AedificareAmends 11 Sep 2026 · The Hand in the Water

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

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

By · · Updated r = cos(kθ) · seed 0902
Film · YouTube · plays here

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. [01]

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. [01] It does not. It belongs to Diego Córdoba and Luis Martínez-Zoroa in Madrid. [02] [03] 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". [02] [04] [05] Fefferman, who wrote the Clay problem statement, told Quanta the heroes here are the two Spaniards. [03]

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. [01] [06] [07]

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. [01] 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. [08] [09] 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. [01]

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. [11]

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. [12]

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. [02]

He replied that he is an academic, and asked why going public would ruin it. [02]

He is a full professor at NYU. He holds an NSF grant for a project titled, with no irony available, Singularities in fluids. [11] [14] 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. [02] [15] [16]

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. [02]

Rather the important thing is instead the significance that a mathematician and an LLM model can now do all this work in a month.Buckmaster, on what he had meant to say [02]

He meant to spend his moment arguing the machines were the story. He spent it, in his own words, "writing about something else". [02]

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. [17] [18] [19] [20]

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. [17] [21]

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. [22] [20]

Then, this summer, his results with chatbots started going public. In July he posted this on X. [07] [02]

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 finalLevent Alpöge on X, July 2026 [07]

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. [07] [24] [02]

05 · Twenty-four days

Twenty-four days from their breakthrough to being beaten to the finish

15 Aug
smooth-forcing blowup for Boussinesq and Euler, after a slow year
22 Aug
Lean verification completes
28 Aug
OpenAI begins training the model that would beat them
1 Sep
OpenAI starts work, on a rumour
2 Sep
Alpöge contacts OpenAI at night
6 Sep
two calls with OpenAI
7 Sep
11:58pm New York, Buckmaster posts four pages
8 Sep
around noon, OpenAI announces

The dates, as the sources give them [02] [06] [26] [07] [03]

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. [02] [03]

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. [02] [29]

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. [02]

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. [30] [31]

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. [32] [30]

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. [32] [33]

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

He joined OpenAI in October 2024. [34] 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. [02] [25]

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. [02]

One preposition,
again

Two men have published irreconcilable accounts of the same two calls. Line them up and the irreconcilable part is almost nothing. [02] [25] [16]

Both accounts, as published 8 to 10 September. A filled cell means asserted; an empty cell, not addressed.
ClaimBuckmasterBubeck
A model resolved forced Navier-Stokesassertedasserted
Two options were put to Buckmasterassertedasserted
A remark about his career was madeassertedasserted
"If you don't want me to be nice" was saidassertednot addressed
Alpöge's Anthropic job was the obstacleassertedasserted
Which paper Alpöge was to come offUnspecified ("removed from authorship")Ours

Filled = asserted · empty = not addressed in any post that could be read

Buckmaster's statement does not name the paper; Bubeck says it was OpenAI's [02] [16] [15] [25] [06]

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. [02] [16] [25]

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. [02] [16] 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. [15] [16] [06]

Notice what the obstacle was. Not the mathematics. An employment contract. [25] [15]

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. [02]

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. [02] [06]

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. [16] [15] 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. [06] Read both accounts, and the posts that followed them. They are the only primary evidence any of us have.

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. [02] [37] 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. [02] [38] [06] [05]

Neither of them was on the calls. Neither of them works for a lab. Neither of them has a valuation. [02] [03]

Córdoba told Scientific American, in two remarks reported on 8 September: [04]

We're a little bit in shock … If it's done, that will be a big surprise for usDiego Córdoba, to Scientific American [04]

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. [03]

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. [02]

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

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. [08] [25] [36] [40]

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. [09] [25] [15] One researcher there, Sholto Douglas, posted warmly about him. [41] 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. [10]

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.) [42] [13]

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. [37] Alpöge contacted OpenAI on the night of 2 September because he had heard they already knew. [07] 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.

Sources

Bracketed figures in the sections above are from these sources. This edition was issued on 13 September 2026 without them. On 18 October 2026 every claim in it was checked against them and the page corrected; the print is left as issued. Where the record moved after the issue date, the page gives the later date beside the change. Where Buckmaster's and Bubeck's accounts differ, each is given with its own source. Posts on X were read through X's public embed, and openai.com, which answers with a bot check, through the outlets that quote it.

  1. 01The Hand in the Water, 11 Sep 2026, this site and its print, as issued: names Buckmaster and never Alpöge; reports OpenAI conceding that it cannot rule out that de-identified usage data helped train the model; closes on a result "contested by the people whose method it was built on."
  2. 02Tristan Buckmaster, statement, four pages, cims.nyu.edu/~tristanb/statement.pdf, 8 Sep 2026, the file created at 02:38 UTC. Page 1: the program's basic idea credited to Córdoba and Martínez-Zoroa, the Fields Medal line, the LLMs used ("Anthropic's Claude, OpenAI's Codex"), "For most of the past year progress was slow", smooth-forcing blowup for Boussinesq and Euler on 15 August, a Lean check on 22 August, blowup for hypo-dissipative Navier-Stokes believed but not released, and what he had planned to say. Pages 2 and 3: his email of 3 September to an OpenAI mathematician, quoted in full; the two calls of 6 September with Bubeck and that mathematician, Alpöge not on them; the two offers; the remarks about his career and about being nice; the text to Alpöge.
  3. 03Quanta Magazine (Konstantin Kakaes), "AI Has Solved One of Math's $1 Million Millennium Prize Problems", 8 Sep 2026: Charles Fefferman, who wrote the Clay Institute's official description of the problem, "I was thrilled that the problem was solved", and the heroes of the story "are Córdoba and Martínez-Zoroa"; Córdoba at the Institute for Mathematical Sciences in Madrid, Martínez-Zoroa at CUNEF University; Buckmaster's statement just before midnight on Monday 7 September; OpenAI's announcement on the morning of Tuesday 8 September, 12 hours after it; a Lean-verified Euler proof by 22 August.
  4. 04Scientific American (Joseph Howlett), "OpenAI claims blockbuster math breakthrough amid swirl of controversy", 8 Sep 2026: Córdoba, "We're a little bit in shock" and "If it's done, that will be a big surprise for us", reported as two quotes; Bubeck, that OpenAI's Navier-Stokes solution "did follow a similar method".
  5. 05Scientific American (Joseph Howlett), "OpenAI's blockbuster Navier-Stokes proof isn't what we thought it was", 13 Oct 2026: OpenAI's officials had "clearly and repeatedly stated that their proof followed the Spanish program"; "closer examination reveals that OpenAI's proof builds its unnatural force in a totally distinct way"; Cao-Labora (EPFL), "it is a different approach"; "OpenAI initially used a smaller team of agents to prove an intermediate result, and some experts say that this more modest squad did follow the program".
  6. 06Tristan Buckmaster, posts on Mastodon, mastodon.social/@tristanbuckmaster: 8 Sep 2026, 03:58 UTC, "Today, Levent Alpöge and I have made public three results", linking the statement, three papers and the Lean repository; 8 Sep, 16:56 UTC, quoting OpenAI's post on the training run begun 28 August; 10 Sep, "Sébastien's statement below is wildly false. Not only did he never apologize, he doubled down on his threat", naming Bubeck and quoting Bubeck's apology in full, and "Sam's tweet that they had a different approach is also false."
  7. 07Levent Alpöge, posts on X, @__alpoge__, read through X's public embed: 20 Jul 2026, 02:19 UTC, the evening of 19 July in New York, "hello there the jacobian conjecture is false", with the map; 19 Aug, 07:02 UTC, the Carathéodory conjecture; 23 Aug, 21:31 UTC, a complex structure on the six-sphere, manuscript at alpo.ge/s6.pdf, with no refereed acceptance found as of 18 Oct 2026; 8 Sep, 06:14 UTC, his email to Buckmaster of 19 Sep 2025, subject "Normal pure math collaboration with ai"; 8 Sep, 17:57 UTC, "i mean props to them for straight coming clean.", then a comparison with "another euler blowup proof we had"; 9 Sep, 04:50 UTC, "i contacted them on the night of wednesday, september 2nd" and "i had intel they had information about math work i was doing".
  8. 08OpenAI, "On the Navier-Stokes Millennium Prize Problem", openai.com, 8 Sep 2026, updated 10 Sep 2026. openai.com answers with a bot check, so the post was read as Buckmaster, VentureBeat and TechCrunch quote it, and the update as Ray Myers (raymyers.org, 11 Oct 2026) and Wikipedia's timeline quote it. The post: "Since August 28 we have been training a new internal model", and the effort begun 1 September. The update: "Following an investigation, we have confirmed that Buckmaster's Codex prompts over the two months preceding this announcement and paper on September 8, 2026, could not have influenced the system in any way, including through training." OpenAI on X, 8 Sep 2026: "we cannot rule out that de-identified data derived from their usage of our products helped improve" its models.
  9. 09Wikipedia, "Navier-Stokes priority controversy", read 18 Oct 2026: no official response from Anthropic recorded; OpenAI's update dated 10 September.
  10. 10Clay Mathematics Institute, claymath.org: Rules for the Millennium Prize Problems, publication in a qualifying outlet, then "at least two years must have passed since publication", then general acceptance; "Navier-Stokes Announcement", 11 Sep 2026, the problem "has apparently been settled" and "The process is deliberately unhurried, but we will provide updates."; The Millennium Prize Problems, read 18 Oct 2026, Navier-Stokes alone under Active problems, apart from the unsolved and the solved, the page last changed on 11 Sep 2026.
  11. 11Tristan Buckmaster, homepage, CV and publications, cims.nyu.edu/~tristanb, read 18 Oct 2026: dual Australian and British citizen; PhD 2014, University of Leipzig and the Max Planck Institute for Mathematics in the Sciences, thesis "Onsager's Conjecture"; the Leipzig PhD prize, 2014; Courant Instructor at NYU 2014 to 2017, assistant professor at Princeton 2017 to 2022, professor at Maryland 2022 to 2023, Professor of Mathematics at NYU from 2022, a member of the Institute for Advanced Study 2021 to 2022; three current projects, on singularities in compressible and incompressible fluids and on wave turbulence; convex integration for non-uniqueness, "stemming from my doctoral work"; the 2019 Clay Research Award for the work with Vicol.
  12. 12Clay Mathematics Institute, 2019 Clay Research Awards, 12 Aug 2019, and its profile of Tristan Buckmaster: a joint award to Buckmaster, Philip Isett and Vlad Vicol for "the analysis of partial differential equations, particularly the Navier-Stokes and Euler equations"; Buckmaster and Vicol proved that weak solutions of Navier-Stokes "can be remarkably wild".
  13. 13Bastounis (King's College London), Circelli and Hansen (Cambridge), "Navier-Stokes lost in translation", arXiv 2610.08144, 6 Oct 2026: OpenAI's Lean code "does not represent a semantically faithful translation" of its paper, two worked examples, Lemma 8.6 (m+5 derivatives in Lean against m+4 in the paper) and the pressure-flux bound (10.19), and showing only two "does not mean that these are the only cases".
  14. 14National Science Foundation, award 2407511, "CAREER: Singularities in fluids", New York University, principal investigator Tristan Buckmaster, 15 Apr 2024 to 31 Aug 2028, read 18 Oct 2026.
  15. 15The Next Web (Ana Maria Constantin), 10 Sep 2026, giving Bubeck's account: he asked why anyone "would risk their career over such accusations", meaning going to the press with "unfounded accusations"; he "retracted the remark on the spot"; the pair had admitted using internal Anthropic models on their Euler proof, so he could not treat Alpöge as an independent academic.
  16. 16ABC News (Dannielle Maguire and Jacinta Bowler), "Controversy erupts as OpenAI claims solution to Navier Stokes maths problem", 10 Sep 2026: Buckmaster's two calls with Bubeck "and another unnamed OpenAI mathematician"; Bubeck's two follow-up posts, "I said that I did not understand why one would risk their career [over unfounded accusations]", "I was trying to care for him", "I deeply apologise for this extremely poor choice of words", that he retracted the words on the spot, that he had suggested Buckmaster lead a rewrite of OpenAI's proof and that an Anthropic employee as an author of OpenAI's work would be "inappropriate"; Bubeck, "our proofs differ significantly"; Altman, "The team threatened us with unfounded accusations of plagiarism."
  17. 17Levent Alpöge, CV, people.math.harvard.edu/~alpoge/cv.pdf, read 18 Oct 2026: born 1 April 1992, Long Island; the Sophia Freund prize, "Highest GPA at Harvard"; "A VTK-based, CUDA-optimized Non-Parametric Vessel Detection Method", The VTK Journal, 2010; PhD Princeton 2020, advisor Manjul Bhargava; Junior Fellow, Society of Fellows, Harvard, 2021 to 2025.
  18. 18NASA JPL Small-Body Database, 25898 Alpoge (2000 YJ41), main belt, with the Minor Planet Center's citation of 28 Feb 2010: "Levent Alpoge (b. 1992) is a finalist in the 2010 Intel Science Talent Search (STS)".
  19. 19Intel Science Talent Search 2010, finalist profile, as reproduced by Mavi Boncuk, 21 Mar 2010: "Levent Alpoge, 17, from Dix Hills", a project on the algorithms used to analyse MRI scans of blood vessels, up to 500 times faster by parallel processing.
  20. 20Levent Alpöge, homepage, alpo.ge, read 18 Oct 2026: "anthropic, pbc / junior fellow, harvard sof"; his first work brought CUDA "to a medical computer vision problem"; "the two hilbert ten papers that came out independently".
  21. 21American Mathematical Society, "Levent Alpoge to receive 2015 AMS-MAA-SIAM Morgan Prize", EurekAlert, 9 Dec 2014: presented annually for outstanding research by an undergraduate at a college or university in Canada, Mexico or the United States; "Although he has yet even to begin graduate studies in mathematics, Alpoge has already authored or co-authored seven research papers"; Harvard's Sophia Freund Prize for the highest grade point average.
  22. 22Alpöge, Bhargava, Ho and Shnidman, "Rank stability in quadratic extensions and Hilbert's tenth problem for the ring of integers of a number field", arXiv 2501.18774, 30 Jan 2025; and Koymans and Pagano, arXiv 2412.01768, 2 Dec 2024. Each shows that Hilbert's tenth problem has a negative solution over the ring of integers of any number field.
  23. 23The Conversation (Melissa Lee), 22 Jul 2026: the counterexample found "using Anthropic's large language model Claude Fable 5".
  24. 24Fortune (Eva Roytburg), 21 Jul 2026: "On Sunday afternoon, while the rest of the world's eyes were glued to the World Cup final, an AI model resolved a problem that had tortured mathematicians since 1939."
  25. 25Sébastien Bubeck, posts on X, 8 Sep 2026, read through X's public embed: 06:43 UTC, "A series of false and inflammatory allegations against me are currently circulating"; 17:39 UTC, "The screenshot is my reaching out to Levent to coordinate our releases", with his texts to Alpöge, among them "an internal model produced a proof (both formal and informal) of NS with very little human input"; among the day's posts, "We began working on the Millennium problems due to viral twitter rumors that Anthropic had resolved 2 Millenium problems" and "I never ever asked for Levent to be removed from authorship of his own work"; and, as quoted on Hacker News and by The Next Web, "it would be simpler if Levent was not an Anthropic employee" and "I therefore felt I could not consider Levent to be an independent academic."
  26. 26VentureBeat (Carl Franzen), 8 Sep 2026: OpenAI "may use content from consumer services such as ChatGPT and Codex to train its models", users of ChatGPT Free, Plus and Pro can turn that off, and data from Business, Enterprise, Edu and the API is not used by default; the article does not establish which settings applied; the model's training "began August 28 and is continuing"; agent groups set to work on 1 September.
  27. 27TechCrunch (Russell Brandom), 8 Sep 2026: "OpenAI reserves the right to train models on Codex interactions, although users are able to opt-out"; OpenAI's post, "specifically saying that the latest effort began on September 1".
  28. 28The Washington Post (Miriam Waldvogel), 13 Sep 2026, as Wikipedia cites it; the Post itself was not opened: OpenAI spokesperson Laurance Fauconnet, "no user inputs past July 3rd could have influenced this system in any way."
  29. 29Diego Córdoba and Luis Martínez-Zoroa: arXiv 2309.08495, 15 Sep 2023, blowup for 3D Euler with a force of regularity C^(1,1/2-ε); with Fan Zheng, arXiv 2407.06776, 9 Jul 2024, hypodissipative Navier-Stokes, Archive for Rational Mechanics and Analysis 250 (2026); arXiv 2410.22920, 30 Oct 2024, the 2D incompressible porous media equation "with a smooth source".
  30. 30Sébastien Bubeck, homepage and biography, sbubeck.com, read 18 Oct 2026: student at the Ecole Normale Supérieure de Cachan 2005 to 2008; PhD at INRIA Nord Europe, Lille, 2007 to 2010; assistant professor at Princeton 2011 to 2014; "VP AI and Distinguished Scientist at Microsoft, spending 10 years in Microsoft Research"; monographs on multi-armed bandits (2012) and convex optimization (2015).
  31. 31Wikipedia, "Sébastien Bubeck", read 18 Oct 2026: born 16 April 1985, French-American.
  32. 32Bubeck and 13 co-authors, "Sparks of Artificial General Intelligence: Early experiments with GPT-4", arXiv 2303.12712, v1 22 Mar 2023 (154 pages), v5 13 Apr 2023 (155 pages), a preprint with no journal reference: "an early version of GPT-4, when it was still in active development by OpenAI".
  33. 33Gary Marcus, "The Sparks of AGI? Or the End of Science?", The Road to AI We Can Trust, 24 Mar 2023: "That claim would never survive serious scientific peer review"; the AGI claim "entirely open to interpretation"; a model about which "absolutely nothing has been revealed"; and, quoting another critic, "this is just completely irreproducible."
  34. 34Silicon Republic (Suhasini Srinivasaragavan), 15 Oct 2024: Microsoft's statement of 14 Oct, "Sebastien has decided to leave Microsoft to further his work toward developing AGI"; and, in the article's own words, "He led the development of the Phi SLMs (small language models)".
  35. 35Fortune, from Bloomberg, "Microsoft artificial intelligence VP Bubeck to join OpenAI", 14 Oct 2024: he "had been overseeing the company's work on small language models".
  36. 36Sam Altman, X, 8 Sep 2026, 18:02 UTC, read through X's public embed and as ABC News quotes it: "Seb--and everyone else--acted with integrity and generosity throughout."
  37. 37Terence Tao, posts on Mathstodon, mathstodon.xyz/@tao, read 18 Oct 2026: 8 Sep 2026, 04:27 UTC, "A remarkable achievement: Alpöge and Buckmaster have managed to push" and "Tristan Buckmaster kindly explained some of the key ideas to me over the phone, which made a refreshing change from AI-based communication modalities."; 8 Sep, 20:32 UTC, after OpenAI's announcement, "even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it" and "The incentives may now be pointing in the direction of no longer sharing any promising research directions"; forced blowup as one of the major approaches, as Córdoba and Martínez-Zoroa developed it; no post through 8 Oct 2026 assesses OpenAI's proof.
  38. 38OpenAI, "Finite Time Blowup for Navier-Stokes", 166 pages, 8 Sep 2026, cdn.openai.com: a smooth force compactly supported in space and time, establishing alternatives (C) and (D) of the Millennium problem statement; Córdoba and Martínez-Zoroa cited as precedent, the construction exploiting dynamical amplification "with a different role for the amplified disturbances".
  39. 39Diari de Tarragona, from EFE, "Sánchez elogia los matemáticos que sentaron las bases para que la IA resolviera un problema del Milenio", 18 Sep 2026: Pedro Sánchez at the Instituto de Ciencias Matemáticas, praising Córdoba and Martínez-Zoroa for the groundwork.
  40. 40Noam Brown (OpenAI), X, 8 Sep 2026, 06:47 UTC, read through X's public embed: "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", a parody of Sholto Douglas's post.
  41. 41Sholto Douglas (Anthropic), X, 8 Sep 2026, 06:22 UTC: "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".
  42. 42NPR (Geoff Brumfiel), 22 Sep 2026: "The Lean code produced by OpenAI's tools did compile as expected, Gómez-Serrano said"; Javier Gómez-Serrano (Brown University), "the community seems to have the consensus that it is correct" and "as of today, the paper doesn't teach us much"; James Maynard (Oxford), "very difficult to really extract any human understanding".
  43. 43Decrypt, "OpenAI Says It's Made Progress on a Second $1 Million Math Problem", 17 Sep 2026, citing The New York Times of 10 Sep 2026, which could not be opened: "substantial progress" on a second Millennium Prize problem, not named.
  44. 44SiliconANGLE (Maria Deutscher), "OpenAI publishes 722 AI-generated math discoveries in major scientific milestone", 7 Oct 2026: the papers "posted to GitHub late Tuesday", 6 October; on the Riemann hypothesis the model "didn't manage to come up with a complete answer", but it proved a quasi-Riemann hypothesis.
He was offered the title of closest human.
He went public instead.