Tristan Buckmaster's post, curated on eChai

Founder Notes

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.

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Meta launched Muse on 8 September: a standalone agent app that keeps working after you close it and comes back when it needs an approval. In Meta's account of how it works, each person's agent runs inside Muse Secure VM, a dedicated virtual machine holding both the agent and their data; a second agent called Sentinel sits on the same machine and blocks its access to the internet unless it approves the request; logins go into secure storage so Muse can use a credential without seeing it; and every account gets an audit trail of what the agent has done and what it plans to do next. It buys as well as plans, checking out through Link by Stripe, which Meta says makes it the first AI agent covered by Link's purchase protections. Free to start, with paid plans at $20 and $100 a month, and it is the United States only for now, on iOS, Android, the web and inside WhatsApp. An agent that browses the open web can be instructed by the page it is reading, which is what has kept agents away from cards and passwords. Meta's answer to that is three things: isolate each agent in its own machine, put a second agent between it and the network, and give it credentials it can use but never read.

Muse 44m

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The co-author, at Anthropic, quoting OpenAI's post back at itself. He had been silent all day: he was on neither of the calls, and everything said about him until now had been said by other people. Three things in it. He picks out the same hedge as the sentence worth reading and credits them for it. He has started reading the proof, which is the first public word from anybody outside OpenAI on what is actually in it, and his read is that it looks closer to a different Euler blowup proof he and Buckmaster already had than to the work they published. And he adds a detail about the calls that was not in Buckmaster's statement, which is his own account and nobody else has confirmed it: that a millennium prize was offered if he would be taken off the paper. What he does not do is take the fight, which is worth noticing on a page this long.

Levent Alpöge 1h

“we cannot rule out that de-identified data derived from their usage of our products helped improve our models.”

i mean props to them for straight coming clean.

(so far the proof looks more along the lines of another euler blowup proof we had, off of whose ansatz naming we were making really stupid puns like “smooth criminale”, unlike the much better “ideal fluids explode”, Tristan)

so i’ll now give a bit on my thinking here. i actually woulda been pumped to collaborate on this, there are a lot of people at oai i like (ok, clearly some were indirectly dicks to me because of being part of the whole situation, but im a big boy, i still like them), idgaf about authorship on that step anyway, coulda been me Tristan and every fte at oai for all i care (on that Tristan would disagree:p). but on hearing the loud convo in the hallway, especially the part where a millennium prize was offered if i’d just be removed from the paper, it was kinda clear the die had been cast and things were locked. pretty wacky, unstrategic, and unnecessary, since on my side things were mostly me and claude having a good time yoloing random stuff in the corner rather than anything institutional. i also like the idea of the labs cooperating, and even better on scientific progress. it’s a shame!
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scientificamerican.com 8 September 2026
OpenAI claims blockbuster math breakthrough amid swirl of controversy →

Joseph Howlett reported the announcement the same evening, for the magazine that ran the misconduct piece in August. Bubeck gave a press briefing and emphatically denied that Buckmaster and Alpöge's work influenced OpenAI, saying "We did not use their prompt or models or proof", that the model solved the Euler problem by totally different means, and that the Navier-Stokes proof was produced over the weekend; he also granted that the Navier-Stokes route does follow a similar method to theirs. The quotation is Diego Córdoba, who with Luis Martínez-Zoroa opened the route everybody has been arguing about, hearing that it may have been walked to the end without him.

Diego Córdoba

We're a little bit in shock... If it's done, that will be a big surprise for us.

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