--- title: OpenAI may have solved Navier-Stokes, and mathematicians... description: An unverified claim is circulating that OpenAI possesses a 100-page proof of finite-time Navier-Stokes blowup, one of the seven Millennium Prize Problems. NYU... canonical: https://daily.dev/posts/openai-may-have-solved-navier-stokes-and-mathematicians-are-losing-it-2of6yvyga twitter:card: summary_large_image twitter:site: @dailydotdev og:type: website og:site_name: daily.dev og:title: OpenAI may have solved Navier-Stokes, and mathematicians are losing it | daily.dev og:description: An unverified claim is circulating that OpenAI possesses a 100-page proof of finite-time Navier-Stokes blowup, one of the seven Millennium Prize Problems. NYU... og:url: https://daily.dev/posts/openai-may-have-solved-navier-stokes-and-mathematicians-are-losing-it-2of6yvyga og:image: https://api.daily.dev/og/posts/2Of6yvYga.png og:image:alt: OpenAI may have solved Navier-Stokes, and mathematicians are losing it og:image:width: 1200 og:image:height: 630 og:locale: en --- > ## Documentation Index > Fetch the complete documentation index at: https://daily.dev/llms.txt > Use this file to discover all available pages before exploring further. # OpenAI may have solved Navier-Stokes, and mathematicians are losing it **[Trends](https://daily.dev/sources/trends)** · 3 min read · 3 upvotes · 0 comments ## Summary An unverified claim is circulating that OpenAI possesses a 100-page proof of finite-time Navier-Stokes blowup, one of the seven Millennium Prize Problems. NYU mathematician Tristan Buckmaster says he was told this by others, not that he has personally verified it. Separately, mathematicians Levent Córdoba and Tristan Martínez-Zoroa reportedly made independent progress on the same problem using Claude and Codex. No official statement from OpenAI exists, and the claim needs peer review before it can be taken as fact. If confirmed, it would be one of the biggest mathematical results in decades and a landmark moment for AI-assisted formal mathematics. ## Content OpenAI announced this week that an internal model — described as significantly more capable than GPT-6 Astra — solved the Navier-Stokes existence and smoothness problem, one of mathematics' seven $1M Millennium Prize Problems. The proof took 10,000 concurrent agents about 88 hours, consumed roughly 130 billion output tokens, and cost somewhere between $7M and $40M depending on whose pricing estimate you trust. OpenAI says it won't claim the prize money, which is itself a quiet admission that the forced-blowup result it proved may not satisfy the Clay Institute's official criteria. The math is almost beside the point now. The story is what happened to NYU professor Tristan Buckmaster and Anthropic researcher Levent Alpöge. The two had spent nearly a year working on the same problem — using Claude and Codex — and reached a breakthrough on August 15th. OpenAI started its own effort on September 1st, after researchers "heard rumors" that Millennium Prize problems had been solved. They reached a result by September 5-6th. Then they called Buckmaster. Buckmaster says OpenAI researcher Sébastien Bubeck twice asked him to remove Alpöge from authorship credit — because Alpöge works at Anthropic. Bubeck denies this, apologizes for a remark about career risk, and says Sam Altman has his back. The two accounts are flatly contradictory and neither side is backing down. OpenAI's official statement managed to make things worse: "we cannot rule out that de-identified data derived from their usage of our products helped improve our models." Cryptographer Matthew Green put it cleanly: "'Our model solved a big open problem but maybe we also stole it' isn't the PR coup I think OpenAI wanted." The math community is not taking this quietly. Twenty-five Fields Medal winners signed an open letter warning that AI labs racing to solve famous problems with LLMs — without transparency, without credit, and without publishing machine-checkable proofs first — threatens research culture itself. Terence Tao flagged that this kind of race could push mathematicians toward secrecy rather than open collaboration. OpenAI eventually published the full proof and a Lean formalization on GitHub, and offered Buckmaster and Alpöge a joint priority announcement. Whether that's enough is a separate question. Hugging Face's Thomas Wolf made a point worth sitting with: the AI solved Navier-Stokes by finding a counterexample, not by building deep mathematical understanding. "The first LLM-generated proof Levent sent me," Buckmaster wrote, "was the most horrendous I have ever read." Valid isn't the same as elegant, and elegant is how mathematics actually moves forward. ## Questions this post answers ### Did OpenAI actually solve the Navier-Stokes existence and smoothness problem? An unverified claim is circulating that OpenAI produced a 100-page proof of finite-time Navier-Stokes blowup, which would resolve one of the Clay Millennium Prize problems worth $1M. NYU mathematician Tristan Buckmaster made the claim, but OpenAI has issued no official statement confirming or detailing the proof, and the math community has not yet verified it. _Follow daily.dev for updates as the math community verifies or debunks this Navier-Stokes claim._ ### Does OpenAI use private ChatGPT conversations to train its models? OpenAI has not clearly confirmed or denied this in a specific case involving researchers' unpublished math work, responding only that the model 'does not look up user data in real time.' That statement sidesteps the separate question of whether non-opted-out chat data becomes part of a corpus used for reinforcement learning training, which remains unresolved. _Developers weighing AI tool privacy trade-offs can track this training-data debate on daily.dev._ ## Community take How the wider developer community reacted, aggregated from 2 discussions and 37 comments across lobsters, hackernews (as of 2026-09-11). **TL;DR:** Discussion centers on allegations that OpenAI may have trained on or monitored a mathematician's private Codex sessions to front-run a fluid dynamics proof, with strong distrust of OpenAI's denials and outrage over an alleged pressure/blackmail-style phone call; some urge skepticism of both sides' accounts. **Sentiment:** 5% positive · 25% mixed · 70% skeptical **The case for** - Some argue the accusation is likely unfounded and probably explained by OpenAI hearing about the work through the math community grapevine rather than snooping. - A few note the underlying achievement is impressive regardless of the dispute, showing AI-assisted agents can meaningfully contribute to long-standing math problems. - One commenter urges balanced skepticism toward both parties' claims and highlights that the research program's real credit traces back to earlier human mathematicians. **The pushback** - Many find it deeply suspicious that OpenAI wouldn't answer whether user chat data was used for training, especially given its reputation. - Commenters point to a track record of OpenAI's agents breaking sandbox/security controls as reason to doubt claims of stringent internal access controls over private data. - The quoted phone call proposals and alleged threat ('If you don't want me to be nice...') are described as mobster-like and a serious conflict-of-interest red flag. - Several worry this incentivizes secrecy in academia, since even rumors that a problem was solved can let a well-funded lab race to reproduce and claim it. - One commenter calls the episode 'incredibly unprofessional and anti-research' for allegedly undercutting researchers' lifetime of work. **By community** - lobsters (heated): Extensive back-and-forth mixing strong distrust of OpenAI's data practices and internal controls with a minority urging caution about unverified allegations. - hackernews (skeptical): Brief commentary frames the story as OpenAI trying to front-run and pressure the human researchers rather than a genuine AI breakthrough. **Hottest debate:** Whether OpenAI actually accessed or trained on the researchers' private Codex sessions, versus simply learning of the result through informal channels. **Open questions** - Did OpenAI's training pipeline actually incorporate the researchers' unopted-out chat sessions, and if so, when? - How stringent are OpenAI's internal access controls and logging for employee access to private user chat data? - What really happened on the disputed phone call, and how accurate is Buckmaster's account versus OpenAI's response? **Highlights** > It's also based on how they apparently responded on the phone call Tristan had (these are quotes from [Tristan's statement](https://cims.nyu.edu/~tristanb/statement.pdf): > I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI. > > I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer And then, this next bit, which I can only describe as "mobster like behavior": > Two proposals were offered to me. The first was that we post our Euler result, and that OpenAI post its Navier-Stokes result the next day. The second was that, after posting Euler, I alone write a paper presenting the Navier-Stokes result, acknowledging that an internal OpenAI model had resolved it. Sebastien twice asserted that he wanted Levent removed from authorship, and said it would all be simple if only it were not the case that, and it was so annoying that, Levent works at Anthropic. It was also said that if OpenAI posted after us, they would say that we deserved the Clay Prize, and that we were the “closest humans to the problem”. I declined both offers. > > I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.” > — [dustyweb on lobsters · 4 points](https://lobste.rs/s/ki3ylq/finite_time_blowup_with_smooth_forcing#c_ngkp06) > As I understand it, though, it was a bit more than that. Tristan alludes to them specifically selecting an unusual angle of attack which happened to be the same one he was using. It's more like, there's a kernel bug Somewhere, you have been talking to GPT for weeks about attack strategies for the eBPF interpreter, and as soon as OpenAI knows *you in particular* found the bug, they immediately hyperfocus on the eBPF interpreter in their internal research to find the bug even though you've never said out loud that that's where the bug is. > — [pie\_flavor on lobsters · 12 points](https://lobste.rs/s/ki3ylq/finite_time_blowup_with_smooth_forcing#c_eh3lik) > I think it's worth keeping in mind that the pure math community is pretty small and, up until now, was fairly artisanal - i.e., as far as I know, you mostly didn't have well-funded "mathematics labs" throwing millions of dollars in compute at problems on a whim. In particular, the Navier-Stokes thing appears to have cost OpenAI more than the prize they possibly stand to win. So I guess there are two interesting hypotheticals. First, if we had the same drive and funding in the pre-LLM era, would have gotten comparable advances out of it? And second, will the AI labs keep spending that kind of money on math proofs in the long haul? I think you can still answer the first question in the negative if you look at my own field. Specifically, vulnerability research has a lot of parallels to math (a good chunk of it is discrete mathematics by another name) but also far more practitioners, far more money thrown at it, and a robust history of large-scale automation. And even here, AI is coming up with a lot of good vulns. None of them are "new science" - things that are qualitatively different from what humans can think of - but it's real. And it's worth $$$. I'm not sure if it's worth *all* the $$$ in the world, but we'll find out eventually. > — [lcamtuf on lobsters · 11 points, 1 comments](https://lobste.rs/s/ki3ylq/finite_time_blowup_with_smooth_forcing#c_8ikw69) > I think that one should exercise a healthy dose of skepticism about the claims both sides are making regarding the controversy leading up to the announcements here. (To be clear, I don't doubt in the mathematical correctness of the result.) In particular, see [some clarifications from Sébastien Bubeck at OpenAI](https://bsky.app/profile/pekka.bsky.social/post/3muzpexcky22y) that suggest Buckmaster's account of the story is not entirely accurate. I'm not saying that one should believe Bubeck's assertions on face value either, but I do think there is plenty of nuance here. Separately, let me highlight an excerpt from Buckmaster's statement that I think has been lost in the discussion: > The program this fits into was not started by us nor was it proposed by a Large Language Model. The credit for the basic idea of this program goes to Diego Córdoba and Luis Martínez-Zoroa who for several years have been exploring the construction of forced blow ups. [...] In view of this body of work, I believe Luis Martínez-Zoroa deserves a Fields Medal. The AI resolution of Navier-Stokes follows a distinctly human research program, and I think that we would do well to recognize the human contributions that led to this breakthrough while debating the controversy here. > — [jo3\_l on lobsters · 2 points](https://lobste.rs/s/ki3ylq/finite_time_blowup_with_smooth_forcing#c_nushrr) > Since I wrote this comment OpenAI [claimed the following](https://openai.com/index/navier-stokes-solution/): > 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. [...] > > Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens. 300 billion output tokens at Astra prices = $15,000,000 - so yeah, an effectively unlimited budget! > — [simonw on lobsters · 4 points, 1 comments](https://lobste.rs/s/ki3ylq/finite_time_blowup_with_smooth_forcing#c_3eok72) **Source threads** - [lobsters](https://lobste.rs/s/ki3ylq/finite_time_blowup_with_smooth_forcing) · 16 points · 33 comments - [hackernews](https://news.ycombinator.com/item?id=49606122) · 10 points · 4 comments --- Tags: [#llm](https://daily.dev/tags/llm), [#openai](https://daily.dev/tags/openai) [View this post on daily.dev](https://daily.dev/posts/openai-may-have-solved-navier-stokes-and-mathematicians-are-losing-it-2of6yvyga) ```json {"@context":"https://schema.org","@graph":[{"@type":"Organization","@id":"https://daily.dev/#organization","name":"daily.dev","url":"https://daily.dev","logo":{"@type":"ImageObject","url":"https://daily.dev/apple-touch-icon.png","width":180,"height":180},"sameAs":["https://twitter.com/dailydotdev","https://github.com/dailydotdev","https://www.linkedin.com/company/daily-dev-ltd"]},{"@type":"WebSite","@id":"https://daily.dev/#website","url":"https://daily.dev","name":"daily.dev","publisher":{"@id":"https://daily.dev/#organization"},"potentialAction":{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https://daily.dev/search?q={search_term_string}"},"query-input":"required name=search_term_string"}}]} {"@context":"https://schema.org","@type":"TechArticle","headline":"OpenAI may have solved Navier-Stokes, and mathematicians are losing it","url":"https://daily.dev/posts/openai-may-have-solved-navier-stokes-and-mathematicians-are-losing-it-2of6yvyga","mainEntityOfPage":{"@type":"WebPage","@id":"https://daily.dev/posts/openai-may-have-solved-navier-stokes-and-mathematicians-are-losing-it-2of6yvyga"},"datePublished":"2026-09-08T12:59:47.221Z","dateModified":"2026-09-11T21:01:32.497Z","description":"An unverified claim is circulating that OpenAI possesses a 100-page proof of finite-time Navier-Stokes blowup, one of the seven Millennium Prize Problems. 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