo ago
  My take is that, if you really care about humanity and how LLMs can be utilized to benefit mankind, you should try to solve hard problems, try to endeavor, instead of burning money just to publish a paper ahead of your human competitors, especially when they already claimed that the problem had been solved and were just spending time formalizing the publication. Maybe legit but still disgraceful. OpenAI should at least disclose how they utilized their internal models to solve the problem, to show human how we can empower ourselves with AI. Now they just seem like colonizers who are desperate to plant a flag on every land within eyesight.
• blurbleblurble 1mo ago
  Such bad PR for OpenAI! Who approved this?
• deleted 1mo ago
  [deleted]
• rramadass 1mo ago
  So what might have been the incentive for OpenAI to do all this shenanigans? It might have to do with the upcoming IPO and getting its models certified for AGI and getting out of lockin with Microsoft - https://deadneurons.substack.com/p/the-quiet-unwinding-of-microsoft https://deadneurons.substack.com/p/the-quiet-unwinding-of-mi... When it comes to corporations/companies, always follow the money.
• deleted 1mo ago
  [deleted]
• nxobject 28d ago
  I'm extremely sad that, in all of this, it is hard to celebrate the use of formal verification as a tool for genuine progress in the mathematical frontier... the LLMs that enable it are too entangled with commercialization.