A year of work, a month of AI, and a fight over who gets to announce it

Before

Five days before any of this, Terence Tao published a case study using Navier-Stokes as his worked example of how an AI-generated solution could damage a field. He was not the only one saying it, and a month earlier three mathematicians had already accused OpenAI of running roughshod over prior work.

• scientificamerican.com 6 August 2026

  OpenAI's latest math breakthroughs commit research misconduct, experts say →

  This is the precedent, and it is why the argument a month later reads as the second round rather than the first. Joseph Howlett reported for Scientific American that three named mathematicians objected to how OpenAI had presented ten results from its Astra model in August. Stephen Miller teaches at Yeshiva University and says the sphere-packing result leaned on his own 2016 paper. Francesco Fournier-Facio at Cambridge said of a group-theory result that "there is the big PR machine that wants to sound as impressive as possible". OpenAI said it would make updates "consistent with standard academic practice". The complaint on 8 September, that credit for a line of prior work was not carried, is the same complaint about the same company five weeks later.

  Stephen Miller

  They are running roughshod over the work of others who came before them.

• mathstodon.xyz 28 August 2026

  Read it on mathstodon.xyz →

  Tao holds the Fields Medal and is one of the two or three people most often asked about Navier-Stokes. Twelve days before Buckmaster apologises for the state of his own Euler paper and calls it AI slop, Tao sets out why that was going to happen to somebody.

  Terence Tao

  The advent of capable AI tools has highighted a variant of Simpson's paradox: a technological advance can improve the quality and volume of each individual's output, and yet the average quality (signal-to-noise ratio) of the aggregate output can deteriorate as a result. [...] whereas previously 90% of the extant literature was well-written, the situation is now completely reversed: 90% of the literature will now be poorly written.

• proofsandprompts.com 30 August 2026

  Care for a little more AI? →

  Duminil-Copin won the Fields Medal in 2022 and works at Geneva and IHES. He says he does not use AI in his own work. His argument is not that machine proofs are worse, it is that solving the problems quickly removes the thing a field is built out of.

  Hugo Duminil-Copin

  These artificial discoveries risk decapitating entire fields before they have had time to develop to their full potential. Even worse, they nuke the mathematical landscape. [...] the current use of AI does not empower us, it petrifies us.

• mathstodon.xyz 3 September 2026

  Read it on mathstodon.xyz →

  Five days before any of it, and the sentence that names what is at stake in the whole week.

  Terence Tao

  Analogously to pre-atomic steel, open problems in mathematics generated before the AI era have, astonishingly, have become something resembling a non-renewable resource. [...] It may become necessary to declare certain classes of mathematical problems off-limits to automated solvers, in order to preserve their broader value to the mathematical ecosystem.

• mathstodon.xyz 3 September 2026

  Read it on mathstodon.xyz →

  The entry that reframes the week, and the reason this page starts where it does. On 3 September Tao published a six-part case study using Navier-Stokes as his worked example of how an AI-generated solution could damage a field. Five days later people were arguing about exactly that. The fifth part describes the scenario in advance: an autonomous harness, backed by enormous compute, running the whole search internally while the company keeps the process out of public view, so the problem is technically solved and almost nothing is added to mathematics.

  Terence Tao

  A concrete example of how AI advances in solving key open problems could inihibit the future development of a mathematical field can be found in the global regularity problem for the incompressible Navier-Stokes equations [...] there is now an increasingly realistic scenario in which a primarily AI-generated solution to the problem appears, but in a fashion that contaminates the problem as a source of further advances.

Back to contents

The rumour

A prediction that Claude had solved Navier-Stokes ran to 3.4 million views over a weekend. Every specific in it was wrong. By Buckmaster's account it is also what put his unpublished work in front of OpenAI.

• Curated from X →

  Where the rumour became public, at 3.4 million views over a weekend. Curran writes about AI to a large audience and is not a mathematician; he later says he had no independent information. Every specific in it is wrong: it was not Anthropic's result, it was not Navier-Stokes, and it was not out for expert review. Buckmaster's statement records that a rumour of this shape is what he wrote to OpenAI about two days later.

  Andrew Curran 3d

  It's fun to make predictions. Here's a new one:
  Anthropic has solved a Millennium Prize Problem.
  And I'll be even more specific.
  Claude has solved Navier–Stokes.
  It is out for expert review.
  And to give myself a hard deadline, they will announce it before the IPO.

• mathstodon.xyz 5 September 2026

  Read it on mathstodon.xyz →

  Asked about the rumour, Tao says he has not heard anything, then says the thing he had been saying all week in one sentence.

  Terence Tao

  A clarification in response to recent rumors about a possible solution to the Navier-Stokes problem: I am not aware of any significant developments in this regard; the above discussion is hypothetical, but not completely implausible at the current level of development of AI technology.

  The point remains that there is a substantial opportunity cost in converting a historically productive and motivating problem (such as Navier-Stokes regularity) into a mere viral social media post advertising some benchmark progress.

• mathstodon.xyz 5 September 2026

  Read it on mathstodon.xyz →

  The same day, Tao re-runs the 2005 to 2014 story of bounded gaps between primes as if today's labs had existed then. In that version Zhang stays an adjunct lecturer and Maynard leaves the field. The fourth part is his own timeline of the days he was writing in, and the last line of it is the whole page in three characters.

  Terence Tao

  Aug 31, 2026: Stadlmann releases a preprint that develops an equidistribution theorem for numbers with a large smooth factor, and uses this to improve the Polymath8 bound of 246 slightly, to 240.

  Sep 3-4, 2026: Various AI companies race to announce their own improvements to the Polymath8 bound via social media.

  Sep 5-, 2026: ???

• Curated from X →

  Glazer runs mathematics at Epoch AI, which builds the FrontierMath benchmark. He spent the weekend trying to source the claim and posted the trace. It is the clearest record there is of what an unsourced rumour looks like from inside: every version came back to an OpenAI employee, none to anybody outside, and the problem being solved changed twice along the way.

  Elliot Glazer 2d

  >Be me
  >Told several days ago thirdhand by OAI employee Anthropic solved a Millennium Prize Problem
  >"No way it wouldn't leak in this way"
  >Told Wednesday by a different friend at OAI that, actually, he heard it was two.
  >"Ok I'm updating against further, obviously it wasn't two."
  >OAI source says they'd actually garbled it, friend informs me.
  >Goes on Reddit and tells people spreading the rumor it is unfounded
  >Terry coincidentally posts a hypothetical about NS getting solved very next day with lots of specifics about the hypothetical proof and its Lean file
  >Anthropic formalizes FLT
  >Curran's "prediction" seems to align with everything.
  >Terry writes follow-up post addressing the rumors, that says he hasn't heard any development on Navier-Stokes, reads sincere to me
  >Curran has no independent relevant info here btw
  >None of the OAI rumor spreaders can trace their beliefs back to any non-OAI source
  >Math prof friend says he heard from a credible source "It was Hodge not NS."

  I'm going back to bed.

• Curated from X →

  When a real result did land, days later, it was neither of the problems the rumour had named, and nothing had been proven true.

  Elliot Glazer 2d

  I’ve been informed the original iteration of the rumor was “Navier-Stokes and Hodge were proven *true* by Claude.”

  Stick a fork in this rumor, it’s DONE.

• mathstodon.xyz 6 September 2026

  Read it on mathstodon.xyz →

  Posted nine minutes after Glazer called the rumour dead. One sentence, and it is the only proposal anybody made all week.

  Terence Tao

  A new proposed competition for AI companies: rather than being the first to announce solutions to unsolved math problems, be the first to announce a new mathematical insight.

Back to contents

The result

What was actually proved, and by whom. Two separate Euler results landed within three hours of each other, by different routes, and only one of them got read.

• mastodon.social 8 September 2026

  Read it on mastodon.social →

  Tristan Buckmaster is a fluid dynamicist at NYU's Courant Institute. Levent Alpöge is a mathematician at Anthropic. Their statement says the collaboration is personal, with no institutional involvement from either employer, and that Buckmaster pays for the tools out of his own research funds. The papers went up with the Lean formalization alongside them. Half an hour later Deane Yang, a mathematician in Buckmaster's own department, posted the bare link with no comment, and that is how most mathematicians first saw it: 920,000 views for a post that added nothing.

  Tristan Buckmaster

  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.

• mathstodon.xyz 8 September 2026

  Read it on mathstodon.xyz →

  Tao had read the papers before they were public and spoke to Buckmaster on the phone about them, which he notes made a refreshing change from AI-based communication modalities. This is the assessment everything else that day is arguing around. In the second half he adds that nothing in principle seems to stop the method reaching Navier-Stokes, and that battering out such an extension with enormous compute does not particularly hold his interest.

  Terence Tao

  A remarkable achievement: Alpöge and Buckmaster have managed to push one of the major promising approaches towards constructing blowup solutions to fluid equations --- as developed by Cordoba and Martınez-Zoroa --- to establish finite time blowup for many key fluid equations, including 3D incompressible Euler, with a smooth forcing term. The arguments have been formalized in Lean.

• Curated from X →

  A second Euler result landed within three hours of the first, from a different group by a different route, and got almost none of the attention because it arrived in the middle of an argument. Anandkumar is at Caltech; the paper is with Ganeshram and Duruisseaux. Their case is the harder one, without forcing. Tao read it the same morning and called it relatively AI-light, using models mostly for literature review and Lean formalization, while noting that the rigorous demonstration of stability is still lacking and may need enormous further effort.

  Anima Anandkumar 9h

  We have found stable singularity on 3D Euler!

  Our starting point is a physics-informed neural network (PINN) to come up with an approximate answer, and then to argue stability around that to complete the proof.

  The challenge so far has been that PINNs have not been successful in discovering singularities on the current problem. A common failure mode is PINNs converging to a trivial solution. We take special care to nudge our PINN to interesting regions through a combination of constraints.

  We believe that such physics-informed and physics-centric AI are critical ingredients across many areas of research involving physical systems, and LLMs lack such physical grounding.

  We have been working on this problem for much of this year, and we just saw the announcement by Tristan on Euler with forcing. In contrast, we consider without forcing and use a PINN formulation.

Back to contents

The argument

Both accounts of the same two calls on 6 September, and what people at each lab said in public afterwards. Nobody outside OpenAI has seen the proof at the centre of it.

• cims.nyu.edu 8 September 2026

  Statement →

  The four-page statement Buckmaster published alongside the papers, because a rumour had been running since Friday and, as he puts it, the alternative was to let a sequence of announcements say something he knew to be false. It sets out two calls on 6 September, with Sébastien Bubeck on both and Alpöge on neither. He says he was told an internal OpenAI model had produced a roughly 100-page proof of forced Navier-Stokes blowup, by the same route he and Alpöge had quietly chosen; that the first prompt was sent only after word of their work reached OpenAI; and that he was asked twice to leave Alpöge off a paper because Alpöge works at Anthropic. He also states the limits of his own claim, and they belong beside everything above: "I have not seen OpenAI's proof. I do not know what their model did, or how. I do not know whether our data was used. I am not accusing anyone of anything."

  Tristan Buckmaster

  I was told that an internal OpenAI model had produced a proof of finite time blowup for the forced Navier-Stokes equations. I was told the proof is about 100 pages. I have not seen it. [...] 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.

• Curated from X →

  Bubeck leads OpenAI's mathematics team and is the person named throughout the account of the calls. He addresses no specific allegation and says a fuller account is coming. At the time of writing it has not arrived, OpenAI has published nothing as an organisation, and nobody outside the company has seen the 100-page proof.

  Sebastien Bubeck 9h

  A series of false and inflammatory allegations against me are currently circulating on social channels. To clarify, I came into the discussion following academic norms, and I'm disappointed that it has come to this. Anyone who knows me knows that academic standards are of the highest importance to me. Will have more to say tomorrow.

• Curated from X →

  Brown is a researcher at OpenAI and co-created the o-series reasoning models. Read this one and the next together, and with the timestamps: they are twelve minutes apart.

  Noam Brown 9h

  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.

• Curated from X →

  Douglas is a researcher at Anthropic. This is the post above with the names and the durations changed. Printed one after the other, the pair is the clearest record of the two labs' postures anywhere in the week, and neither needs a word of explanation: week long against year long is the whole argument in two adjectives.

  Sholto Douglas 9h

  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

• mastodon.social 8 September 2026

  Read it on mastodon.social →

  Six hours after the statement, and the last thing Buckmaster said. It is also what his own statement said it had wanted to be about: a mathematician and a model did in a month what he expected to take years, and he calls it a Deep Blue and Kasparov moment for how the field trains students, assigns credit and decides what is worth a life's attention.

  Tristan Buckmaster

  I want to again express my profound gratitude to the outpouring of support from the greater mathematical community. I also want to remark that there is a far bigger story here than the one in my statement: the sheer magnitude of what frontier models can now do, and what that means for us all. I hope the labs can see this and set the petty posturing aside.

• Curated from X →

  Bryan is an associate professor of strategy at Toronto's Rotman School and chief economist at CDL Toronto. By late morning the reading that OpenAI had trained on private Codex sessions had taken over X, and this is the most substantial public pushback on it: he accepts that OpenAI pursued the route after hearing the rumours and still calls the training insinuation unfair. It is the strongest version of the account that does not assume the worst, which is why it sits here rather than among the reactions.

  Kevin A. Bryan 5h

  1) Navier-Stokes result will be shown soon, by humans+AI. This is "Nobel-level" result. 2) OAI has an internal proof also. 3) They had AI pursue a path partly based on rumors of a strategy that might work. 4) OAI did not "train on the humans' GPT input"- insinuation is unfair

Back to contents

The reaction

Everybody else, reading the same documents at speed and disagreeing about what they say. In timestamp order, with what each post was read by.

• Curated from X →

  The widest-read account of the day at 533,000 views, and one of the few at that reach that states it correctly: major progress, and a claim by somebody else that has not been shown.

  MTS 10h

  SITUATION DETECTED: Mathematicians Tristan Buckmaster and Levent Alpöge have made major progress toward solving the Navier-Stokes existence and smoothness problem, one of the most important problems in mathematics, and say OpenAI may have solved it fully.

• Curated from X →

  347,000 views, linking the statement, which says the opposite. Navier-Stokes has not been publicly solved by anyone. This is here because correcting it is most of what a page like this is for.

  Yifan Zhang 9h

  Breaking:

  The Millennium Problem
  Navier–Stokes Is Solved

• Curated from X →

  183,000 views, and the widely shared version that got the caveat right in its own third paragraph.

  AI Notkilleveryoneism Memes 9h

  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.

  DRAMA: The mathematician who spent a year on this (with AI) says OpenAI raced to the finish after his work leaked to them, then pressured him to drop his co-author, who works at Anthropic

  To be clear, what's actually verified is the mathematician's result on Navier-Stokes next-door neighbor problem. OpenAI's proof of the real thing hasn't been revealed yet, and OpenAI hasn't responded to the accusations

• Curated from X →

  Gerko founded and runs XTX Markets and funds the AI Mathematical Olympiad prize, so he pays for this kind of work himself. He goes on to argue that the same result was a few months away on consumer hardware and an ordinary budget; the rest is at the link.

  Alex Gerko 6h

  On the topic of Navier-Stokes mess: what if, hear me out, Anthropic and OpenAI just completely stopped competing on who can deploy obscene amounts of compute into a non-public model to solve some long-standing math problem?

• Curated from X →

  The most careful summary written by anybody outside mathematics, and the only widely shared one that carries Buckmaster's own disclaimer rather than dropping it.

  Andrew Akbashev 5h

  1. The authors - Alpöge and Buckmaster - showed how to achieve a blowup with smooth forcing for 2D Boussinesq equation. Then they also worked it out for 3D incompressible Euler equations. These are Navier-Stokes but without viscosity.

  Now, Tarrence Tao says that this approach may likely be extended to actual Navier-Stokes.

  BUT there's a big drama behind it:

  - OpenAI had learned about their progress before it was published and pushed their AI to quickly come up with a similar solution.

  - However, OpenAI's solution was based on the same smooth-forcing approach that Buckmaster/Alpöge had quietly been developing. Buckmaster said that he does not know if their data was used, so he is “not accusing anyone of anything.”

  - However, Sébastien Bubeck (a research lead at OpenAI) didn’t want to see Alpöge as the author because Alpöge works at Anthropic.

  Bubeck from OpenAI called these allegations “false and inflammatory”. As of now, there are no further comments.

• Curated from X →

  By late morning this was the highest-engagement account of the day at 5,300 likes and 263,000 views, and it is the version most people will have read. Every line of it is in the statement. What is not in the statement is the conclusion a reader draws from the last two: Buckmaster asked about training and got no answer, and he is explicit that he does not know what the answer is.

  NIK 4h

  >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 within days
  >"funny story, our model also solved it"
  >using his exact approach
  >asks openai: did you train on my sessions?
  >no answer