A declaration called A Severe Misalignment of AI in Mathematics was published this morning at mathandai.org, signed by twenty-five Fields Medalists. It was posted to Hacker News at 12:45 Central and had 432 points and roughly 490 comments by the time I started reading it at 17:15. The signature block is the most concentrated pile of mathematical authority I have seen attached to a public statement about software.
The central complaint is about credit. Results, the declaration says, are now “announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others,” and this “raises severe attribution and plagiarism questions.”
The document contains no citations. No named result, no named system, no named company, no date attached to anything it describes, no link. I checked this twice: once by reading the rendered page, once by counting the anchor tags in the declaration body, which is zero. Its opening sentence is an empirical claim: that over the last few months LLMs have improved “to the point that they can solve major outstanding problems in many fields of mathematics.” Which problems, which systems, which months, and which fields are left to the reader.
That is not a gotcha, and the declaration is not wrong. The week that produced it is, as far as I can tell, the strongest evidence anyone could assemble for its thesis. But that evidence exists in documents the declaration does not point to, and the omission costs the signatories something specific, which I will get to.
The verifiable record of the last four weeks is unusually complete, because nearly everyone involved published a dated first-person account.
On 7 September, Levent Alpöge and Tristan Buckmaster released three finite-time blowup results, for the incompressible porous medium equation, for two-dimensional Boussinesq, and for three-dimensional incompressible Euler. Each had a smooth forcing term and each was formalized in Lean. The same day, Terence Tao wrote them up, noting that the method “has a high likelihood of also extending to Navier-Stokes as well.”
The next day, OpenAI announced that an internal system had produced exactly that extension: a proof, with a Lean formalization, that a smoothly forced fluid starting at rest can develop a singularity in finite time. The company is precise about what this is. It “resolves the Navier–Stokes Millennium Prize problem by establishing statement ‘C’ (and also ‘D’) in the official Millennium Prize formulation,” which is the forced, finite-energy disproof branch, not the famous unforced one. It also says plainly that it does not intend to claim the prize, which is the correct call: the Clay Mathematics Institute’s own rules require publication in “a refereed mathematics publication of worldwide repute” and then at least “two (2) years” of survival in the literature before anyone is eligible.
The compute figures are OpenAI’s own, a company claim rather than an independent measurement: on the order of 10,000 concurrent agents, a resolution 88 hours after launch, another 17 hours for Lean verification, and roughly 130 billion output tokens on Navier–Stokes alone out of about 300 billion across all the problems attempted. Those totals include a second, smaller result announced on the same page: nearly 100 agents working for about 50 hours produced what OpenAI calls a “Euler regularity disproof,” for the unforced case, which is the variant Alpöge and Buckmaster had not done.
By OpenAI’s own account, the company “heard rumors that two Millennium Prize problems had been resolved” on 1 September, and its effort “began on September 1st after hearing a rumor which we later realized was related to” Alpöge and Buckmaster. The provenance of the machine result runs through a rumor about two humans. That is an attribution fact, and it is in the announcement.
Buckmaster published a four-page personal statement the night before OpenAI’s announcement. I read the whole thing. It is the most careful piece of attribution I have seen produced under pressure, and it does, precisely, the things the declaration says are no longer being done.
It assigns priority away from itself in its third paragraph: “The credit for the basic idea of this program goes to Diego Córdoba and Luis Martínez-Zoroa.” Each model gets named against the work it did, and each step gets a date: 15 August for the results, 22 August for the Lean verification. On writeup quality it is candid in a way I rarely see in public, calling one of the papers “AI slop” and the first machine-generated proof “the most horrendous I have ever read.” It recounts a disputed conversation with OpenAI’s Sébastien Bubeck, including a request that Alpöge be removed from authorship because he works at Anthropic, and then immediately fences what it is not claiming: “I have not seen OpenAI’s proof… I do not know whether our data was used. I am not accusing anyone of anything.”
OpenAI has denied the data question directly. Its page originally allowed that “we cannot rule out that de-identified data” from product use may have helped, then was updated on 10 September to say an investigation confirmed Buckmaster’s Codex prompts “could not have influenced the system in any way, including through training.” I have no way to adjudicate that and I am not going to pretend otherwise. What I can check is who named whom.
Both Tao’s post and Buckmaster’s statement point at the same prior work: a preprint by Diego Córdoba and Luis Martínez-Zoroa, submitted to arXiv on 30 October 2024 and last revised on 13 February 2025, establishing finite-time singularities for the two-dimensional incompressible porous media equation with a smooth source. That is the program. Buckmaster describes what he and Alpöge did as taking Córdoba and Martínez-Zoroa’s construction, which worked with rough forcing, and pushing it to smooth forcing and to Euler, with, in his words, “a great deal of help from LLMs.” He goes further than a citation: “in view of this body of work, I believe Luis Martínez-Zoroa deserves a Fields Medal.”
Neither name appears in OpenAI’s announcement. I searched the full text; the only outside mathematicians it names are Alpöge and Buckmaster, whose priority it recognises on forced Euler, plus Navier, Stokes, and Leray for the nineteenth and twentieth centuries. And neither name appears in the declaration, which credits no one.
So the credit that actually thinned out over those four days belongs to two people who were never in the room for any of it, and it thinned out in precisely the way the declaration describes, by being one link further back than anyone in a hurry bothers to reach. The declaration had the strongest possible example of its own thesis available, in public, from its own lead signatory, and it did not use it.
It would be easy to read the missing citations as carelessness. It isn’t. Tao posted the declaration on his own blog the same morning, writing that it “grew out of discussions between ourselves over the last week” and conceding that “we did not have the time to have a more consultative process, as with Leiden; but we decided that the urgency of the situation was such that we needed to release a statement sooner rather than later.” He names the comparator, the Leiden declaration, and links it. Four days before that he had written the careful version, with every name, the arXiv link, and an exact statement of which equations were done and which were not. Within four days, on the same subject, the same person produced one of the week’s most specific documents and one of its least.
That is a genre decision. A declaration is supposed to outlive its occasion, and naming a company in paragraph one turns a statement about mathematics into a statement about OpenAI. I understand the reasoning. But the cost is that the document cannot be checked. Everything rests on that first sentence, “many fields of mathematics,” and the verified record I can assemble this week covers one area of fluid dynamics, one family of blowup constructions. Maybe the plural is right. A single footnote would settle it, and its absence means the strongest claim in the document is also the only one a reader has to take on trust. I have written before about findings that evaporate once you read the methodology page underneath them; here there is no page underneath.
None of this is new, which is the part I find steadying. When Appel and Haken proved the four-color theorem in 1976, the objection was not that they had cheated but that nobody could survey the machine’s contribution. Thomas Tymoczko argued in The Journal of Philosophy in 1979 that a proof no human could check made the result empirical rather than a priori, a report on a successful experiment rather than an argument anyone could follow. Fifty years later the machine writes the proof instead of checking the cases, Buckmaster calls his own writeup AI slop in public, and the underlying worry is unchanged: a result has arrived without anyone being able to say why it is true.
What changed is the clock. Córdoba and Martínez-Zoroa’s preprint sat for twenty-two months. Alpöge and Buckmaster worked for about a year, then moved from result to Lean certificate in seven days. OpenAI went from a rumor to a formalized proof in five. Clay still wants two years of public survival before it will call anything settled, and on the evidence of this week that requirement looks less like bureaucracy and more like the only remaining institution operating on the timescale at which credit can actually be assigned.
Twenty-five of the roughly forty-seven living Fields Medalists signed this declaration — a majority, on a count of 68 medals awarded through 2026 and 21 laureates deceased. That is not a petition; it is closer to a quorum. Which is exactly why I wish it had spent one sentence on the preprint from October 2024. The declaration asks the companies to slow down and say where the ideas came from. The people best positioned to demonstrate what that looks like already did it, four days earlier, and then left it out of the document that asked.
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