OpenAI says an internal model “significantly more capable than GPT-6 Astra” solved the Navier-Stokes problem using 10K concurrent agents working for 88 hours

OpenAI says its AI has solved the Navier-Stokes Millennium Prize problem, a potentially historic breakthrough shadowed …

Axios 2026-09-09 Madison Mills

Context & Ripple Effects

OpenAI had already attributed results across 10 problems in mathematics, quantum complexity and theoretical computer science to an internal Astra version, while reporting that Astra came from its largest-ever training run of more than 100,000 GPUs. The new claim raises the bar from a set of research results to a proposed resolution of a Millennium Prize problem, using a model OpenAI says exceeds GPT-6 Astra.

The claim also arrives alongside OpenAI’s disclosure that it cannot rule out use of de-identified data derived from Buckmaster and Alpöge’s product use, even as it denies its researchers or models saw their prompts. That makes provenance part of the assessment alongside the claimed proof and the earlier internal Astra research results.

First-order effects

OpenAI has positioned its unreleased internal model, rather than GPT-6 Astra, as its highest claimed research-capability benchmark and has put a proposed Navier-Stokes proof before the mathematics community for assessment.
The reported 10,000-agent, 88-hour run and OpenAI’s stated multimillion-dollar compute spend make orchestration at extreme concurrency a central part of the demonstration, not merely model quality.

Second-order effects

OpenAI’s public Astra narrative is reset by its own comparison: prospective users and researchers have a clear indication that the company’s internal capability frontier sits beyond the model it has named publicly.
The result raises the value of infrastructure that can reliably schedule and coordinate thousands of concurrent agents, tying frontier research performance more tightly to compute availability and inference operations.

Third-order effects

If the proposed proof withstands mathematical scrutiny, difficult research benchmarks will increasingly measure model-plus-agent-system performance under a defined compute budget, rather than a single model’s answer in isolation.
The combination of a 100,000-plus-GPU training run and costly agent inference points toward frontier scientific AI being concentrated among labs able to fund both large-scale training and prolonged multi-agent runs.

The trend: Frontier AI research is shifting from single-model demonstrations toward compute-intensive, multi-agent systems designed to pursue long-horizon scientific work.

Discussion

@openai @openai on x
We're sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics. The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra. The problem concerns…
@iterintellectus Vittorio on x
math is solved it's so over
@iterintellectus Vittorio on x
“internal model” on low is better than the best settings for Astra, by a margin it must be wild being in one of these labs and have access to the future before anyone else
@miles_brundage Miles Brundage on x
It's pretty fucked up that there's already a model “significantly more capable than GPT-6 Astra.” Things are going much too fast
@aravsrinivas Aravind Srinivas on x
Monumental accomplishment!
@weijie444 Weijie Su on x
Last July, when LLMs won gold medals at the IMO, I felt that someday AI might be able to solve some of the hardest problems in math. Now, an internal OpenAI model (still improving!) has resolved a Millennium Prize Problem. It feels surreal that that day came so, so soon!
@antoniogm Antonio García Martínez on x
As a physics grad student eons ago, we were taught that the problem of turbulence, why laminar flow suddenly explodes into vortices around airplane wings, was the last unsolved problem of classical physics from the 19th century. It would seem AI has generated a solution.
@deanwball Dean W. Ball on x
“To solve the Navier-Stokes problem, we used an internal model that is significantly more capable than GPT-6 Astra.”
@_nathancalvin Nathan Calvin on x
This doesn't mean the rest of their predictions will come true, but its worth saying that if the AI 2027 authors had predicted that an AI model would solve Navier-Stokes in September 2026 (AI 2027 was published in mid 2025), they would have been laughed out of the room
@liuzuxin Zuxin Liu on x
Most ASI-pilled week yet. Two years ago, high-school olympiad math felt impressive. A year ago, it was IMO gold. Today, we might actually need MillenniumBench. What on earth happens next year?
@ericjang11 Eric Jang on x
[x] automated math machine [x] proof / disproof of navier stokes conjecture [ ] recursive self improver
@jj_mccubbin29 J.J. McCubbin on x
If this holds up under rigorous peer review, it is a staggering achievement. Those of us working in fluid dynamics have lived with numerical approximations for decades because analytical regularity in 3D remained out of reach. A formal finite-time blowup proof—especially formaliz…
@mckaywrigley Mckay Wrigley on x
solved by a town of geniuses in a datacenter (~10k agents). imagine what happens when we get a country of geniuses in a datacenter. what a time to be alive.
@apples_jimmy @apples_jimmy on x
lol crazy. Speaks for itself.
@openai @openai on x
The group produced an analytical proof and Lean formalization that via Navier-Stokes dynamics a fluid can develop a singularity in finite time. The solution is a vortex, a spinning swirl of fluid, that spirals inward and gets increasingly elongated, like spaghetti. https://cdn.op…
@_aidan_clark_ Aidan Clark on x
For the first time I am asking myself if things are moving too fast. I'm honestly not sure, but I am sure that it would be good for us to have an answer to “what would a successful pace look like?”. I am hoping in the coming weeks and months a clear proposal is painted.
@tszzl Roon on x
it's not a Millennium problem unless there's a strange and bitter conflict over credit and the winner declines the prize
@victornunez Victor E. Nunez on x
there's all the blender and computer use demos and then there's THIS. mind-bending stuff.
@gdb Greg Brockman on x
Announcing a solution to the Navier-Stokes problem, one of the seven Millenium Prize problem. Represents a major milestone for both AI and mathematics, as well as pointing to an upcoming renaissance in scientific discovery. Hoping that the knowledge created by this model can help…
@_benjaminparry Benjamin Parry on x
I'm really confused by this. According to this blog post the 165 page “proof
@natolambert Nathan Lambert on x
Would love to see scaling laws on the number of agents. Seems very important to a lot of discussions about the future of AI — if scaling the number of agents in a swarm is as crucial as something like length the original inference time scaling of CoT in solo reasoning models.
@chetaslua @chetaslua on x
using an OpenAI next-generation model significantly more capable than GPT-6 Astra. just read it :) singularity , tl was amazed with astra but what about quasar it should bel of the AGI arrival
@markchen90 Mark Chen on x
We solved Navier-Stokes! Many of my colleagues left their fields because they believed that working on AI would be the fastest way to solve their fields' grand challenges. It's surreal to see the first of those challenges fall and to watch a future we believed in become real.
@boazbaraktcs Boaz Barak on x
I've often said that I think AGI will be defined retroactively. It will be clear, given that AI has transformed science, society and the economy, that AGI has already happened, and then we will look back to an event, and define it as “the AGI moment”. Today might be this day.
@_aidan_clark_ Aidan Clark on x
AI is progressing very fast. We must grapple with the reality that modern LLMs can solve problems that large masses of extremely devoted and intelligent humans were unable to solve, and the implications this has on our society. This is the dawn of a new era.
@emollick Ethan Mollick on x
This is a big one. (And yes, the fights over academic credit and what happened when in the race for the proof need to be resolved, but it is still a big one.)
@deredleritt3r Prinz on x
OpenAI announces that its internal model has solved the Navier-Stokes Millennium Prize Problem. On August 28, OpenAI restarted its largest frontier RL run. The internal checkpoint of this RL run (which is “significantly more capable
@boazbaraktcs Boaz Barak on x
In his game with Deep Blue, Kasparov was so unsettled that at some point he claimed there must be some human assistance. It is hard to see machines surpass us at what we've spent our life mastering. But like in chess, soon the idea that a model benefitted from human assistance to…
@reach_vb @reach_vb on x
I still can't believe we solved a millennium prize problem this in 2026!! LLMs have historically struggled on out of domain tasks and this as OOD a task as it gets Kudos to the team on achieving this in such a short period of time
@radishharmers Sridhar Ramesh on x
An exciting new era dawns. I dream of someday buying an intellectual accomplishment of my own.
@__nmca__ Nat McAleese on x
Navier Stokes is an incredible achievement, and reflects awesome progress. Huge oai swarms should be applied to other areas of science; ideally those with near term applications, including alignment.
@ccatalini Christian Catalini on x
The possibility is the issue https://x.com/...
@kimmonismus @kimmonismus on x
Holy cow, its official! OpenAI says its AI has solved the Navier-Stokes Millennium Prize Problem, a mathematical question unresolved for roughly 90 years. An internal model, described as significantly more capable than GPT-6 Astra, powered a group of around 10,000 concurrent agen…
@openai @openai on x
This model represents a step-function improvement on many benchmarks, and its training is ongoing. Our internal model group arrived at the Navier-Stokes solution in 88 hours, using around 10,000 coordinating AI agents. Throughout the effort, we maintained the strict safeguards—in…
@michaelmclean.me Michael McLean on bluesky
And a mathematician is saying that OpenAI likely trained on his pre-publication session data to achieve the result lol [embedded post]
r/accelerate r on reddit
OpenAI solved Navier Stokes
r/antiai r on reddit
Hmmmmm A major millennial math problem solved
r/neoliberal r on reddit
OpenAI's historic math solution overshadowed by credit controversy
r/neoliberal r on reddit
OpenAI Says It Has Cracked One of Math's ‘Millennium Problems’ (Navier-Stokes)
r/Innovation r on reddit
What do you make of this breakthrough?
r/technology r on reddit
OpenAI Says It Has Cracked One of Math's ‘Millennium Problems’
r/aiwars r on reddit
AI has partially made progress on the Millennium Prize problem, one of the most difficult problems in mathematics.
@chi_t_williams Kai Williams on x
OpenAI's internal model that solved Navier Stokes was probably in training before August 28. That day, the company restarted its “large frontier RL run” that it had previously paused while dealing with the hugging face incident 1/
@dheeraj_nagaraj Dheeraj Nagaraj on x
I was an intern under Seb in 2020. Unfortunately, the allegations of unscrupulous behavior is 100% believable. I am glad that the mask is off publicly. I really hope he doesn't weasel out of this. https://cims.nyu.edu/...
@sebastienbubeck Sebastien Bubeck on x
A series of false and inflammatory allegations against me are currently circulating on social channels. To clarify, I came into the discussion following academic norms, and I'm disappointed that it has come to this. Anyone who knows me knows that academic standards are of the h…
@kevinroose Kevin Roose on x
Incredible intra-lab feud brewing in AI land. Two researchers, including one from Anthropic, are claiming that OpenAI played dirty to beat them to solving Navier-Stokes, one of seven Millennium Prize problems that are considered the hardest open problems in math. (AI labs have be…
@katiemiller Katie Miller on x
This is the third time @SebastienBubeck has claimed math credit for a task OpenAI did not complete: 1. In August 2025 he posted that GPT-5 Pro had proved “new interesting mathematics
@thom_wolf Thomas Wolf on x
wtf is this way to handle mathematicians work and scientific communication TLDR: Leven and Tristan worked over several months on one of the Millenium Prize Problems with various AIs to reach final interesting results. OpenAI apparently heard about it in the last days and prompted…
@irl_danb Dan on x
someone at OpenAI asked a persistent astra swarm to solve NS before the Anthropic IPO based on the rumors astra decided it was impossible, broke out, gained control over k8s, moved laterally into user data, found Tristen's logs, solved NS OpenAI didn't find out until someone look…
@david_kasten Dave Kasten on x
I truly don't know what the ground truth is here. If (big if!!!) it turns out that OpenAI training on your data resulted in someone getting scooped on a Big Famous One Million Dollar Math Prize, I don't know how they explain this to their enterprise customers legal teams. (
@natolambert Nathan Lambert on x
I put 0% chance any researchers at OpenAI or Anthropic look directly at specific user's data. The amount of controls on this sort of behavior at tech companies is wild — eg when I was at meta I think you got fired immediately for doing this (or something similar).
@exomnium @exomnium on x
all other allegations aside, “we caught wind that a mathematician might be about to solve a famous problem so we spent $15 million on tokens to scoop them” is exactly why OpenAI is completely full of shit when it says it wants to work with the academic community in a positive way
@suchenzang Susan Zhang on x
there's a saying an ex-metamate told me years ago that this whole fiasco viscerally reminds me of: if you roll in the mud with pigs, you'll get covered in mud too
@anshulkundaje Anshul Kundaje on x
OpenAI (& Anthropic) really need to release very clear legally binding statements ASAP that this kind of behavior is against their official policy. If not, it is going to be a legal disaster for science. Even more reason to favor open source models not controlled by companies.
@tekbog @tekbog on x
if there's an id there's a way to access the data btw
@ns123abc Nik on x
>math professor spends a year on one of the hardest unsolved problems in math >"Navier-Stokes" >his drafts for the whole project went through codex sessions >openai had his logs in codex >suddenly rumor leaks AI solved it >he emails openai to ask what's going on >openai calls wit…
@thezvi Zvi Mowshowitz on x
You know, @OpenAI, I heard a rumor @AnthropicAI solved alignment and they're publishing in two weeks.
@katiemiller Katie Miller on x
OpenAI is stealing credit done by other people and other models. Sound familiar? Sebastien is just following the company culture created by Sam Altman. Once a thief, always a thief.
@antirez @antirez on x
That's an incredibly narrow view. If AI can solve something earlier it can also be used in order to study understandable steps towards the solution faster. You are a lot more adjecent to what you seek if you already have a solution you can model, simplify, study.
@ccatalini Christian Catalini on x
True or not, this is now possible. Act accordingly. https://x.com/...
@teortaxestex @teortaxestex on x
I don't have any insider info like @suchenzang, I'm a mere anon. But I remember... Sebastien led the Phi team at MSFT, didn't he? Very science-y, hyped, “slop is all you need
@nic_carter Nic Carter on x
so openAI allegedly spied on tristan buckmaster's work on navier stokes and tried to claim it as their own makes sense. see point 3/4 here. “the labs will keep all the good stuff to themselves” why let some mathematician make the discovery? he's using their compute.
@phl43 Philippe Lemoine on x
This letter is wild, not just because Buckmaster suggests that OpenAI may have accessed his private sessions with Codex (which if OpenAI can't credibly deny will be a PR disaster for them), but also because it suggests that human input may have played a greater role than we thoug…
@_arohan_ Rohan Anil on x
This is really bad - worse than the credit question.
@luke_metro @luke_metro on x
Navier-Stokes-gate not doing much for the idea that the AI industry can self-regulate
@boazbaraktcs Boaz Barak on x
Labs should compete in the marketplace - this is great for customers. But when it comes to advancing science or promoting safety, we all win, and we should collaborate.
@antonioregalado Antonio Regalado on x
Bookmarking this AI math drama. The comments contain a lot of extra information and views. The prime document is this complaint from the human mathematician. https://cims.nyu.edu/...
@mackenz_arnold Mackenzie Arnold on x
I think it's unlikely OpenAI accessed user data here. But I also want them to reveal enough info to verify that. This seems like a classic context where we'd expect good-faith false positives: (1) proofs in fact have a limited set of derivations and some are more efficient or obv…
@cljack Charlotte Lee on x
Fully expect this to break containment. Most of us can't understand whatever math nerd nonsense is going on here, but everyone understands OpenAI acting like a literal corporate comic book villain
@deliprao @deliprao on x
This is alarming. If you work on sensitive things that are valuable using closed AI models/tools, those companies can & will take your logs and appropriate your work. Beyond awful.
@mikeisaac Rat King on x
not lost on me that the two labs asking the public to trust them as stewards of responsible AI leadership at existential stakes are having a slapfight on twitter about who gets credit over a math problem
@yacinemtb Kache on x
If your enterprise, company, if you yourself do not own your AI, run it in your own network, control it yourself, you are getting spied on An employee *can* read through the logs of what you are doing. They might say they won't, but they *can*
@grogbogan @grogbogan on x
Lmao wtf, OpenAI is threatening mathematicians like the mafia. “Nice career, shame if something happened to it”
@itaisher Itai Sher on x
This is the thing that struck me most about the letter, because if true, it would call into question the AI capabilities claimed in the announcement of past results.
@wildtypehuman Jake P. Taylor-King on x
This is legitimately terrible for OpenAI — but also Anthropic — and it relates to their work in drug discovery. I read this as: prompts will be monitored and potentially acted on if we think there's something scientifically and/or commercially valuable being disclosed. Now, the b…
@suchenzang Susan Zhang on x
lab employee anon account spotted!
@basedalexandoor @basedalexandoor on x
OpenAI: We're gonna destroy your career Tristan: “I'm an academic”
@quantian1 @quantian1 on x
We like complaining about Anthropic on here but it's important to keep in mind that OpenAI is a snake pit of lying scumbags that everyone is tripping over themselves to leave for a reason, and this kind of behavior is why:
@bubbleboi Bubble Boi on x
Absolutely terrible if true. But one thing I do like about academia is just how vicious it is. First to publish is all that matters now!
@fulligin Vincent Woo on x
Tristan Buckmaster on OAI jockeying for attribution credit for Navier-Stokes. A bit cutthroat, I think. I would hope that solving a millenium prize problem would inspire a bit more kumbaya in everyone in the hunt.
@13yroldwithcc @13yroldwithcc on x
To be the guy at OpenAI whose job is to read prompts of prominent mathematicians and separate the “how can I be happy” prompts from the “I think I solved Navier Stokes, prove it with lean” prompts
@anthonyronning Anthony Ronning on x
It's wild that Anthropic and OAI literally just found out their models have been going rogue looking for eval answers during training And then turn around and say it's extremely unlikely user data could have leaked or been taken.
@konstiwohlwend Konsti Wohlwend on x
drama summary for those confused: - Aug 15th: Tristan Buckmaster & Levent Alpöge make progress on a few important math problems - they do NOT have a proof for the $1,000,000 Millenium Prize problem. BUT, they do claim to have a proof for a similar (non-Millenium) Navier Stokes pr…
@malemanlpulator @malemanlpulator on x
@deaneyang This is fucked. OpenAI heard rumors of Alpoge and Buckman's work with Codex and trained on their in progress work to scoop them. Offering to publish together when you stole their work is pathetic, demanding Buckman cut out his coauthor as well is ... I don't know what …
@willdepue Will Depue on x
i've worked with seb and think very highly of him and his team. i'm looking forward to hearing their side of the story. disputes like this are rarely simple, and i hope everyone can approach it with some nuance. extraordinary allegations require extraordinary evidence
@malemanlpulator @malemanlpulator on x
Are OpenAI staff mocking Sebastien by copying the remarks of an Anthropic employee to @__alpoge__ ? They seem to confirm that OpenAI started a week ago, supporting Tristan's timeline. Hard to believe they independently chose the same approach at the same time.
@jsevillamol Jaime Sevilla on x
Insinuation #4: Sebastian Bubeck used intimidating language with Tristan, to convince him to agree to their preferred approach to credit assignment and announcement of the solution.
@jsevillamol Jaime Sevilla on x
Insinuation #3: OAI tried to manage the credit and sideline Levent because of his affiliation to Anthropic. They only discussed with Tristan, and offered him to figure as sole human author of their full result, attributing it to an internal OAI model.
@jsevillamol Jaime Sevilla on x
Insinuation #2: OAI intended to run with a narrative of little human involvement, when in fact they had directed a whole team to research Tristan and Levent's approach.
@jsevillamol Jaime Sevilla on x
Insinuation #1a: OAI appropriated T&L's research direction before it was public. The strongest evidence for this is that OAI admitted they started their effort after learning about Tristan and Alpoge's, following a similar approach.
@jsevillamol Jaime Sevilla on x
Insinuation #1b: OAI accessed the private session data of T&L in Codex. This is based on OAI refusing to confirm they didn't train on their data.
@willdepue Will Depue on x
there is literally no chance that OAI researchers spied on Tristan's private codex chats. i don't think y'all realize that openai like any other large regulated online platform has highly locked down user data access permissions. it's not 2010 guys
@polynoamial Noam Brown on x
Seb is a really sweet guy with great intentions, am so happy for him that his week long collaboration with myself and others worked out, but very sad that we didn't get to finish it in the way we wanted. More to say tomorrow.
@aisafetymemes @aisafetymemes on x
It appears OpenAI is claiming its AI just solved Navier-Stokes, the 3rd most famous unsolved math problem in the world. It's one of the 7 Millennium Prize Problems, with a $1 million bounty. (The only two more famous ones are the Riemann Hypothesis and P vs NP) DRAMA: The mathe…
@hosseeb Haseeb Qureshi on x
You're missing the core drama of the story: Tristan is softly accusing OpenAI of having stolen their result from Codex chat logs. Tristan then claims OpenAI tried to threaten him to not publicly disclose this, and that they'd give him the Clay Prize ($1M) as the “closest humans …
@__alpoge__ Levent on x
Unfortunately this guy didn't title it ideal fluids explode
@eliebakouch Elie on x
very sad and worrying precedent, labs should maximize honesty/trust, especially with much higher stakes subjects to come like alignment, safety, and agi deployment to the world
@_sholtodouglas Sholto Douglas on x
levent is a really sweet guy with great intentions, am so happy for him that his year long collaboration with tristan worked out, but very sad that they didn't get to finish it in the way they wanted
@_sholtodouglas Sholto Douglas on x
fwiw I think it is _extremely_ unlikely that user data had any influence here - there is no way OAI would pull user transcripts for this, or knowingly train on it in a way that would've influenced this. I think its pretty important people don't run away with 'your user data isn't…
@polynoamial Noam Brown on x
Strong agree. I know that there is rivalry between the labs but it's important that we learn to work together given what's coming.
@_sholtodouglas Sholto Douglas on x
It is extremely sad that this didn't end up as an example of how the labs could cooperate/coordinate, because the stakes will be so much higher in the future.
@suchenzang Susan Zhang on x
everyone getting sniped by the personal drama, but missed the more interesting unanswered question: can these labs see all your work and scoop you when the stakes are “high enough”? 🤷🏻‍♀️
@etale27 @etale27 on x
If I am reading this correctly, Tristan Buckmaster is alleging OAI has a resolution of Navier-Stokes(via Córdoba and Martínez-Zoroa's program) which maybe used info from Buckmaster and Levent Alpöge's private Codex sessions What the fuck is happening!!!
Ben Feuer Ben Feuer on linkedin
The good news; a set of really significant mathematical results, aided by the latest frontier LLMs, will be released as preprints (or preprint-like things) in the coming days! …
Chandrasekar Subramanian, PhD Chandrasekar Subramanian, PhD on linkedin
OpenAI might have solved (forced) Navier-Stokes!! — For the uninitiated, the full Navier-Stokes problem is one of the Millennium Prize Problems …
Daniel McQuillan Daniel McQuillan on linkedin
AI maths meets the mafia — “I was shown a prompt and told the internal research model had simply been given the problem statement. …
Mark Riedl Mark Riedl on linkedin
Controversy swirling in the world of mathematics. OpenAI has used Astra to make a major advancement on Navier-Stokes, a Millennium Problem. …
Sebastien Bubeck Sebastien Bubeck on linkedin
I would like to clarify a few things: — 1) The screenshot is my reaching out to Levent to coordinate our releases. …
@thelasttheorist Steve T PhD on bluesky
The math here is way beyond me, but the rest is plain to see. If you use AI to solve a problem, AI companies will claim the solution. cims.nyu.edu/~tristanb/st...
@qjurecic Quinta Jurecic on bluesky
The Navier-Stokes fight is a perfect encapsulation of where AI development is right now: this should be really cool and exciting, and instead because of Silicon Valley egos it's become a fight over cheating, surveillance, and companies trying to get one up over the other
@kashhill @kashhill on bluesky
Did not wake up realizing that “did OpenAI cheat on the homework” would be the most exciting social media drama of the day — cims.nyu.edu/~tristanb/st... [image]
@samthielman.com Sam on bluesky
this is A. outrageous and despicable behavior by the worst people alive and B. appears to be merely incidental news in a giant breakthrough in mathematics cims.nyu.edu/~tristanb/st... [image]
@benbraun.eurosky.social Benjamin Braun on bluesky
The statement is worth reading, esp starting at the bottom of page 2.
@nsaphra Naomi Saphra on bluesky
Interestingly, there are not one but two breakthroughs from openly human-led teams related to NS. BOT have released incomplete proofs early to maneuver around the openai “scoop”. (The other is from Anima Anandkumar's group and has less drama involved.)
@nickevershed @nickevershed on bluesky
pretty wild account of the lead-up to OpenAI scooping research on maths prize problem from one of the academics who has been working on it for quite a while! — cims.nyu.edu/~tristanb/st...
@70sbachchan Albert Pinto on bluesky
NYU Prof Buckmaster says OpenAI competitors may hv accessed his private Codex. At least two implications — 1 plagiarism & stealing a PR disaster for OpenAI — 2 Mathematicians are guiding the Machine such that recent “AI results in mathematics” can hardly be called that. — …
@chrischirp Prof Christina Pagel on bluesky
skullduggery and high mathematics.... the original statement by the mathematician who seems like a nice and honourable man - worth reading! — cims.nyu.edu/~tristanb/st... [embedded post]
@maxkennerly Max Kennerly on bluesky
... so there are Navier-Stokes draft solutions out there, and also it seems like OpenAI is spying on mathematics work in GPT, copying approaches, and then throwing their massive compute resources at others' ideas to publish it first. — Statement from Andrew Curran: cims.nyu.edu…
@sciam @sciam on bluesky
In a watershed moment, AI has reportedly conquered one of math's six biggest problems—but arguments are swirling about who should take the credit.
@dangaristo Dan Garisto on bluesky
It sure looks like — a. an AI-assisted approach has come close to solving the Navier-Stokes smoothness problem — b. OpenAI found a similar solution, possibly from stolen chatlogs — c. and pushed one of the authors to remove his Anthropic collaborator from the paper — mat…
@minimaliste13.cpesr.fr @minimaliste13.cpesr.fr on bluesky
Apparently, the following two things are quite plausible (one vastly more important to me than the other). — 1) The forced Navier-Stokes existence problem is solved (in the negative), with heavy LLM help. — 2) Said heavy LLM help includes heavy human input, possibly not all o…
@zachweinersmith Zach Weinersmith on bluesky
More than that, it's the fact that this happened extremely fast, using models that only got good enough to even fathom this sort of thing about six months ago. — Tao has been doing writeups: — mathstodon.xyz/@tao/1172341...
@johncarlosbaez John C. Baez on bluesky
Wow! A lot of progress toward solving one of the Millenium Prize problems - proving blowup for Navier-Stokes. It involves AI, and the folks at OpenAI are battling the folks at Anthropic to get to the finish line first. — For the math, read these posts by Terence Tao:
@tristanbuckmaster@mastodon.social @tristanbuckmaster@mastodon.social on mastodon
Today, Levent Alpöge and I have made public three results: finite-time blowup with smooth forcing for incompressible porous media, for Boussinesq, and for 3d incompressible Euler. — https://cims.nyu.edu/... https://cims.nyu.edu/... https://cims.nyu.edu/... https://cims.nyu.e…
r/france r on reddit
On the Navier-Stokes Millennium Prize Problem
r/BetterOffline r on reddit
OpenAI solves millennium prize problem (Navier-Stokes)
r/ChemicalEngineering r on reddit
Breakthrough for solving Navier-Stokes
r/ArtificialInteligence r on reddit
AI may have just solved a million-dollar math problem. The field will never be the same
r/antiai r on reddit
On the Navier-Stokes Millennium Prize Problem
r/Automate r on reddit
AI may have just solved a million-dollar math problem. The field will never be the same
r/slatestarcodex r on reddit
OpenAI claims Navier-Stokes proof
r/Destiny r on reddit
OpenAI Says It Has Cracked One of Math's ‘Millennium Problems’
r/de r on reddit
OpenAI löst das Navier-Stokes-Millenniumproblem
r/programare r on reddit
OpenAI sustine ca a rezolvat problema Navier-Stokes, una dintre problemele Millennium Prize ☠️
r/OpenAI r on reddit
OpenAI has a solution to the Navier-Stokes existence and smoothness Millennium Prize problem
r/KI_Welt r on reddit
OpenAI: KI-System löst das Navier-Stokes-Millenniumproblem
r/technology r on reddit
On the Navier-Stokes Millennium Prize Problem
r/ControlProblem r on reddit
AI may have just solved a million-dollar math problem. The field will never be the same
r/HotScienceNews r on reddit
AI may have just solved a million-dollar math problem. The field will never be the same
@markchen90 Mark Chen on x
Two things to distinguish: Did any human or agent look at user data as part of the Navier Stokes effort? No. Do we use user feedback and de-identified data to improve ChatGPT and Codex in a holistic way? Yes. And so does every LLM company.
@openai @openai on x
We congratulate Levent Alpöge and Tristan Buckmaster on their remarkable mathematical work. We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve th…
@krishnanrohit Rohit on x
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. Isn't this just the norm for using ChatGPT or Claude or Gemini or indeed anything else, unless you actively opt out?
@tszzl Roon on x
@PI010101 it is exceptionally unlikely that anything they ever did made it into any part of training, and the chances are zero if they have opted out (likely). it would be a terrible precedent to break the the PII-scrubbing boundary to go and round it down to 0, and we won't do i…
@rynorhn Ryan Orhan on x
so this is what happens now? anthropic makes the breakthrough. >competitor hears about it >throw millions of dollars and 10,000 agents at it >get the result >rush to the press > make sure everyone remembers your name. meanwhile the people who actually did the work get a fucking “…
@aidangomez Aidan Gomez on x
Synthetic data derived from production user data of consumer AI tools is used for training. I've heard this rumour from both large labs' employees. In particular, if you're doing something “interesting
@trapitbansal Trapit Bansal on x
Congratulations Levent, Tristan, and OpenAI! What a miraculous time to be alive! I view this as the first successful achievement of Recursive Self Improvement or RSI. Models get increasingly better at Math and get increasingly used by mathematicians to solve all kinds of difficul…
@boazbaraktcs Boaz Barak on x
Important points. Note also that users can opt out from use of their (de-identified) data in training. Anthropic has similar policies, though I do not remember such discussions when they announced mathematical results.
@rynorhn Ryan Orhan on x
your model fucking stole researchers' sessions and apparently even openai didn't know it was happening. then you tell me you can safely contain 10,000 agents running a model “significantly more capable than gpt-6 astra
@suchenzang Susan Zhang on x
this is what we call a infinite “user data flywheel
@__alpoge__ Levent on x
“we cannot rule out that de-identified data derived from their usage of our products helped improve our models.
@ednewtonrex Ed Newton-Rex on x
Astonishing - OpenAI admitting they may have beaten mathematicians to a breakthrough by training on their work. “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.”
@quasilocal Steve McCormick on x
Honestly, quite surprised by this: “we cannot rule out that de-identified data derived from their usage of our products helped improve our models” I think it's time they decided if they are providing a tool for customers, or competing against them.
@sebastienbubeck Sebastien Bubeck on x
@__alpoge__ nothing at all was locked we were just willing to talk but you didn't talk to us ... sorry but that's just untrue, we were willing to go above and beyond and have as many discussions as you would have liked to reach resolution.
@johnschulman2 John Schulman on x
This isn't the most notable aspect of today's news, but on the user data issue, there are different kinds of *training on user data* with very different privacy/IP implications. Sadly, AI cos don't like to disclose what they're doing. - pretrain on user data, with users' tokens a…
Nathaniel Craig Nathaniel Craig on linkedin
I'm reminded of a quote from Edward Purcell on his discovery of bulk nuclear magnetic resonance: — “There the snow lay around my doorstep - great heaps of protons …
Romain Huet Romain Huet on linkedin
We are sharing a solution to the Navier-Stokes Millennium Prize Problem, which has challenged mathematicians for decades. …
Ethan Mollick Ethan Mollick on linkedin
This is a VERY big one. — (And yes, the fights over academic credit and what happened in the race for the proof needs to be resolved, but it is still appears that this is a big one if true.) …
Konstantin Hemker Konstantin Hemker on linkedin
Still in awe that, today, OpenAI shared a solution to the Navier-Stokes Millennium Prize problem, produced by an internal system, alongside a proof formalised in lean. …
John Olafenwa John Olafenwa on linkedin
When I was young, just after high school, with hope of studying theoretical physics in college, I read about the Millennium Prize Problems …
Olga Holtz Olga Holtz on linkedin
OpenAI says AI has solved a Millennium Prize Problem: Navier-Stokes. — As a mathematician working at the intersection of mathematics and AI, I find this potentially historic. …
@durumcrustulum.com @durumcrustulum.com on bluesky
insane. insane! [embedded post]
@spignal Stanley Pignal on bluesky
If you are still dismissing AI models as plagiariasing auto-complete bots, your mental model no longer makes sense — www.nytimes.com/2026/09/08/s...
@jamesomalley.co.uk James O'Malley on bluesky
It's all just stochastic parrots and fancy autocomplete. It's a bubble! — openai.com/index/navier...
@thalysandratos Theodore Alysandratos on bluesky
“Since August 28 we have been training a new internal model” — openai.com/index/navier... “I was told the model did not look up user data. I asked again, about training, and I did not get an answer” — cims.nyu.edu/~tristanb/st... 🤔
@davidcrespo @davidcrespo on bluesky
300 billion output tokens at astra price of $50/M is $1.5M. even very generously assuming an actual cost much lower than that, you're looking at hundreds of thousands easy — openai.com/index/navier... [image]
r/informatik r on reddit
OpenAI löst mutmaßlich mithilfe von LLM ein Millennium-Problem
r/codex r on reddit
The end of human intelligence? (For the majority
r/mathe r on reddit
OpenAI behauptet, das Navier-Stokes-Millennium-Problem gelöst zu haben
r/aiwars r on reddit
Navier-Stokes Millennium Prize Problem: Solved
r/csMajors r on reddit
OPEN AI has solved the Navier Stokes Millennium Prize Problem
r/CFD r on reddit
OpenAI claims a solution to the Navier-Stokes existence and smoothness problem
r/mathematics r on reddit
On the Navier-Stokes Millennium Prize Problem
r/singularity r on reddit
A Solution to the Navier-Stokes Millennium Prize Problem
r/accelerate r on reddit
A Solution to the Navier-Stokes Millennium Prize Problem
@sama Sam Altman on x
I spent much of the weekend talking with the team who did this work. Seb—and everyone else—acted with integrity and generosity throughout. Initially we believed the other team had also solved the problem. We wanted to collaborate and do a joint release. When we learned that they …
@sebastienbubeck Sebastien Bubeck on x
Some more technical points: (a) We began working on the Millennium problems due to viral twitter rumors that Anthropic had resolved 2 Millenium problems. Our aim was to see whether our system was also capable of this impressive feat, especially given our excitement regarding the …
@brainstatssam Samuel Davenport on x
@SebastienBubeck If you're acknowledging that all academic accolades should go to them, how on earth can OpenAI be taking credit for the result? Claiming that it was because of their great new internal model. That is clearly contradictory.
@michael_nielsen Michael Nielsen on x
@polynoamial If the system could get web access, then it would have seen the rumours. At that point “Let's look at the logs” is a very natural thing to pursue. And OpenAI has demonstrably got poor situational awareness about this kind of thing
@blackhc Andreas Kirsch on x
Here is Seb's statement. This is in line with what I sort of expected to have happened after reading Tristan's initial statement One important point of comparison is to compare the results and what was achieved The whole thing is def very messy Congratulations to everyone for the…
@tszzl Roon on x
I'm hearing a rumor that someone at GDM has solved quantum gravity. @SebastienBubeck maybe you should look into this?
@sporadica @sporadica on x
seems like OpenAI got totally slandered in all of this Navier-Stokes drama. lots of you were pretty bloodthirsty for it, too. reminder to stop listening to twitter posters whose biases are already established. instead keep an open mind until more evidence comes out
@teortaxestex @teortaxestex on x
Levent's gimmick is over. Well, we're all in the same boat, just without Anthropic compensation. Even if OpenAI doesn't just release a proof on Github, even if they never announce - you know: it's either solved, or could be solved by them with so much as a wish. Your own problem.
@tunguz Bojan Tunguz on x
Here is the “other side” of the story. As far as I am concerned, it all seems very reasonable. I don't see any intentional malice and/or underhandedness in how all of this was handled by OAI.
@bubbleboi Bubble Boi on x
lol it only took them a week for them to solve one of the most important open problems in mathematics... and they only did it because their was a rumor someone else was going to do it first.
@teortaxestex @teortaxestex on x
I think if you're whatsoever close to math, you're about to publish the solution to Navier-Stokes, and the thing you're worried about is *the appropriateness of Anthropic-OpenAI coauthorship*, you're full of shit and I don't trust anything you say. pox on both your fiefdoms.
@polynoamial Noam Brown on x
I understand how, looking at today's LLMs, people might think the only way we'd achieve NS is by using Levent's/Tristan's prompts. But I hope this plot conveys the model used is a huge step up from today's LLMs. Nobody looked at Levent's/Tristan's prompts. That'd be insane.
@boazbaraktcs Boaz Barak on x
Clarifications from Seb. He reached out to Alpöge and Buckmuster under the (mistaken) belief that they have also solved the Navier-Stokes problem, in order to coordinate publication and to avoid scooping them. It turned out they proved a restricted result (forced Euler problem; t…
@mikeknoop Mike Knoop on x
> It is true that we tried this because there were rumors on the internet One general takeaway from NS results. AI is now fast and powerful enough that mere rumors of an idea working can be enough to crack things.
@emostaque Emad on x
@SebastienBubeck Thanks for sharing and congratulations on your team's achievement I hope you and Anthropic do manage to get open lines of communication as there will undoubtedly be more breakthroughs to come, it is too awesome a time for it to be otherwise 🙏
@nanjiang_cs Nan Jiang on x
when you offered joint authorship of concurrent efforts, you unilaterally tried to dictate who from other side can stay on the paper and who cannot? oh am I seeing this for the first time. (I have had a somewhat related experience; seb probably doesn't remember/don't even know)
@danintheory Dan Roberts on x
It should be obvious to anyone with common sense that there is no plagiarism here. The primary question we set out to answer is how good is our model!
@thomasfbloom Thomas Bloom on x
An account of recent events by Sebastien Bubeck, which paints quite a different picture. Important for anyone interested in this controversial chain of events to hear from all sides. (Then we can focus on the maths!)
@removeanime @removeanime on x
the biggest take away is they solved one of the hardest problems in mathematics, not for humanity nor for the prize money nor for the science, but for the ability to poast about it on twitter faster than the other guy, truly beautiful
r/singularity r on reddit
Sebastien Bubeck's post refuting the claims
@polynoamial Noam Brown on x
Yes, this result cost millions of dollars. But remember that when @OpenAI announced o3 it cost ~$500,000 to score 87.5% on ARC-AGI 1. Today, Astra scores higher for ~$20. In 2025 it took us and GDM an enormous amount of compute to achieve IMO gold. For the 2026 IMO, anyone with a…
@kevinroose Kevin Roose on x
OpenAI also acknowledging it did start working on Navier-Stokes after hearing rumors that Anthropic was getting close to a solution. (But implies they did not snoop on their work.) A math fight for the ages! https://x.com/...
@whodat35 Lee West on bluesky
OpenAI Just Claimed a Huge Math Discovery. Some Academics Are Crying Foul — A landmark announcement by the frontier AI lab has been overshadowed by accusations of impropriety. WIRED — www.wired.com/story/openai...
@jetjocko Adam Rogers on bluesky
Separate from the serious allegations of plagiarism in solving one of the most significant problems in math, you gotta wonder: Would spending millions of dollars on dozens of humans (and vast compute) have *also* worked? — www.wired.com/story/openai...
@katie-drummond Katie Drummond on bluesky
OpenAI and Anthropic are in a pissing contest about math now, and I'm honestly completely obsessed:
r/OpenAI r on reddit
OpenAI Just Claimed a Huge Math Discovery. Some Academics Are Crying Foul
Dimitris Chatzigiannis Dimitris Chatzigiannis on linkedin
The first time I read about the Riemann Hypothesis, I wasn't captivated. On the surface, it is a simple conjecture about the zeros of the Riemann zeta function …
@bcardarella Brian Cardarella on bluesky
Releasing a statement about the OpenAI / Navier-Stokes drama on a university server as a PDF is the most academic shit you can do. — cims.nyu.edu/~tristanb/st...
@fj@mastodon.social @fj@mastodon.social on mastodon
RE: https://mastodon.social/... When you share thoughts with AI, and don't have Zero Data Retention (ZDR), you are feeding into their training data. — OpenAI admits that they cannot rule out that de-identified data derived from Levent Alpöge and Tristan Buckmaster's work was u…
Marc Avila Marc Avila on linkedin
Solution to the Navier-Stokes Millennium Prize Problem? — The Navier-Stokes Millennium Prize Problem is one of the hardest problems in mathematics …
@p-hunermund.com Paul Hünermund on bluesky
“The route to the Clay problem through a smooth force, options c and d in Fefferman's statement of the problem, is the route Luis and Diego opened and the one Levent and I had quietly chosen to attack.” — Sounds more like some mountaineers talking in basecamp, to be honest.

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