The
Closest
Humans

Five 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. NS-01 described a priority fight with "the mathematicians whose method it builds 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. Both teams in this fight are standing on their work. 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, on the evidence of the last two months, the more aggressive user of these tools of anyone in the story.

OpenAI has since hardened its denial. NS-01 quoted the concession that it cannot rule out de-identified usage data helping its models. On 10 September it added that an investigation confirmed the Codex prompts could not have influenced the system, including through training. Both statements now stand. Weigh them yourself.

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, which is the highest honour an American undergraduate mathematician can receive, 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 helped close a problem David Hilbert posed in 1900, showing that his tenth question has a negative answer over the integers of every number field.

Then, this summer, he started breaking things with chatbots.

Sébastien Bubeck is forty-one, French, trained at the École normale supérieure 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. Authors with a commercial interest through Microsoft's stake in OpenAI. A definition of AGI that critics called vague. 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 phone call telling a tenured fluid dynamicist that an internal model had resolved the problem, with 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.

Here is the detail I cannot stop turning over.

Among the things offered to Buckmaster, 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 reported 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.

Buckmaster declined both offers. He said he would go public. That is when 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 apologised for that phrasing without reservation, says he retracted it on the spot, and says he was trying to protect a man he thought was about to damage himself over an accusation that would not hold. Read both accounts. They are short, and they are the only primary evidence any of us have.

OpenAI answered on every channel it owns. A company post, a rebuttal from Bubeck, a defence from Altman, mockery from staff engineers.

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 posted warmly about him as a friend. That is the entire corporate response.

The Clay Mathematics Institute has said nothing, and still lists the problem as unsolved.

No named expert in partial differential equations or in Lean has published a read of OpenAI's formal statement. Five days on, that remains the hole in the middle of all of it.

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

Tao named the cost before the announcement even landed. If a rumour that you are close can summon ten thousand agents, the rational move is to stop telling people what you are working on. 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.