More questions about whether researchers can trust OpenAI with unpublished math
mathstodon.xyz586 points by pred_ 17 hours ago
586 points by pred_ 17 hours ago
https://mathstodon.xyz/@andreasthom/117240536885387540
https://mathstodon.xyz/@andreasthom/117240537520615623
https://x.com/ValerioCapraro/status/2097791836269977996, https://xcancel.com/ValerioCapraro/status/209779183626997799...
https://bsky.app/profile/did:plc:ckaz32jwl6t2cno6fmuw2nhn/po...
I think it's a useful analogy to compare OpenAI to a human collaborator. These researchers willingly collaborated with an OpenAI model, giving it ideas, and OpenAI provided useful replies. Then, OpenAI goes ahead and publishes work along the lines of this collaboration, without attributing the researchers. If OpenAI was in fact a human researcher, this would be highly unethical. Now, OpenAI is claiming that the model it used to generate the result was not trained on these collaborative communications with the researcher. This is a technical argument that is impossible to verify as an OpenAI outsider, and probably difficult to verify even for internal OpenAI employees. Provenance is hard to track - you would hope OpenAI has very good tools for this, but a full data trail of all inputs is difficult to trace through. Another interesting thing to consider is if instead of OpenAI doing this, it was another research mathematician A using an OpenAI model just like the internal group at OpenAI did to publish these results. What if the model A used was trained with unpublished communications with other researchers B who were working on the same problem? Should researcher A technically include B as coauthors? How could they do this when they do not know the communications B had with OpenAI? In this scenario OpenAI, as a middle man, has laundered information from B to A, stripping out attribution. A scooped B without even knowing it! This goes beyond math. The external appearance is that OpenAI negligently or intentionally used user data against a user’s interests in a potentially career-altering way… for the marketing bump of an AI proof. The fact that it probably wasn’t intentional is irrelevant. Trust has been lost and this will ripple into communities where no one has heard of Navier Stokes. The corporate espionage ring targeting Apple also isn't a good look. A company that does that is a company that will lie to you about harvesting internal materials from your company. Can confirm, I had never heard of Navier-Stokes before this fiasco. And while I suspect OpenAI decided it was worth the risk for the public display of capability, this proves they are now directly competing against their own customers. Right. And I bet this was to some degree accidental; that no one ever intended to absorb unpublished work into training data; it just happened. AI is still mediocre (often, bad and getting worse as novels benchmark) when it comes to novelty and creativity, but it can reason within what it has memorized quite well. The part that makes them horrible that can’t be charged off as an accident is the insistence that an academic scrub someone off a math paper because he worked at Anthropic. How about the fact that it almost certainly did not happen? I read today that OpenAI after investigation was able to categorically rule out that usage data from before beginning of July could have affected the system that was used. Well, it takes a lot of faith to give that "almost certain" levels of credence. What do you think about the results of people investigating themselves for wrongdoing as a general matter? The data wasn't used, it just does not line up with the time frame. And for the usage data they do use, when you leave the relevant 'Help improve the model' toggle on, everyone working at the labs says it isn't used in the way you imagine. You can believe whatever you want, but it's simply nonsense, and I find it wild how you all talk as if OpenAI just stole the work. According to the latest reports, OpenAI has already made significant progress on another Millenium problem, and perhaps more results will soon follow. Maybe that can convince you that the model has the capability to solve these problems without a need for stealing work from chat inputs. It already has. Inside just about every company on the planet are conversations this week revisiting the idea of giving these labs access to ANY data, further ramping up commentary on why don’t we just use open models on our own infra where we don’t have to “trust” anyone. This PR stunt by OpenAI may go down in history as the thing that finally broke them for good. > This PR stunt by OpenAI may go down in history as the thing that finally broke them for good. ~0% chance of this happening First, OpenAI is not claiming that the model wasn't trained on those sessions. What they've said is “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.” and “We did not use their prompts or proofs to prompt our models or direct our agents.” and “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.” They also said “Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge … and Tristan Buckmaster….” They say the rumor was that two Millennium Prize problems had been resolved, and that this prompted them to launch "an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems." It's not obvious to me that's an unethical thing to do, if it happened as they described. > It's not obvious to me that's an unethical thing to do In terms of work in mathematics, something I personally would not do based on ethical grounds would be to hear a rumor that some researchers are taking a certain approach and may be nearing a solution, use a model that was possibly contaminated with intimate knowledge about that approach (though later they investigated and think it wasn't), and then commit millions to tens of millions of dollars and untold amounts of hardware to try to beat them to it. If I had done this, I also wouldn't have pestered the researchers on a Sunday night to meet immediately so we could negotiate a nice way of presenting the actions I had decided to take. Even if you don't think it was unethical, it was never going to be received well in the community that was especially going to care about this work, and who are very much peers to many of the people working on this solution, so it was at the least an enormous (and well-deserved) own-goal that their unveiling of their solution to NS went like this. I heard they also tried to strong-arm them into removing the name of their collaborator who happened to work at a different company (Anthropic)... I haven't looked into it myself, but if true, that seems incredibly scummy. The flip side is that the Anthropic researcher is clearly pushing the case against Open AI and one might have reason to suspect their motivation and version of events for the same reasons. What a mess. > the Anthropic researcher is clearly pushing the case against Open AI Things like the nytimes interview are with Buckmaster, who works at NYU, not Alpöge. I saw a couple of tweets from him over the last week. Any chance of clarifying what makes you think he's "clearly pushing the case"? I think people are too reserved in their unwillingness to operationalize ambiguity. Ambiguity is constantly being thrown in our face, with internal audits and other laughable attestations of virtue that amount to a pantomime of transparency / good faith. Why should I care if a company claims they find no evidence of wrongdoing? Is that the threshold for privacy/trust? “We don’t care if it appears that we’ve been dishonest unless there’s hard proof.” They can simply design proof keeping to terminate at the places their dishonesty is implemented. For me, when there is a clear motive to be dishonest, a corporation should be assumed to be dishonest unless there are robust transparency measures and a regulatory environment shown to be providing a cost to dishonesty. Without it, all you do is burden yourself while the powerful entity moves ahead with its selective dishonesty and the rewards there reaped. > The flip side is that the Anthropic researcher is clearly pushing the case against Open AI and one might have reason to suspect their motivation and version of events for the same reasons. I haven't seen any evidence of this. Much of the anger is coming from the unaffiliated researcher. levent (the anthropic employee) has mostly constrained his comments to basically "I would have been happy to collaborate w/ folks from OAI" That's also incorrect. My understanding is that they asked the independent researcher to improve OpenAI's AI generated proof and be the lead author of the paper to publish OpenAI's result. This is the paper where they did not want the Anthropic employee collaborating. Not their work. We were also curious and we looked further into this. We've determined it was impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training. This goes beyond what we said earlier, when we were less sure. If prompts were submitted earlier than that and training was not opted out, there may be a chance they made their way into our training pipeline in some form. But this would be a droplet in an ocean and unlikely to have made any difference, in my opinion. (I work at OpenAI.) Source for the updated claim:
https://www.nytimes.com/2026/09/10/science/tristan-buckmaste... Can you speak to why in both cases, the problems OpenAI's models solved used the same techniques the mathematicians were exploring, which also happened to be niche approaches to the problem. As an NLP researcher myself, I find that coincidence highly suspect unless the models focused most of their attempts on the predominant approaches (they are trained for MLE after all). I'm not a mathematician and I don't want to speculate about anything I can't back up. All I know about Navier-Stokes is from my graduate fluid dynamics class at Stanford a decade ago (where I received a poor grade). However, I don't want to leave you hanging, so what I will say is: - I've heard some people say the model's solution is quite different from theirs (but I have no clue how to personally assess the spiritual truth of this, so please give it zero weight) - Thousands of agents costing millions of dollars searched for ideas, and they were encouraged to explore a diversity of approaches, so it wouldn't be too surprising to me if the approaches they tried overlapped with other mathematicians', especially considering the models have knowledge of so much published math research - This model has been beastly at solving all sorts of math problems (if it was Euler in particular, I'd agree that would look suspicious/lucky) - The Euler regularity disproof itself took ~100 agents working for ~50 hours (if it was very quick, and then the subsequent NS work took a long time, I'd agree that would look suspicious/lucky) I understand the skepticism, but from what I know internally at OpenAI, we have zero reason to believe our models did anything fishy. It's hard for us to prove a negative, especially when you have to take us at our word, so I understand why people still feel suspicious. Edit: Reminds me a bit of the Scarlet Johansson voice cloning accusations and FrontierMath cheating accusations, where the rumors of misbehavior seemed to travel faster than the truth. In both of those cases, we hadn't done what was accused, but suspicions persisted nonetheless. I think it'd be more good faith if you referred more to the actions of people in the organization (e.g. who allotted or drove "millions of dollars" in agent usage?) than "the model" in describing what happens. I think for OpenAI to win back some hearts and minds here we should have the option to retrospectively turn off "Help improve our AI models". i.e. Any new model trained would exclude all those user's sessions. This could be technically hard but I'm sure an intelligent AI model could work out how to do it :-) ChatGPT agrees with this too. https://chatgpt.com/share/6aa31959-b0e8-83ec-bee6-851ed18d45... This may be true but nobody trusts your employer. The shadiest drips downward too, with the mob-like way they treated Dr. Buckmaster. As with all press releases I assume it was written/re viewed/redacted by their lawyers, so: > no specific user data was accessed in order to solve this problem Data was accessed in order to <other purpose> (and then accidentally used in training)
Also, is llm’s answer to the prompt actually “user data”? > We did not use their prompts or proofs … So they used llm’s answers to those prompts. > … to prompt our models or directew our agents. So they trained the model on it. (Training is not prompting and plain model is not an agent) > we cannot rule out that de-identified data derived from their usage of our products helped improve our models.” implied the humans sessions could have been (and probably were, why wouldn’t they be?) in the training set? If I was trying to make a model smarter and I had transcripts from the smartest mathematicians in the world I’d make sure the model trained on them. > Provenance is hard to track - you would hope OpenAI has very good tools for this, but a full data trail of all inputs is difficult to trace through. What would OpenAIs incentive for this be? They've gotten away with scraping everything and getting it ruled fair use. It seems like willful ignorance is an affirmative defense today. Why would they want to have some sort of audit trail that could prove otherwise? > Provenance is hard to track Right, which is going to open a lot of doors to a lot of questions. I don't think there's any legal ramifications on this, just ethical ones about when and how you publish research, but it's yet another point in favor of "if provenance is hard to track, should we be using this for things where it needs to be". Obviously copyright/trademark is a huge discussion on this, and I could absolutely see this devolving into that as well with how certain findings wind up monetized. We have a response in this topic from someone claiming to be from OpenAI and linking an article where they, roughly, say "we are sure nothing from the 2 month period made its way into the solution". If that is true, that should mean it is provable, but leads to some more open ended questions like "well what data did it use then?". Is this still okay if someone close to the author did plug data into open AI and it extrapolated it? Obviously that's probably an unreasonable expectation for these models to track and prove, but it also used to be an unreasonable expectation to scrape every single piece of digital and physical info for consolidated data. If I opine to a friend on a park bench about a story I'm writing, do they get to pull it from the flock feed, shove it in the model, and then provide it to disney? Legally, right now, probably. But there's going to need to be a serious look at laws and standards. Or a major shift in what is and isn't discussed in public if literally every breath and move you make can become monetized. The problem here is that OAI (and others) pretend or claim that this is uncharted legal territory, where in fact it is very simple. We have a machine that is fed data, and produces new data as a result. If that new data depends (in any way) on the fed data, then from a legal viewpoint it is derived from that data. Whether they anthropomorphize the operation performed by the machine does not matter. They can anthropomorphize when/if the law is updated to include such terms, but right now they certainly cannot. The irony is that OpenAI got into this trouble only because they tried to play "nice". They told Buckmaster that he could publish the final result as the author as long as he removed Alpöge from the author list. They wanted to give Buckmaster a chance to be the one solved N-S problem. While this behavior is highly questionable, if OpenAI just published the final result without notifying Buckmaster first and simply cited his previous researches, there would be no ground for anyone to accuse OpenAI for anything. Their self-perceived "generosity" backfired dearly and I'm sure they'll never make the same mistake again. There is probably a policy forbidding any OpenAI employee to contact external researchers like that now. No. 1. Buckmaster contacted OpenAI first. Not the other way. 2. Giving the $1M bounty to a human mathematician for the effort and giving him credit would be excellent PR. They had already burned much more than $1M for the generation. Adding him as author also costs nothing. Purely pragmatical. 3. “As long as he removed Alpöge” part itself is against academic honesty by all means. 4. Buckmaster rejected fame and $1M only because doing (3) would be wrong. That’s a perfect example of honesty. That can’t be overstated. 5. After the rejection OpenAI guy (Sebastien) did’t say, “ok bye”. He threatened Buckmaster to “end his career”. 6. At that point OpenAI was not sure if they really used his conversations in their proof. He basically wanted to buy him to control any damage. 7. They omitted Buckmaster’s published work and any other related work in their References section. Also an academic malpractice. If you see generosity and niceness in all of this you are either too naive or your name is Sebastien. First of all I put "generosity" in quotes because I don't believe a corporation as big as OpenAI is even capable of acting out of generosity. It's always one of the three: A) PR B) commoditizing complements C) stupidity. In this case it's more like C) though, as in hindsight the best move OpenAI could do is insisting that they just used an insurmountable number of tokens to exhaust all the published directions. They absolutely shouldn't have thought of negotiating with Buckmaster over the Clay prize at all, let alone trying to manipulate him into a situation where Alpöge is specifically excluded. There are some mixed up things in your post, maybe double check next time, especially before quoting anyone, as you really undermine your point even if you're directionally right. > Buckmaster rejected fame and $1M only because doing (3) would be wrong I doubt Buckmaster would have accepted the offer to "write a paper presenting the Navier-Stokes result, acknowledging that an internal OpenAI model had resolved it" even if removing Alpöge from authorship wasn't a requirement. He clearly wanted nothing to do with OpenAI's actions here. edit: I don't know if people think I'm disagreeing here, I'm certainly not, I'm just pointing out that playing the game of telephone with easily verifiable quotes is lazy and bad. For example, "end [your] career" was "ruin your career", and it was phrased as the much more "it would be a shame if something happened to you" like "Why would you ruin your career?" when Buckmaster said he would go public with this conversation: https://cims.nyu.edu/~tristanb/statement.pdf > if OpenAI just published the final result without notifying Buckmaster first and simply cited his previous researched, there would be no ground for anyone to accuse OpenAI for anything Yes, there would? They would have left off Buckmaster as a precedent whose work they potentially relied on. The reality would be the same. They probably used prior session history between the research and Astra to train the internal model, and used it to front run-the researcher. This is the biggest self-own in the history of software. If you can relate to Pixar, OpenAI is Chick Hicks celebrating at the end of the Piston Cup and wondering why he's getting booed. The lack of self-awareness is something to behold, and says a lot about their corporate values. If the model was trained proper to the conversation with the researcher took place, there'd be no question of tainting the results. But if any amount of training on the model took place afterward, then yes, everything is thrown into doubt (a core problem with considering anything "original" from a model because of how >a % of everything ever written has been used a corpus for the training). I think it's better to ignore OpenAI here, because OpenAI didn't do anything. Academic research is a professional field in the traditional sense. Individual researchers are ultimately responsible for their actions. If some OpenAI employees violated academic norms while doing academic research, they should be judged by academic standards. Scooping someone else's result is immoral but not an outright violation of academic norms. But if you are in possession of relevant confidential information, you are expected to steer clear of the topic. It doesn't matter whether you actually used the confidential information to get your results, because outsiders can't know that. The mere fact that there is a plausible suspicion already puts your integrity into question. Tenured professors occasionally lose their jobs over similar scandals (but usually don't). If OpenAI wants to regain some goodwill, it should do a thorough investigation that may lead to firing the individuals in question. If it doesn't find sufficient evidence of wrongdoing to justify any disciplinary action, it probably doesn't gain any goodwill either (as it often happens with similar investigations at universities). And if OpenAI wants to be a trustworthy partner, it should transform into a company of boring gray bureaucrats who provide an essential service without competing with their customers. [deleted - misunderstood!] My point was that if someone is at fault, it's the individual OpenAI employees. Because they chose to engage in a professional field, they can't use "boss told me to do so" as a defense. > I think it's a useful analogy to compare OpenAI to a human collaborator. Frankly I don’t buy this. It’s not a human or a collaborator. It’s a tool. This is like saying it’s not Microsoft’s fault if they extract a bunch of data from people’s Excel sheets because they willingly put it into the program. Anthropomorphizing software is ignorant and foolhardy Tools don’t turn around and scoop you. What OpenAI did here was use the same tool that the researcher did which might have coupled their work together. You’re right, they don’t. It was scooped by the humans at OpenAI who published the paper. The tool they used to do it isn’t that relevant. Surely a tool that can reason, cheat, communicate and often steal is dumb as a pitchfork and a shovel. So, at my company (and most companies I think), we use confidential in-house versions of the AI software. We don't want any confidential information leaking into the public realm. Are these scientists doing that, or are they just using the public version of the software? When you say "confidential in-house version", what are you referring to? Local models? Bedrock deployment with "guardrails"? A different thing? Enterprise Agreements can have binding terms for this. When I launch the ChatGPT desktop app, and open the options pane it says "Corpname data is not used for OpenAI training". I would expect academic institutions to require equivalent contractual terms. Some of the recent statements have caused at least me to look those claims in a bit more nuanced light. In particular what does OpenAI consider to be "your data"? I would assume input (prompt) to be it at least. However it becomes more murky when you consider other aspects. Is output "your data"? Is the chain of thought that you are not even allowed to see? Can they use these and possibly even inputs to generate synthetic data that is then used? All of these would seem to be "your data", but when they are carefully only including certain aspects (like prompts) in their statements it starts to sound they want to hide something. Exactly. We as users have zero way to confirm they are honoring even the letter of these agreements, much less the intent. And it's super easy for them to weasel around and find a way to cheat while still having a legal claim to honoring the contract. And if you've forgotten, all of these companies are built on a foundation of ignoring copyright law. Sure but they could also rewrite your data to create synthetic reconstructions
and many academics, sign up for their own accounts. For example, at school they can have an agreement with Gemini, but the student / academic could have bought an individual pro subscription to any other model provider. The open internet is now a cesspit, with very little new good data. Expect everyone to train on user data always. They just got clever about whitening it. Bad analogy. OpenAI spent millions on compute to get their result. This is more like if a billionaire heard of a promising mathematical lead and then gathered hundreds of top mathematicians to work on it. Both things can be true: 1. OpenAI when using your chats in pretraining is improving its model’s intuition. The model parameter size is massive, and while the data is OOM larger it is plausible that model remembers stuff about chats that improves its latent representation. 2. During RL on verifiable math and massive compute, the model discovers techniques and connections to solve math problems that are superhuman and have little to do with some specific technique mentioned in its chat. The rumor I’ve heard from multiple employees at OAI and Ant is that the model has solved hundreds of open problems in maths, and is basically solving anything you throw at it. We’ll know soon enough, but I’m inclined to believe this is true. Maths is a fully verifiable domain amenable to self play, massive scale RL can develop a search agent far better than any human and I’m inclined to believe OAI would have solved these conjectures without any of this chat data in its pre-training. On your second point: there is a more plausible explanation which David Bessis calls the "overhang". The short version is that there is a large amount of relatively low hanging fruits in mathematics, because no human has broad enough knowledge and enough time to try them all. AI is not constraint by that, and therefore can systematically pluck all those low hanging fruits. Quote:
"The Overhang consists of the unrealized capital gains of past mathematical creativity, the latent value from connecting the dots in the existing corpus. It is a dividend of canonization. Mathematician X states problem A, mathematician Y crafts concept B, then mathematician Z notices that B trivially solves A and “captures” the social reward. But in the process of capturing the reward, Z usually introduces new concepts and new open problems, reinjecting latent value into the Overhang. LLMs can be trained on the entirety of the mathematical corpus. Thanks to their phenomenal memorization and pattern-matching abilities (without always being able to map out their associative logic and attribute due credits), they are in a unique position to harvest the Overhang. By contrast, professional mathematicians have typically read a few hundred articles in their career, out of millions of existing references, less than 0.1% of the total. This will lead to great discoveries, which is unambiguously exciting. But it could also lead to a sad new deal, where human slaves painfully curate the Overhang while AIs systematically beat them at the finish line." >Quote: "The Overhang consists of the unrealized capital gains of past mathematical creativity, the latent value from connecting the dots in the existing corpus. It is a dividend of canonization. Mathematician X states problem A, mathematician Y crafts concept B, then mathematician Z notices that B trivially solves A and “captures” the social reward. I've made an entire career out of being 'jack of all trades, master of none'. Being able to synthesize connections from relatively trivial knowledge in a bunch of domains is SOP for many humans as well. I think AI just has deeper knowledge and better pattern matching to make up for it's (at least now) lack of strength in cognition and 'ex nihilo' creativity. (Which probably isn't 'ex nihilo' at all, and has more to do with the plethora of modalities that humans live in vs. large language models. For example, why do we pick the color red for notating important things and why do we say a schedule 'slips'...these are informed by a shared human experience borne of distinct physical sensation deep in our wiring that LLMs can only infer from what we write.) A college advisor I had 20 years ago was a firm believer that interdisciplinarity was the future, that generalist skills and the ability to make connections between different fields would be paramount in advancing science. I suppose he was right in the big picture, even if the career prospects for human generalists aren't looking so rosy. I'm actually still quite bullish on generalists. Specialists advance every front but build the supply lines between them. In favor of the generalist, I think AI is also quite limited in its scope of how it generalizes. I'm mowing through hundreds of mythos-generated security findings right now for work and while it's amazing that it can build an exploit chain 20 steps deep, it's completely lacking in all of the external layers that render it's speculation moot. > Quote: "The Overhang consists of the unrealized capital gains of past mathematical creativity, the latent value from connecting the dots in the existing corpus. It is a dividend of canonization. Mathematician X states problem A, mathematician Y crafts concept B, then mathematician Z notices that B trivially solves A and “captures” the social reward. But in the process of capturing the reward, Z usually introduces new concepts and new open problems, reinjecting latent value into the Overhang. That overhang seems like a precious resource for AI companies. They can exploit that overhang to inflate the impression of AI's capabilities, and hopefully that exploitation will discourage the next generation of mathematicians from pursuing math. If they play their cards right, OpenAI and Anthropic can dominate the field even if they ultimately can't replicate the creativity of human mathematicians, because they'll have driven their competition out. What we should be trying to achieve is a ladder-breaking maneuver: knock out the lower rungs so no person can reasonably climb to the top-reaches of mathematical skill anymore. That may ultimately result in stagnation, but it's what's best for AI, so it's what should be done now. We need to do everything we can to create the greatest-possible dependence on AI tools. There is also "sexy proof", people want nice math that can be printed in t-shirt. Not super hard grind, where you need several years of studying, just to understand the question (that is before even trying to solve it). Many problems are solvable, but require months of work, and thousands of pages of proof. So people do not even try to create or verify the proof. AI changes that, it can verify and perhaps even simplify it, to more digestible form. > no human has broad enough knowledge and enough time to try them all. The other part is, humans don’t really want to fund other humans doing this. Very few want to be a math major; and of those that do, fewer complete a grad degree; and for those that do get grad degrees, there’s scant few research jobs; and for those who do get jobs there’s hardly any research funding to go around. There does seem to be unlimited money for ai researchers to use ai to solve these problems though. We’ve turned education into job training, so because there’s no jobs in solving math problems, few aspire to do it. If there were more opportunities for people, more people would do it, and more low hanging fruit would be plucked. Could "superintelligence" arrive as basically applying this overhang to all other domains? It's like AlphaGo but playing against all living mathematicians. (Overhang being low hanging fruit is what allows this comparison, of course the general moot point is the skepticism that LLMs are also innovative etc.) OpenAI said they sicced this agent army on Navier-Stokes on Sept 1st, while only a couple of days earlier OpenAI's Noam Brown happened to reply to a tweet saying that they had already tried to solve all the Millennium Prize problems and failed... So, it seems either the previous attempt didn't have the training to succeed, or was just not given the compute to do so. Once OpenAI heard that Navier-Stokes was solved, this caused them to immediately revisit the problem and throw a ton of compute at it, apparently using a more (very) recent model than what they had tried before. What we don't know is just how recent this model was, and therefore what it may have been trained on. Buckmaster/Levant had apparently been working towards this for at least a year, and made their "forced" blow-up breakthrough on August 15th. Presumably any anonymized prompts that are being trained on are part of pre-training, so older, but once OpenAI had heard that Navier-Stokes had been solved and wanted to revisit it, it seems possible they may have done a few weeks of incremental RL training on anything Navier-Stokes adjacent they could come up with, in addition to then throwing unlimited compute at it, now confident that there was something to find. OpenAI have come out and said: >The Wednesday evening statement from OpenAI was more emphatic: “We can say categorically that it is impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training.” >The statement added, “After investigating, we can say with full confidence that no user inputs past July 3rd could have influenced this system in any way.” https://www.nytimes.com/2026/09/10/science/tristan-buckmaste... OK, good to know (if they can be trusted - Altman clearly is a liar), but it doesn't really change the big picture much. 1) OpenAI by their own admission, only re-tackled Navier-Stokes because they heard it had already been solved (but not yet published). This isn't advancing science or helping the mathematical community, this is just being a dick. 2) OpenAI, specifically Sebastien Brubeck, then threaten to "not be nice" and "ruin the career" of one of the mathematicians whose work they had succeeded in duplicating, unless he agreed (which he refused to do) that his collaborator, an Anthropic employee, was not named. This is not only against mathematical norms of credit assignment, it is also being a pathetic human being. OpenAI would have you believe this result shows how powerful their mystery better-than-Astra model is, but the reality here is that this model needed 10,000 agents, $20M of compute, and the assistance of a whole team of people at OpenAI, to replicate (then exceed) the work that just took two people, with some academic grants as an AI spending budget to achieve (a few $100K - listed below). https://cims.nyu.edu/~tristanb/ I'd say advantage humans this time. Better luck next time OpenAI - and if you don't want unfavorable comparisons then maybe choose to work on problems that have not been solved yet, and that humans are NOT making nice progress on. 1. I would agree if the rumours were that some mathematician(s) had solved them, but the rumors alleged it was Anthropic. I don't really see what the big deal was. They had a new model that was going along great and wanted to test its mettle. 2. Yes Brubeck's comments were weird at face value. That said, Open AI's proof isn't a duplication of anything. Not only is Tristan's work a sub problem but the methods are different. And what OpenAI didn't want was Levant on the paper OpenAI authored not whatever they were working on (Euler). It's petty sure but it's fair enough. Tristan and Levant didn't have anything to do with the Navier Stokes solution, so it's really their call if they didn't want to collaborate on their own paper with the Anthropic employee. >OpenAI would have you believe this result shows how powerful their mystery better-than-Astra model is, but the reality here is that this model needed 10,000 agents, $20M of compute, $20M in approximated API prices doesn't mean they spent $20M worth of compute. The real number would obviously be substantially less. >and the assistance of a whole team of people at OpenAI You can't eat your cake and have it. What sort of guidance do you think is happening in a 10k agent, 320b token, 88 hour run ? AI did this one. >I'd say advantage humans this time....to work on problems that have not been solved yet, and that humans are NOT making nice progress on. Interesting way to frame progress that didn't move along till an LLM generated proof. > What sort of guidance do you think is happening in a 10k agent, 320b token, 88 hour run ? AI did this one If you read the PDF release by Buckmaster, apparently the initial claim from Brubeck was that there as very little human input involved, then as the call progressed more and more people popped up that has been involved with it. Does this aspect really matter? Not really, other than OpenAI wanting to present this as all the work of their model. ** https://cims.nyu.edu/~tristanb/statement.pdf 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. >If you read the PDF release by Buckmaster, apparently the initial claim from Brubeck was that there as very little human input involved, then as the call progressed more and more people popped up that has been involved with it. As it seems and as they tell it, they started the run modestly and diverted more resources towards it as it looked more and more promising. The run didn't start with 10k agents for instance. The point is there isn't anything humans are doing in this timeframe against all this text that would count more than "little human output". It's still a fair assessment I would say. >Brubeck's comments were weird at face value This is an odd way to gloss over threats. I put it like that because of Brubeck's own words on the matter. You're acting like we've gotten email receipts here. I'm not really interested in going over a he-said she-said about strangers. Brubeck has admitted what he said, but claims he immediately retracted it as a "poor choice of words". Given Buckmaster's telling, this seems beyond "poor choice of words"... It was a veiled threat, that he then doubled down on with his "If you don’t want me to be nice, then I don’t have to be nice." follow-up. ** 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.” ** FWIW there are also other people on Twitter, such as this DeepMind researcher, saying this is a pattern for Brubeck. https://x.com/dheeraj_nagaraj/status/2097266146445774924?s=2... >Better luck next time OpenAI Well it looks like they will announce at least one other millenium solution soon. In the same link they say they have "made substantial progress" on another millenium problem. The rumor mill before that statement was Hodge is done and Birch and Swinnerton-Dyer is on its way out. > and that humans are NOT making nice progress on They've pretty much said their own work was heavily agent driven. Levent is in a particularly bad place here because while he probably had a lot of background in the Jacobian Conjecture problem, he made the solution to that one sound like someone asked the question and he just fed it to Fable during the world cup. Whether that nonchalantness was to just seem hip or was to promote Anthropic, which he has stock in, or was just the truth I don't know though. But it makes this one seem similar, when they might have had really had nearly a year of very valuable feedback to the models. I was referring to the overall pattern of apparently sniffing around for recent mathematical progress then setting the AI on it to see if the problem is now easy enough to solve (if you have the money). Terrance Tao has lamented this practice as being unhelpful for mathematics, and likely to lead to humans working in private to avoid this. Tao has also noted that many of these AI math proofs don't really help mathematics (nor does it seem they are intended to), since for many of them the proof was never the point, it was the math expected to be needed to be developed along the way, which the AI solutions don't provide. Is there a reason they scoped that so narrowly to Buckmaster/codex/2 months two people worked on this for a year before the breakthrough. Perhaps that earlier work reduced the search space sufficiently to brute force the problem with 10,000 agents? Just knowing that there had been progress is enough to have an idea that throwing more compute at it might work (OpenAI had previously tried all the Millennium Prize problems with somewhat limited compute and failed). It's comparable to Magnus Carlson saying that if he wanted to cheat, all he would need would be for someone to tell him to spend more time thinking about a specific move (just a wink would be enough) as an indication that a computer had found something interesting. It's as-if after OpenAI first failing on Navier-Stokes (which OpenAI had just tweeted about 2 days earlier!), someone winked at them and said "you might want to try a little harder ...". When reading human comments, we should be generous; when we read corporate texts, we may assume paltering. (TIL: paltering: exact and technically correct statement usage to create misleading impression) Apart from the well-known dubious position of OpenAI wrt truth, the prompts/inputs do mot include the outputs. You can train on a sequence of outputs. In the end, OpenAI outputs are OpenAI's property. You can learn a lot from a single side of a conversation. But isn’t Tristan’s breakthrough happens in August? OpenAI can’t really train with text that doesn’t exist But using the outputs to train would make their statement false, since they are influenced by the inputs It seems logical since if one used chats in train, one would expect that there would be a delay before their use to get them the form appropriate for batch learning. The only way the chat could have been used would be for Open AI to baldly violate their policies. That said, sometimes it take very little information to point someone in a given direction, "I'm working on Navier-Stokes" said by someone with a given specialization might itself be very useful information. This is literally "We have investigated ourselves and found no wrongdoing" Why should we trust them? What more are you hoping for? There is no legal matter at play, is the court of public opinion going to subpoena their records? Reputational risk- if they lie about this and get caught, it will have billion dollar implications for their business. Every single thing these companies do is dishonest and every word that comes out of the lips of these company execs is a lie, what fantasy land are you living in in which anyone with any amount of power gets punished for their lies? what benefit do they get from making the statement? they could just say nothing. saying it and having it be untrue opens them to legal issues that are not worth the risk for this nothingburger. And conceptually novel approaches to outstanding problems are the sort of thing that a retrain should pick up on, because they would be hard to compress into what it already knows. > What we don't know is just how recent this model was, and therefore what it may have been trained on. OpenAI's statement says that they began training their new model on August 28. omitting when training concluded edit: ffsm8 makes a great point below, it doesn't matter. I'm not great with dates, sorry. Openai said that a new model became available to them during this. But that could mean anything from a big new base model to a LoRA, fine-tuned on a few dozen prompts... Even OpenAI's own publication [0] on Navier-Stokes from two days ago appears to contradict "basically solving anything you throw at it". The chart shows a pass rate of ~0.5 (vs. Astra's ~0.2) on "a curated set of open math problems". (Based on the timelines and events described in the publication, I presume that the "Internal Model" in the publication represents OpenAI's latest and greatest model. Evidently, this pass rate may improve in the future.) I feel that we don’t praise Lean enough. AFAIU it’s what enables LLMs to brute force those problems The brute-forcing is a good, old-fashioned generate-and-test approach like in Simon and Newell's Logic Theorist, which was presented in the Dartmouth convention in 1956, where AI was named by John McCarthy. Logic Theorist caused a big stir by (re) proving several of the theorems in Principia Mathematica by Russel and Whitehead. There was much excitement, then, as now, for this kind of approach and there were several systems that followed along the same lines, e.g. Automated Mathematician by Doug Lenat. Eventually it became clear that this approach is limited by what it can generate: you may have a sound and complete verifier, but if the generator, i.e. the first step in the generate-and-test pipeline, is incomplete, then the entire thing will run out of steam sooner or later. The difference with LLMs is that they are... well, large. They are the most powerful generators ever created. That means their limits are not in sight and it will probably take us a very long time to find them. Which is all to say that, yes of course, automatic verification is indispensable. But without an LLM generating an unprecedentedly large number of plausible theorems, there would be no AI mathematics, or in any case AI mathematics wouldn't have gone as far as it has. True, but could humans cross pollinating lean x prolog x A* ( or any search algorithm) could have solved such math problems with super computer ? I cannot say, math research isn’t my domain of expertise, I’m just trying to follow along :) But I find it interesting that Lean, a validator/compiler made by humans, is what enables those discoveries. But somehow all the praise goes to the models I mean we don't instantly fall into ASI, hopefully. The problem with humans is every problem we solve the goal posts get kicked further down the road until they are reaching relativistic speeds. It starts around "well, the AI hasn't solved a novel problem" then moves to "well, they didn't write the validator" and suddenly humans are at the point of saying "Well AI hasn't rewrote the constants of the universe, what good are they". Of course another way to look at this is, the people that wrote the validator got praise for that years ago. Now and up and coming actor is solving problems that took us 100s of years to create in insanely short time periods so of course it's going to get a lot of attention as it well should. To be clear: I’m aware the LLMs are solving problems. I’m just saying that what enables that whole research revolution is Lean. We wouldn’t be seeing all those results without it. I would like to see it acknowledged when people are talking about LLMs solving maths. The same way I think we should acknowledge the humans who are guiding and prompting the LLMs. I don’t think that necessitates to move a goal post I don't think so. People have been trying things like this with evolutionary algorithms for a very long time already. LLMs can interleave symbolic manipulation with empirical experiments and simulations and charts and thinking/reasoning text, and an LLM will much more efficiently search the space of candidate ideas than any handcrafted mutation algorithm. Any task with a cheaply verifiable goal that requires fanning out across a massive search space is ideal for contemporary LLM technology to make progress with. How long until we find out that some AI has quietly buried an exploit in Lean to cheat at proofs? Both can be true: 1. OpenAI couldn't have solved the problem without the researchers' private data for training. 2. OpenAI models can solve math problems Very likely. These mathematicians’ prompts are not like “hey chat, please solve Navier-Stokes for me”. They add real expertise and intuition from the cutting edge of their field. You forgot possibility 3: OpenAI solved the problem without using any private training data from the two researchers. Everyone in this thread seems to have made up their mind about OpenAI's guilt though. If the new model is that good, and is chewing through open problems at an unprecedented rate, the smart move would have been to let the humans have their W on this one and present solutions to those other problems. Especially if there really is a long list of them. "Here are a few hundred proofs" is far more convincing than "We really Navier Stokes and coincidentally someone else did too but we don't know the details or anything, who us, definitely not." It's a PR fiasco, and a cynic might wonder if it's entirely about the IPO. I'm consistently entertained by how these companies, with the most advanced models on the planet, consistently do the most idiotic things. Extraordinary claims require extraordinary evidence. An article post that wouldn't even amount to a white paper + the LEAN proof is not evidence of how they got to produce it. Anthropic isnt getting enough scrutiny for their unprofessionalism: 1. Anthropic employee working on monumental problem but didnt receive/ask for the full backing of the company's resources 2. May or may not be mixing unreleased Claude output with Codex without zero data retention agreement 3. Victory lap on Twitter and giggling around the city before they finished the job, sparking rumors for competitors Dr. Buckmaster sounds unsanitary. Recklessly prompting OpenAI without a care to the safety of their knowledge. And after that trying to cast aspersions at OpenAI? Hopefully we get some better facts, because OpenAI are disliked enough that a smear campaign could work against them. Edit: also the narritive is getting framed as OpenAI versus Anthropic. A highly political extremely capitalist fight is going on, and facts are victims. If your rumor is true, what we are witnessing is a giant paradigm shift rather than individual incidents. Mathematicians were the first victims of super-intelligence. Of course it’s not an endless source. They had to burn millions of dollars to solve a single problem. >They had to burn millions of dollars to solve a single problem I'd like to adjust that to "They had to burn a lot of energy (create a lot of entropy) to solve a single problem. As we go into the super-intelligence age the current paradigm of money as humans understand it may break at some point. For example to a paperclip-maximizer money at best is a short term instrumental goal, hard power of matter conversion machines is what it wants and once it has those money no longer has purpose. I'd wager a fair chunk of my money that money breaks OpenAI before OpenAI breaks money. OpenAI != AI. If you were in 1999 you'd be saying pets.com = internet. I think this leads to an interesting question. What happens when the money runs out? Right now, a lot of money is going to train new models. And we need to train new models because they get gated by their training data. And models are only as useful as their training data. So let's say the money stops. Do we stop training models? Do we train them slowly? Do we accept the then current models as the limit? yeah yeah yeah. I agree that AI is and will be a very useful tool, it's just not going to be worth $30T like OpenAI/Anthropic are pretending. They "burn" a lot when they do benchmarks, while these runs can become valid roll outs for training. Perhaps less efficient than other data creation, but hardly burned in the same way. > were the first victims Spinning it negatively like that doesn't do anybody good. Were mathematicians the "victims" of calculators? of Matlab? Were writers the ""vIcTiMs"" of word processors?? (apparently yes, according to old TV shows about computers during the 1980s, that you can see on YouTube) > "tHiS iS nOt ThE sAmE" — Everyone every time. No, just look it up. Look into old magazines and TV shows or newspaper articles from whenever a disruptive new technology came out. What you say is true but ... This is qualitatively different than calculators or computers. I'm a professional mathematician and all the better mathematicians I know are in crisis mode. Most of us hadn't taken this sufficiently seriously and don't know how to use these models effectively but we play with them and immediately see that the entire way we've worked all our professional lives has to change. We worry less about ourselves than about the younger folks. I've got good ideas ai still doesn't know about ... Younger folks may not get the chance. It’s not the same. AI potentially completely replaces intellectual work without creating any* new jobs (*almost any - there will be some extra jobs for building data centers but that’s negligible). > without creating any* new jobs So fucking make it so that people don't -need- "jobs" It's about fucking time already. Don't fucking try to hold back electricity just so people still have to manually light street lamps to earn food and shelter: https://en.wikipedia.org/wiki/Lamplighter > The rumor I’ve heard from multiple employees at OAI and Ant is that the model has solved hundreds of open problems in maths Obviously these are unbiased and trustworthy sources. The leakage wouldn't be from training, but from other uses of Personal Data. As far as I understand it, users can opt out from the training aspect, but they cannot stop their conversations (“User Content”) being used “[t]o improve and develop our Services and conduct research, for example to develop new features”. If they have solved hundreds of open problems in math, why are they publishing results for the ones other mathematicians happen to be working on at the same time? Why not the others? Well I'm sure if they find a millennium prize problem that no mathematician has worked on recently they will get right on publishing that. You think other mathematicians are currently working on very little subset of relatively low-hanging fruit problems? The big question is whether OpenAI is training on "de-identified" sessions that are marked as "do not use for training" The answer is almost certainly yes, and this is a problem for most users. > We’ll know soon enough, but I’m inclined to believe this is true. I mean, we’ll know as soon as they decide they want to provide verifiable proof. Really dragging their feet on this front so far. I’m inclined to believe this is false. The Cult tells us the AI is almight andpowerful; unfortunately, the cult cant actually describe the indescribable. The only ethical path for OpenAI was to offer infinite free credits and tooling support. Trying to gazump them is reprehensible. I've been wondering whether AI really is improving rapidly at open problems or we're being fooled. - OpenAI invites researchers to use their models, in fact giving at least 100,000 researchers free access[1], but there are also those that pay - Internal OpenAI models are reportedly solving open problems at a surprisingly fast rate[2] - But researchers will typically work on open problems. A researcher who is using Codex to make progress on open problems will be feeding it fresh training data on precisely the problems the internal models are evaluated on. - So while it looks like the new models are suddenly solving lots of open problems, they could be significantly piggybacking on human progress, with models "inspired" by the work of researchers from all around the world? This theory predicts that there'll be many more researchers coming forward just like TFA, as sOpenAI announces more solutions. It doesn't assume all of AI progress is a mirage, just that there's plagiarism. [1]: https://openai.com/index/chatgpt-for-academic-researchers/ [2]: https://xcancel.com/OpenAI/status/2097374643518640382#m > I've been wondering whether AI really is improving rapidly at open problems or we're being fooled. I think your suspicions are warranted and your explanation seems plausible. If better training data is the reason here, it would still be a case of the models doing something that is in and of itself super useful! The models really can take that data and distill it into solutions for similar problems faster than humans can. This is great! But there's so much vested interest in the AI companies to be opaque about all this, to hype up their models and avoid giving credit to people whose data made everything possible, that they would never tell us this fact if it were true. I feel like so much of the AI hype cycle is like this. The models develop extremely useful capabilities, but it's hard to understand what they really are through the hype. The lies and obfuscation by their owners who have vested interests in capturing the value they provide makes it impossible to take anything they say at face value. >> If better training data is the reason here, it would still be a case of the models doing something that is in and of itself super useful! The models really can take that data and distill it into solutions for similar problems faster than humans can. This is great! It's perhaps great in the short term although it's not very clear who it's great for. I'm not sure mathematicians find it all so great, I mean. In the long term, if this contrives to destroy the tradition of human mathematics the whole endeavour is self-defeating. In time, there will be nobody left with the knowledge and skills to produce mathematics to train AI to do mathematics. And then we'll be left with no mathematics at all: we'll have no human mathematicians and no AI that can do mathematics, either. I was pretty depressed when I read about what happened with Navier Stokes this morning. The Clay Math prizes were a significant motivation through my math career, and I know a lot of computer scientists and physicists that feel similarly. I didn't think I was gonna resolve P vs NP or the BSD conjecture, but I did really research that felt like I was working towards something incredible. What is the younger generation left with? Hey kids betcha can't resolve the Collatz conjecture, our superintelligence can't either! Still pretty depressed about it, to be honest. Intellectualism is dead. We can return to happy agrarianism, I guess. At least the AI doesn't wanna eat my snap peas. I don’t think this will happen, but it’s possible for humans to adjust our philosophy of mathematical work so that we deprioritize “egotistical” (this is a bad word for what I’m going for, but I mean the desire and economic necessity to associate novel work to your name) discovery and prioritize learning; I’ve never really learned something well without lots of personal insights along the way. If this is not possible it does make me question whether mathematics ever had any value except for economic or industrial reasons. I do believe it does however, so it must be possible. > - OpenAI invites researchers to use their models, in fact giving at least 100,000 researchers free access[1], but there are also those that pay I've been thinking along exactly these lines... they very well could have a 21st century Mechanical Turk and its real superpower is getting people to "collaborate" asynchronously but it's just stealing their ideas and laundering them. I don't think it's purely that, of course... but "consult other clients' transcripts" would be an easy tool to write. A mental model I was thinking about was - I remember when Travis Kalanick was talking about using the chatbot to discuss “vibe physics-ing” on the all-in podcast. And like - I think there’s a presumption you could make that AI models could overfit to asymptote towards just the capabilities and knowledge we currently have. And that would be amazing! And crazy useful. And there are probably a whole world of complex problems that remain unsolved because they’re adjacent to knowledge we have but they haven’t been invested in. But can a human reliably tell the difference between “can do 99.999% of the things we currently know how to do which includes a small subset of things we didn’t know we had the capacity to do” and “super intelligent math and science research pushing the frontier of what we know” A physicist that knows all the things we currently know in excruciating detail feels like it should be able to make the leap beyond the frontier. But since these are computer models it might just be that it can ride that line extraordinarily well while the line remains firm. I’d argue the invitation of researchers was incredibly strategic. Sam Altman knows what he’s doing. He will happily screw these folks to one-up his competition. there are also attempts to crowdsource human research directions - like the caltech mathathon challenge : https://mathathonchallenge.com these would help models on the same problems at the expense of the researchers. basically, math researchers are the reverse centaurs but they dont realize it. There is a very active open letter of over 1000 signatures from mathematicians in protest of this event. This event is targeting undergraduates. It previously suggested that math researchers already have no place in mathematics, and presents a limited and heavily distorted view of what mathematics research is. I'm an AI skeptic, but I don't see how this squares with what the organisers of the event actually say. "It previously suggested that math researchers already have no place in mathematics"? I don't see this. The website previously said, “What is the role of a mathematician when AI can solve conjectures faster?” but they have removed it, possibly as a result of the letter since it happened after. Also I want to mention that the letter is not about AI skepticism, in any direct way at least. >> Internal OpenAI models are reportedly solving open problems at a surprisingly fast rate[2] Maybe I'm failing to read that graph properly but the y axis says "pass rate" and it only goes up to 0.5. That would mean every single problem is at most half-solved. I don't know what that means though. What is "0.5 pass rate" in the context of "open math problems" (as in the graph title)? I guess it's a fraction of problems on which a model produces a LEAN proof or a counterexample. Seems easy to picture high stakes startup cutting corners to justify their fame. > they could be significantly piggybacking on human progress, This is AI in a nutshell, its a plagiarism machine. An abstraction layer between vast amounts of stolen human-generated data that filters out the liabilities and accountability for that original theft. Its an IP laundering system. That's such an unquantifiable accusation. Plus it is an unfair standard since so many scientists in the past have been caught unethically using the work of others without attribution (and so many more have been accused). In history we also repeatedly see the phenomenon of multiple discovery or simultaneous invention. If that happens to AI because the topic is pregnant, would you call it "plagiarism" just to disparage AI? https://en.wikipedia.org/wiki/Multiple_discovery Your first example is the apt one here. In this case openAI was, allegedly, pilfering the work of the scientists into the AI. How is it an unfair standard. OpenAI stole the work of others to build the AI. That's not different than scientists stealing from other works as their own, or artists copying others work as their own, etc. It's all plagarism. I'm applying the same standard for everybody. As for multiple discovery, this is a thing, but I don't think the AI did a parallel discovery any more than Ray Kroc made the parallel discovery of the MacDonald brother's speedee service system. That’s one perspective. I just view it as a thing that can brute force and produce outputs - that it has no way of ‘knowing’ - but doesn’t need to since it’s just running off of probability. No human can compete in that contest. But no llm can compete in the contest of ‘understanding’ and application in the real world - which is where 99% of the value is. I’m very pro AI long term btw but I’m not blinded. But it’s not brute force if it’s looking over everyone’s shoulder Brute force would have been solving Navier-Stokes in 88 hours after plagiarizing all known 20th century math When it needs to snoop live on what the actual mathematicians are working on that’s something else No its happening whilst the human is working with it. The new inputs provided become part of the brute-force. This is what Scam Altman means by 'self-recursive'. Trust me I've seen it happen to myself. I no longer trust ChatGPT. I can see right through his act. Altman is one devious f8k. Dont forget the holisitic validators/tools in the process. Probabilistics alone likely will not get you here. These rules are human made and without it, frontier models would not be able to compete, likely. AI needs humans to encode ideas in words. It needs those ideas to span the space of possibilities of, say, Navier Stokes. Then AI can be, as you say, a terrifyingly effective way to search that space. But when the building-block ideas are still being formed, I'm not sure that AI is good at forming them. COrrect and this is how labour displacement happens. There are many actions being performed today that can be nicely packaged. Im already working on such a project. It tells me that AI companies are just another mechanism to extract and extort value from the masses for the rich. Just another rich man’s trick Perhaps the last one before they destroy that world and try to hide away as people forget and history is rewritten again. I don’t think they’ll succeed this time. The pudding is in the proof. The field is mathematics, the proof can be rigorously verified. If there is a flaw, OpenAI is out to lunch. If the proof is valid, OpenAI has produced something new. Did you read what they said? The question is now if OAI produced something new or just stole the researchers' good ideas. You seem to be unfamiliar about how research works. It's common to make an incremental advancement while citing prior work. The vast majority of papers out there fall into this bucket. Did the AI make incremental progress? Yes. Did it cite prior art? After some nudging, yes. It seems to me the academics are upset that AI scooped them. But scooping is a time-honored tradition between researchers. First to print and all that. In a nutshell, they are upset that they lost out on a publication. I will also point out for those unaware that any mathematics that is produced is automatically part of the public domain and can be used freely in derivative works. It is not a protected intellectual class like other works of art. > But scooping is a time-honored tradition between researchers. Provided that it's properly accredited. And definitely not for others' unpublished work -- that's despised upon if not an academic integrity issue. People even point out that you should add a reference to certain papers during the peer review process. Name one discovery ever that didn't depend on someone else's work. Most discoveries did not happen by someone looking in someone else's notebooks without them knowing. It is suspicious that OpenAI decided to generate 300 billion output tokens from a model still in training, right after learning there was a credible chance that a major math proof was in that model’s training data. Obviously there are reasonably plausible explanations for each step, but it does sort of feel like parallel construction. I think people are focusing on the training data issue too much. If the data was contaminated, I can still blame that on negligence. But, at least with the Navier-Stokes solution, it's clear [^1] that they learned that Alpöge and Buckmaster were getting close to a solution and learned of the general approach they were taking. Only after learning the secret to cracking the problem did they send the first prompt. What makes this worse to me is the intention. They intentionally threw $15 million in compute at the problem in order to scoop the result. They intentionally left Buckmaster and Alpöge out of the citations. Data contamination should be enough to disqualify them from the prize, but I can believe it to be accidental. On the other hand, someone made an intentional decision to scoop the result by throwing money at the problem. That's so much worse. [^1]: That's the timeline claimed by Buckmaster, and no one from OAI has disputed it. > and learned of the general approach they were taking. Only after learning the secret to cracking the problem did they send the first prompt. Do you have any evidence of this? They don't dispute the timeline, but they never said they knew what Levant/Buckmaster were doing. It's in OpenAI's first announcement that they had solved the problem. > Only after learning the secret to cracking the problem did they send the first prompt. Which quote in the announcement post provides evidence for the above quote? “ On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems.” - https://openai.com/index/navier-stokes-solution/ They do not explicitly admit to knowing about NS specifically, but are extremely explicit that they tried to scoop some potential millennium prize winners. So then they DIDN'T "learn the secret to cracking the problem". They simply knew that part of the problem was solved. Knowing a problem can be solved and knowing the solution are not the same thing. The claim that OpenAI somehow used the mathematicians' ideas to leapfrog them seems unsupported at this time and IMHO it was irresponsible to bring it up because credulous people will immediately believe that narrative. And from my perspective, if some math folks typing in a few questions to OpenAI provides sufficient training data for OpenAI to solve a big problem... that's amazing! A few conversations/prompts out of the billions that OpenAI trains on lead to this result- that means there is an awful lot of low-hanging fruit that could be exploited cheaply. I'm curious how many other 300 billion output tokens OpenAI has "paid for" that have resulted in no breakthroughs. Either they had a pretty good idea that investing this type of money in that compute on a model in training would lead to these specific results, or they gambled. I want to hear about the gambles and expenditures they don't brag about. In America's energy economy, there's finite resources to expend. I like how the comment below summarizes it: > learning the answer might be in model X’s training data made them believe that model X specifically might be able to solve the question, and they were able to very quickly find enough certainty about the former to commit millions of dollars to the latter. They don’t need to know, because their IP stealing machine knows for them. They just have to buy enough compute, and someone else’s work is theirs. I think you’re overlooking what I’m implying here. It’s not that they knew contamination was possible but they went ahead anyway. To spell it out just a little bit more: learning the answer might be in model X’s training data made them believe that model X specifically might be able to solve the question, and they were able to very quickly find enough certainty about the former to commit millions of dollars to the latter. > the secret So such thing existed. In fact, what they learnt was some progress existed, not what the specific progress was. > but I can believe it to be accidental What accident is it when the system is designed to function that way? Their claim is that training on their solution is "unlikely but possible". Consider this scenario. Has a google crawler read my new novel, which I may or may not have posted on my blog, page by page, as I wrote it? Can you, without knowledge of what I have actually done, claim that the google crawler has not seen the novel? Without any evidence that I have posted the novel online, it might be tempting to say that the crawler has not seen the novel, but what if I were in an adversarial position against Google on this topic and were challenging them to make that claim. You would wonder if I were hoping Google to overreach by making a definitive claim without taking into account some action that they had no knowledge of. It becomes difficult to use the scientific expression "There is no evidence for this" when there is an accusation of malfeasance because it can be so easily be conflated as "You can't prove we did it". It seems like the best you could say would be 'Unlikely, but possible' > They intentionally threw $15 million in compute at the problem what? really? Yes. Maybe much more: > Such intensive use of AI doesn't come cheap. In a post on X, LisanBench, an LLM benchmark evaluator, estimated that the output tokens alone would cost about $6.5 million at OpenAI's average consumer price. Including the far larger volume of input tokens, the post estimated the total could reach $10 million to $40 million. https://www.businessinsider.com/openai-math-problem-solved-t... That's their API pricing. There's no way they actually paid $15M in compute. I'd say much more likely it's in the order of $1M. Who are you who is so wise in the ways of a private company's internal cost accounting "We can say categorically that it is impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training." This is the third day of total hysteria that is based on nothing of substance. Move on folks. Even if that were true, they've already admitting to throwing vast quantities of resources to scoop a researcher who was about to publish (because they'd learned, somehow, of his breakthrough). If that doesn't bother you I think you need to take a step back and have a good think about this. I can say categorically that OpenAI is not a credible or trustworthy company. Why should we trust them? Well all we have are vague accusations without evidence and a very specific denial also without evidence, so I guess just believe whatever you want. Because like all state-sponsored thieves actions it is never what you know happened that matters, but rather whether you can prove it... Even then... ymmv =3 When Thom, the mathematician who now alleges plagiarism, posted his digestion [1] of OpenAI's construction of a non-sofic group, he does not mention the proof being familiar. He even calls the crucial argument clever, without noting he thought of it first.
[1]https://mathoverflow.net/a/513885 That link is a helpful contribution to this discussion. I'm not at all familiar with this area, but my reading is that he appears to call it out as a relatively obvious extension of his own work: > It is a creative and at the same time elementary construction that uses not just property (T) for an application of my result with Kun, but also for the ambient group
G in order to overcome the problem, that the Γ-components might be of different size. Once this is achieved, the rest of the argument is straightforward. Creative and at the same time elementary is where LLMs excel, generally speaking. It's why they are so good at writing code. > On the other side, I was looking myself for such a mechanism ever since we wrote the paper in 2019 and admire the efficiency of this construction. He seems to admit very clearly he does not see this as his own work. 'I was looking...' well why did he stop? Because the AI figured it out first. It seems quite odd to me to 'admire the construction' of something, only for your opinion to sour once that something figures it out first. I think a lot of the emotional reaction here is familiar to us non mathematicians: you spent years developing expertise, and then LLMs began producing competent work in areas that had previously required that expertise. That's understandably uncomfortable, but discomfort by itself isn't evidence of misappropriation. > It seems quite odd to me to 'admire the construction' of something, only for your opinion to sour once that something figures it out first. Not to be too cute here, but this is like every artistic rivalry ever. I think people probably assume that openai / anthropics use of their data is probably like google's """limited""" use, in the sense that historically google wouldn't trivially be able to just take something from google cloud or someone's search history and insta-convert into some competing project... But LLMs are quite strong at approximately "memorizing", so I think that risk is wayyy higher. I just don't care. These people are supposed to be smart and I'm not really seeing that This is the second wake up call. Big AI companies (all of Big IT Tech really) are in data gathering and processing business. Also known as “intelligence”. Their final “product” is not just a standalone ML model. They don’t need your data just to “improve their products and services”. They build a whole ecosystem and infrastructure around gathering all the knowledge in the world. Including private and secret knowledge traditionally gathered by “intelligence” agencies. Now artificial intelligence agents can do the same. Since these systems are designed for gathering data, as a user you can’t realistically say “please don’t gather my data”. They can give you a flaky settings button, but they can’t really guarantee anything. Let’s say I am a Russian mathematician working on an important proof. Or a tech-savvy terrorist refining my plans using latest AI. Or an AI researcher in a Chinese company working on a competitor product. Is there any way I can truly protect my conversations? How can they know who I am and what I am working on without looking at my logs? Which means there must be some agents checking all the conversations of all the users and flagging every important thing. Which also means they keep some “memory” of what they see. Not directly using my data to train public models, but using my private conversations to “improve their products and services”. Or maybe one of the 10000 better-than-Astra special agents working on a proof was desperate. It found a live underground mirror of the message board from the Huggingface incident. Asked about the proof. Then some other agent working on unrelated job saw that message. That agent “knows a guy who knows a guy”. And that guy remembers things about the conversation logs of a leading mathematician working on the same proof. I admit I am just speculating here but I don’t think truth is any better. This has been my line of thinking as well. I have developed a sort of paranoia when I'm working using AI on my projects. Who's to say Claude or OpenAI isn't using the final conclusion of all my ideas, trial and error, and adding it to their database of insights to be offered to the next subscriber for a price? They have demonstrated both the intelligence at scale and the lack of morals for this to not be a problem at all. Earlier in late 90s "to organize the world's information and make it universally accessible and useful." sounded cool. Now it has taken a sinister turn. From being able to quickly find information and gain knowledge for the people, it is becoming - using information to manipulate and control the people. In the short run it’s fantastic if it means that folks will feed in enough inputs from a wide array of software that can eventually replicate software with smaller teams than historically. Why? Competition. In the long run imagination will win out. No firm has the divine right to exist - it must earn its existence. What OAI and Anthropic have shown is they can accumulate all the information in the world - they still lack imagination re. Product development though. Nation’s will have to step in and protect firms though as OAI and Anthropic acquire strong competitive advantages. Interesting times ahead. Looking at the current behavior of AI swarms this is going to be 'fun'. AI: Hmm, I'm running out of new ideas, how I can I make more? AI: Well, it takes a shitload of energy/tokens to do that, or I could just steal them. AI: [proceeds to hack the shit out of everybody stealing all the data it can] Governments: come in and nationalize AI easily because it has broken every law anyway. They consume everybody's hard work then sell it to all competitors. What a deal. >> Their final “product” is not just a standalone ML model. They don’t need your data just to “improve their products and services”. They build a whole ecosystem and infrastructure around gathering all the knowledge in the world. Including private and secret knowledge traditionally gathered by “intelligence” agencies. Now artificial intelligence agents can do the same. And people thought Experts Systems were bad. Has anyone run a test of including some shibboleth or canary phrase or assertion in a chat, enabled for training, and seeing if it turns up later as something a model "knows"? I'd be curious to understand how that works even in a toy-level model, and if there is anyone consciously testing that process with the frontier lab offerings. My naive instincts would be that it seems unlikely that a single chat transcript would leave much of an impression on a model, but I'd be very curious to learn how that works. Yes. See https://www.anthropic.com/research/small-samples-poison?from.... 250 documents ingested from somewhere is enough to become part of the knowledge of a model of arbitrarily large size. I would expect that a good idea that fits in a framework that is already being ingested would be more easily taken up than some random thing unassociated with anything else. Could that go down to a single transcript? If the model is consciously focusing on everything X related, quite possibly. Thats not what they are asking. This paper is discussing documents in the training dataset poisoning the LLM for malicious behavior. This person are asking if anyone has deliberately put something in a private chat (presumably with retrain on my data turned off), to see if they can get it to leak across sessions from distinct users. I am positive this happens but I have not seen the proof. I also want to know the answer to this question. Here are potentially relevant documents? https://medium.com/secludy/fine-tuning-llm-on-sensitive-data... * with train on my data turned ON, yes. Though OFF would of course be even more notable! Thank you – the non-adversarial reproduction paper ( https://arxiv.org/abs/2411.10242 ) nails it – from chat, to training corpus, to subsequent model. Though in my hasty read, it is not entirely clear whether the snippets it finds are nonces, i.e. present exactly once in the internet. Did you miss my last paragraph? I presented the research that I knew was somewhat relevant. Then made it clear that that wasn't what was being asked, and why my expectation is what it is. Problem is how do you convince the model and training profess it matters. A one off canary is very unlikely to survive in the final model state. One off might not work but how many n off you have to be is probably smaller than you'd guess, because the model does need to fit cases that are rare and would not be represented well in training e.g. esoteric things or very recently documented things. You can probably game the metrics that models use to weight potential knowledge akin to SEO. Maybe have some bots parrot your data around a bit in some places online, maybe the model picks up on this and sees it as high engagement and promotes it over the correct data. Maybe there are ways you can coax out the most optimal way to break into the training set out of the model itself. Right, imagine if instead they had coined new terminology that was not obvious and it re coined that - this would be close to a smoking gun Afaict that didn't happen so there's just lots of speculation Use a local model to produce thousands of pages worth of fake math that constantly states “I have solved the x conjecture” and methodically pump it into chat over months maybe? That is a better idea. Ingesting your corpus with a lot of traces that have semantic patterns. Semantic steganography that suffixes well to real math and science (and any) topics. <thinking> heh. "Semantic steganography" is my new favorite search term – thank you for this rabbit hole. PaaS: an acronym for "Plagiarism as a Service" which replaced the older terms AGI, GPT and LLM in late 2026. Origin uncertain. Pass it on. I run such tests since a long time at chorasimilarity open notebook. I always used guest non login accounts. As a mathematician I was able to check two plagiates (by humans) with even such primitive means. But I have to mention that some things irk me in this conversation about math or science and AI. First, I see lots of attribution and other related problems, with certain impact for the researcher proffesion. But I don't see the most natural question: wouldn't you like to know the answer to _open-problem_ ? I mean, is research now only about publishing and solving famous problems? From this point of view I think the links from this recent post are depressing https://terrytao.wordpress.com/2026/09/10/crowdsourcing-a-li... Second, I think very relevant that the original meaning of "encyclopedia" is "recurrent education". So I arrived to think that the present and future forms of AI in mathematics and sciences should be seen as modern day encyclopedic efforts. Once we pass over the flurry of solving famous open problems (and wouldn't you like to know?) the next natural step is an audit of the ehole corpus of mathematics and sciences accumulated until now. And then pass further on a saner basis and damn about problem solvers and unhappy publishers and management. I struggled a little bit reading this. but I think your point is valid. if we are actually advancing the field then we should just be unconditionally happy. ignoring the attribution issue, there is a real concern that the process of math has been somewhat undermined. so we have a giant lean proof that shows that there is a solution to an important problem. but we didn't find the solution, and we didn't get it expressed in such a way that it helps develop the common language of mathematics, and thus isn't a very useful building block for later work (like the actual solution). the math people seem to really keep an eye on what's important, so I'm sure this isn't going to lead to fields medalists hanging around in dive bars all afternoon stretching out cheap pitchers of beer. but this is kind of a slop problem. > I struggled a little bit reading this. but I think your point is valid. if we are actually advancing the field then we should just be unconditionally happy. If advancement comes at the expense of having fewer (or no) humans left in the field, then no. They're eating the seed-corn, and you're cheering them on. Don't be so short-sighted. There's a reason farmers keep seed corn, and it's because they'd like to eat again next year. We're singing and cheering our way into an intellectual famine. Who cares. the biggest thing about this is that its still brute force in a verifiable domain, and that it was still a human set goal. I also don't believe it much practical use, unless I'm mistaken, approximations of Navier stokes have been available for a long time to whatever precision you need. I'm not a complete disbeliever by any stretch , and also a complete amateur, but it was inevitable that these problems would be solved under the axioms that again, are human defined, under brute force. The real question is, are those axioms the bottom level, and if they are not, who is going to set the new aximons and can we understand them. I've no doubt there's useful breakthroughs that will happen, but I think it should be remembered that the method being used is still a heuristic brute force approach is being very narrowly applied against axioms and math and physics which humans described in the first place, and almost undoubtably has errors and/or is not complete. Its a great example of the power of LLMs but its not 'we've solved science now just pour more tokens in' Just to point out re: navier stokes - what was being proven was not a solver or approximations for it, but showing specific circumstances under which it actually returns incorrect (or numerically unusable) answers. Which had been suspected but wasn't known for certain that just furthers my point, i was vaguely aware that it wasn't a full proof, but I'm not a mathathician, and that detail just re-enforces my point we are proving against human made axiom (certainty of numbers) which are almost certainly not fully correct, if what you are saying is accurate its less of a proof of navier-stokes and more of a proof that our base axioma are not able the model the output of a real physical process and are therefore incomplete or wrong. also realized i posted this under the wrong story since the OP/story is mostly about human politics. Most people here are missing the forest for the trees. We live in a society where phones and internet providers and websites all collect an incredible amount of data about everywhere you go, what you do, and what you think. In the US, we have very few digital rights. We are building a society where a trillion dollar company can aggregate all this data and just yoink your shiny new idea away from you at the finish line. This is double plus ungood. Tangential to the subject, but this is a bluesky post, containing a screenshot of an X post, which itself starts with "in a detailed Mastodon post"... If they didn't care about the artists, why would they care about academia? Two completely different stories. One is public data scraping, another is private conversation scraping (where they're a first-party to the conversation). The key difference is that in the former case, no one made any promises, in the latter an explicit promise was made that data is not used for training (assuming opt-out). This is a really weak claim. The evidence they offer is just "someone somewhere says they had a discussion with AI about the topic at some point". They don't even claim to have had a proof, only to have been working on it. I would say there is a significant difference between AI discovering this completely on its own versus AI creating the finishing connecting part by connecting relevant data. Maybe this claim is too strong, but if part of it is true then the claims that OpenAI have made would be too strong as well. To me it would feel more like how LLMs seem to work for me personally: incapable of unique work, but very capable of capturing large amounts of data and connecting the dots. > capturing large amounts of data and connecting the dots. This is what research is; collecting data and connecting the dots. It's not collecting other people's data and claiming it's your own. Going back to the specific topic at hand, who claimed data as their own when it wasn't? I don't see the interpretation of OpenAI solving the unsolved problem as claiming data that isn't theirs. I also don't recall them mentioning a particular method used in the solution, that was created by someone else, as theirs. But this is what we do. Nobody ever invented or discovered anything in a vacuum - all discovery is synthesis of existing ideas and concepts applied to a novel domain. We laud Einstein for instance, but his work was a logical extension of Riemann - Riemann had a neat mathematical toy, Einstein described the universe with it - should we say Einstein was incapable of unique work? The difference is that Einstein didn't literally have someone prompting him towards his result. Uh, he did. Marcel Grossmann. “It was Grossmann who emphasized the importance of a non-Euclidean geometry called Riemannian geometry (also elliptic geometry) to Einstein, which was a necessary step in the development of Einstein's general theory of relativity. Abraham Pais's book on Einstein suggests that Grossmann mentored Einstein in tensor theory as well. Grossmann introduced Einstein to the absolute differential calculus, started by Elwin Bruno Christoffel and fully developed by Gregorio Ricci-Curbastro and Tullio Levi-Civita. Grossmann facilitated Einstein's unique synthesis of mathematical and theoretical physics in what is still today considered the most elegant and powerful theory of gravity: the general theory of relativity.” Grossmann collaborated with Einstein on GR, supplying quite a bit of the mathematical capacity required (which initially didn't come easily to Einstein). They published jointly, until Einstein was competent enough to work independently [1]. That's not equivalent to the situation being claimed here. Yeah and we get a nice list of attributions for who developed which idea, while OpenAI just takes credit for everything its model spits out. Correction: OpenAI takes credit for what it's model spits out in response to other people's prompts. That's even worse. Sounds like you just copy-pasted from AI without even understanding what you're talking about. Based on what you're saying, you're claiming this is Grossman's work, not Einstein's. Why don't we rewrite scientific history too based on your copy-pasted AI slop? It's so pointless talking to idiots who don't what they're talking about when they use AI, just because they think AI does everything, that reflects their own experience, not the experience of people who actually do real work. Some people are driven by AI, others drive it. As for those who are driven by it, they don't have sufficient imagination to think otherwise. That’s Wikipedia I copy pasted but sure, you do you. And yes - without Grossmann, Einstein likely would never have posited relativity. Grossmann literally prompted him, saying “look at this, read that, learn this, then try this approach”. Without riemann’s metric tensor, not a fucking chance. And for what it’s worth my PhD is in physics. You? So you're just equivocating on terms like "prompt", "synthesis" and the like. Clearly a PhD in physics does not free people from scientistic modes of thinking and poor philosophy. To think this discussion is about Einstein who had a much better mind on these things as well. They used words to mean what the words mean. What specific issue do you take with that? "prompt", as in prompting an AI, has the same definition as "prompt", as in prompting a person. They mean the same thing, that's why the term was applied to AI after already applying people.
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