The Closest Humans: the film. Amends The Hand in the Water on whose method it was, and on two calls on a Sunday

0:00 · The Closest Humans

Two men, one year, and two calls on a Sunday.

What The Hand in the Water got wrong

Two days ago I published a document arguing that caveats die in transmission. Here are mine, before anyone else finds them.

The method was never theirs. The Hand in the Water said the result was "contested by the people whose method it was built on." That reads as though the forcing method belonged to Buckmaster and Alpöge. It does not. It belongs to Diego Córdoba and Luis Martínez-Zoroa in Madrid. Buckmaster and Alpöge built on their work. OpenAI said in September that its proof did too; on 13 October Scientific American reported that closer examination shows it builds its force "in a totally distinct way". Fefferman, who wrote the Clay problem statement, told Quanta the heroes here are the two Spaniards.

I named one man when there were two. Alpöge is not a supporting character. He is a co-equal author, and in July and August he announced three results found with AI models.

OpenAI has since hardened its denial. The Hand in the Water quoted the concession that it cannot rule out de-identified usage data helping its models. On 10 September it added that an investigation confirmed Buckmaster's Codex prompts from the two months before the announcement could not have influenced the system, including through training. Weigh the two yourself.

The Hand in the Water was about a preposition. Water that tears itself against water that can be torn. This one turns out to be about a preposition too, and I did not expect that.

1:57 · The man who already won

Tristan Buckmaster is Australian and British, trained in Leipzig, and has spent most of his career on one family of questions: can fluids break, and how badly.

In 2019 the Clay Mathematics Institute gave him its Research Award. Not for another subject. For work with Vlad Vicol showing that weak solutions to Navier-Stokes can be, in Clay's own phrase, remarkably wild.

The institute that owns the million dollar problem had already given him a prize for work on the same equations.

Which is what makes one line from the calls land the way it does. When Buckmaster said he would go public if OpenAI released its result as proposed, he writes, he was asked why he would ruin his career.

He replied that he is an academic, and asked why going public would ruin it.

He is a full professor at NYU. He holds an NSF grant for a project titled, with no irony available, Singularities in fluids. Whatever that remark meant, it was said to one of the established figures of the field. Sébastien Bubeck of OpenAI, who was on both calls, says he asked why anyone would risk a career over unfounded accusations.

The saddest line in Buckmaster's statement is about the announcement he never got to make. He had planned to say that the results are not the important thing.

Rather the important thing is instead the significance that a mathematician and an LLM model can now do all this work in a month.

He meant to spend his moment arguing the machines were the story. He spent it, in his own words, "writing about something else".

3:55 · There is an asteroid

Levent Alpöge is thirty-four, from Long Island, and there is a rock in the asteroid belt named after him. Number 25898. He earned it at seventeen as an Intel Science Talent Search finalist, for a CUDA program that found blood vessels in MRI scans.

He is not a fluid dynamicist. He is a number theorist, and a decorated one. Top of his Harvard class. Morgan Prize in 2015, the AMS, MAA and SIAM's annual prize for outstanding research by an undergraduate in the US, Canada or Mexico, awarded when he had already co-authored seven research papers and had not yet started graduate school. PhD at Princeton under Manjul Bhargava, a Fields Medalist. Junior Fellow of the Harvard Society of Fellows.

Last year he and three co-authors showed, independently of Koymans and Pagano, that the question Hilbert posed in 1900 for the ordinary integers also has a negative answer over the integers of every number field.

Then, this summer, his results with chatbots started going public. In July he posted this on X.

hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final

That is the register. All lowercase, no punctuation, an eighty-seven year old conjecture dispatched during a World Cup final. Hold it next to Buckmaster's four careful pages and you have the two halves of what mathematics is currently becoming.

5:50 · He paid for it himself

Alpöge has published how it began: an email to Buckmaster on 19 September 2025, sent "as a shot in the dark", asking if he had considered working on the problem "in the traditional mathematical way".

The collaboration ran for about a year. Both men have said in writing that it was personal rather than institutional, and Buckmaster has said who paid for his group's tools.

I pay for the tools my group uses out of my own research funds, including footing a large bill to OpenAI.

Read that sentence again with its date: 3 September, two days after OpenAI says its own effort began. He wrote it to an OpenAI mathematician, to set out the facts behind a rumour about his own work.

They ran the work through Codex. Every draft, for the whole project, into a product owned by the company they would later be racing. When Buckmaster asked on the call whether the model had been trained on those sessions, he was told it had not looked up user data. He asked again, specifically about training. He says he got no answer.

7:10 · Twenty-four days from their breakthrough to being beaten to the finish

Their breakthrough came on 15 August: blowup with a smooth force for the Euler and Boussinesq equations, the Euler proof checked in Lean by 22 August. OpenAI announced its own result on 8 September.

They believed they had something else too, and did not publish it: blowup for hypo-dissipative Navier-Stokes, a variant with weakened dissipation. The Lean check had not finished, and there was no presentable writeup.

They believed they had a result on a weaker variant, and held it back because the checking had not caught up with the claim. Hold that thought for one section.

7:58 · Sparks

Sébastien Bubeck is forty-one, French, trained at the École normale supérieure de Cachan and Lille, and was a Princeton professor before most people had heard of a transformer. His early work on bandits and convex optimisation is standard reference material. He is, by any normal measure, a serious scientist.

Then he spent a decade at Microsoft Research, where in March 2023 he became lead author on a hundred and fifty-five page paper called Sparks of Artificial General Intelligence.

The criticism of that paper is the relevant biography here. Not peer reviewed. A definition of AGI that critics called vague, Gary Marcus among them. Experiments run on a private pre-release model that nobody outside could reproduce.

The charge was never that he was wrong. It was that the announcement arrived ahead of the checking.

He joined OpenAI in October 2024. Twenty-three months later he was on a Sunday call in which Buckmaster was told an internal model had proved blowup for forced Navier-Stokes. Alpöge had been told by Bubeck that it took very little human input.

By the end of the call, Buckmaster says, it had emerged that a whole team had worked on it, that easier problems had been tried first, and that even the prompt he had been shown was itself written by prompting Codex.

9:35 · One preposition, again

Two men have published irreconcilable accounts of the same two calls. Line them up and the irreconcilable part is almost nothing.

Buckmaster says Bubeck twice asked that Alpöge come off the authorship, because he works at Anthropic; his statement does not say of which paper. Bubeck says he never asked that about Alpöge's own work, only about a proposed rewrite of OpenAI's proof, where an Anthropic employee as author would have been inappropriate.

Whose paper. Buckmaster's statement never says, and Bubeck says it was OpenAI's.

Neither man has published a recording. A third person, an OpenAI mathematician, was on both calls and has not gone on the record. Where they do collide, on whether the career remark was taken back on the spot, two careful people remember one afternoon differently, which is the most ordinary thing in the world and the reason this will never resolve.

Notice what the obstacle was. Not the mathematics. An employment contract.

10:50 · The closest humans

Here is the detail I cannot stop turning over.

Among the things offered to Buckmaster, he writes, if he agreed to publish first and let OpenAI follow the next day, was that OpenAI would say publicly that he and Alpöge deserved the Clay Prize. And that they were, in the phrase Buckmaster reports from the call, the closest humans to the problem.

Closest humans. Not closest mathematicians. Not closest team.

Somebody chose that word, on a Sunday, on a call, under pressure, and it is the most honest sentence anyone said all week. It concedes the entire frame. There is a category of solver now, and there is a separate category for us, and the gap between them is a thing you can be measured against and found nearest to.

There was a second offer, he writes: that he alone write up the Navier-Stokes result, acknowledging that an internal OpenAI model had resolved it. He declined both, and said he would go public if OpenAI released its result as proposed. That is when, he writes, he was asked about his career, and told that if he did not want Bubeck to be nice, Bubeck did not have to be nice.

Bubeck has since written, in two follow-up posts, that he apologises for the career remark as an "extremely poor choice of words", that he retracted it on the spot, and that he was trying to care for him. Buckmaster quoted that apology on Mastodon on 10 September and answered that the account is "wildly false": "Not only did he never apologize, he doubled down on his threat", the line about being nice. Read both accounts, and the posts that followed them. They are the only primary evidence any of us have.

12:52 · Meanwhile, in Madrid

Diego Córdoba and Luis Martínez-Zoroa opened the door. The idea of getting blowup by applying a force, rather than waiting for the fluid to do it alone, is theirs. Buckmaster and Alpöge's results descend from their work. Whether OpenAI's does was disputed. In October Scientific American reported that its final proof builds its force in a totally distinct way, though some experts say an earlier, smaller team of OpenAI's AI agents did follow their program, for an intermediate result.

Neither of them was on the calls. Neither of them works for a lab. Neither of them has a valuation.

Córdoba told Scientific American, in two remarks reported on 8 September:

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

Charles Fefferman, who wrote the Clay problem statement in 2000 and therefore knows better than anyone what counts, told Quanta he was thrilled the problem was solved and then named the heroes of the story. He named the two men in Madrid.

Buckmaster, on the first of his four pages, before he turned to his own fight for credit, stopped to say something else. He wrote that in view of this body of work he believes Martínez-Zoroa deserves a Fields Medal.

A man being scooped used his own statement to champion somebody else.

14:30 · Who has not spoken

OpenAI answered on every channel it owns. A company post, a rebuttal from Bubeck, a defence from Sam Altman, and a parody from one of its researchers, Noam Brown.

Anthropic has said nothing. Its employee is at the centre of the biggest story in mathematics this decade, his work is being cited as evidence that he is not an independent academic, and the company that markets itself on trust has issued no statement of any kind. One researcher there, Sholto Douglas, posted warmly about him. That is the entire corporate response.

The Clay Mathematics Institute has said only that the problem "has apparently been settled" and that its process is "deliberately unhurried", and lists the problem as active, neither solved nor unsolved.

Five days on, no named expert in partial differential equations had published a read of the formal statement OpenAI proved. (Since then others have weighed in on the proof, not the statement: in NPR's report of 22 September Javier Gómez-Serrano, a mathematician at Brown University, said the Lean code compiled as expected but that "as of today, the paper doesn't teach us much", and on 6 October Bastounis, Circelli and Hansen showed two places where the Lean proof departs from the written one, and said there may be more.)

Three silences, near enough, and each one is a decision somebody made.

Terence Tao named the cost within hours of the announcement: even the rumour that someone is working on a problem can trigger a massive AI-powered effort to flatten it, so the incentives may now point toward no longer sharing promising directions. Alpöge contacted OpenAI on the night of 2 September because he had heard they already knew. That is a researcher discovering that his own privacy had become a strategic asset.

The capability is real, and nothing here touches it. What this week established is not whether machines can do mathematics. It is what a field does in the first seventy-two hours after it finds out.

16:59 · Sources

The Closest Humans. 13 September 2026. Eleven sections, 44 sources, at aedificare dot art. CC BY 4.0.