Levent Alpöge's post on X, curated on eChai

The Navier-Stokes Week

Curated from X →

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 8 Sep 2026

“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!

More from The Navier-Stokes Week

Curated from 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, in scientificamerican.com

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

Read it in full on scientificamerican.com →
Curated from X →

Three minutes after the announcement, the direct answer to the allegation, and the reason this part carries both posts rather than only the first. Read the third paragraph as closely as the second: the denial is that no specific user data was accessed, and the sentence after it, that de-identified data from their usage cannot be ruled out, is OpenAI's own hedge rather than anybody's inference. On the last point their account and the reporting below sit differently. OpenAI says the proofs differ significantly and that the Euler results are not even the same statement, forced against unforced; Scientific American's account of Bubeck's briefing the same evening has him granting that the Navier-Stokes route does follow a similar method to Buckmaster and Alpöge's.

OpenAI 2w

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 this problem.

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

However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs. unforced).
Curated from X →

The announcement, from the company's own account. The post itself links to nothing and carries an illustration of a spiralling, stretching fluid; the write-up and the Lean formalization are on OpenAI's own announcement page. Read it against what is not in it: no mention of Diego Córdoba and Luis Martínez-Zoroa, whose programme the route belongs to, or of Buckmaster and Alpöge, who published on it that morning. Being certified in Lean is a claim about the argument holding together, not about who got there first.

OpenAI 2w

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 whether the description of smooth three-dimensional fluid motion modeled by the Navier-Stokes equations can break down. It has remained unresolved for roughly 90 years.

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