OpenAI's 700-manuscript proof release stalls where mathematicians have to check it

Kevin Buzzard, a mathematics professor at Imperial College London, went through OpenAI's release looking for theorems in his own area, algebraic number theory. He found numerous ones, and around six that immediately stood out, The Verge reported ^[2]. Few, if any, of those six appeared to be formally verified in Lean ^[2]. "Hence, I either have to read possibly-not-correct slop, or wait for others to do the same, or wait for someone to formalise them before I can say for sure that the results are even correct," Buzzard said ^[3].

Getting that far took time. Several mathematicians told The Verge that working through the roughly 40-page table of contents and abstracts took them the better part of an hour ^[1]. "Just going over the entire list of abstracts is overwhelming," said Alvaro Lozano-Robledo, a mathematics professor at the University of Connecticut ^[1].

Users narrowed the release to their own specialty and looked for a Lean file. Where there wasn't one, they waited for someone else to do the reading ^[2][3]. Release teams tell themselves users read the headline count and start building on it.

What shipped, and who it was built for

OpenAI put more than 700 manuscripts on GitHub on October 6, claiming solutions to hundreds of open problems ^[4]. The counts vary with the counter. Exponential View tallied 722 manuscripts in 372 families ^[5]. The Verge reported nearly 400 results ^[6]. OpenAI's own verification figures, as The Verge relayed them, used a base of 719 manuscripts ^[11]. The repository was big enough that OpenAI published guidance on how to navigate it ^[6].

A LessWrong post describes how it was produced. A single model, mostly working from a single prompt, was asked to attempt about 4,000 problems and spent an average of three hours of compute per solution found ^[7]. The prompt included the line 'Even if the problem is "open," the intention is that you should resolve it and present a full solution.' ^[8] Set against The Verge's count of nearly 400 results, the hit rate is roughly one in ten ^[39].

Johannes Schmitt, one of the researchers whose responses The Decoder collected, argued the papers were a secondary result of OpenAI's work on its models. In his view, the company used unsolved problems as tests because its frontier models had outgrown easier ones ^[9]. If he is right, the first customer for this release was OpenAI's own model team, and mathematicians received the by-product, more than 700 manuscripts at once ^[4][9].

A machine check, and the cost of checking it

Lean is what makes any of this usable at speed. Formalizations in the proof assistant have been instrumental in assessing OpenAI's earlier math claims, The Verge reported, because they give researchers confidence that a claim is logically correct even when they do not fully understand the argument ^[10].

Coverage was partial. On GitHub, OpenAI said the results are "at different stages of verification" and that "many, but not all, of the manuscripts have been formalized" ^[11]. By its count, 300 top-line results out of 719 manuscripts had been formalized, around 42 percent, and it said it "will update the repository with more formalizations as we obtain them" ^[11]. Counted as a share of manuscripts, as The Verge did, that leaves 419 without a formal proof ^[40].

Researchers also have to confirm that the formalization proves what the manuscript claims. Several mathematicians told The Verge the quality was inconsistent and the verified statements did not always map neatly onto the claims in the papers ^[12]. Some papers have already been withdrawn, and others drew criticism for being difficult to read, according to The Decoder ^[13].

Time-to-value for the people expected to build on this work is measured in years: the mathematicians The Verge spoke with agreed that simply understanding the release could take that long, and many feared OpenAI would move on, or release more, before then ^[14].

A correct proof with nobody behind it

Terence Tao's response separates correctness from use. He wrote that the proofs appeared to "introduce clever new ideas that will be fruitful once digested," and said he was "deeply frustrated" that nobody was available to discuss the work, present it in talks or teach it to students, The Decoder reported ^[15]. Bryna Kra, a mathematics professor at Northwestern University, made the same complaint to Business Insider. "Mathematics is an extraordinarily collaborative field," Kra said. "There is nobody at this company who could possibly give a talk or answer technical questions about any of these results." ^[16]

The field has seen a proof without a presenter before. Ian Agol compared the release to Grigori Perelman's 2002 proof. Perelman gave few talks about his work, and several research teams spent years reconstructing the missing steps ^[17].

Exponential View, writing about knowledge and the ability to share it coming apart, put the requirement on the machines: "We could bring them together if we insist our AI systems provide explanations, not merely proofs. If we don't, we'll have more answers and less understanding." ^[18]

OpenAI's stated plan addresses part of this. The company said the release included protocols for revisions and citations, and that it planned to improve the papers' presentation and fund workshops to help researchers understand the results ^[19]. It did not respond to Business Insider's request for comment ^[19].

What verification does not reach

Most of the reaction was about something other than checkability. Of more than 100 researcher responses collected by the blog Proofs and Prompts, few focused on the quality of the solutions, The Decoder found; many described shock, paralysis and fears about their future in the profession ^[20].

Ben Green said some results were "absolutely shocking to me." According to Green, the release resolved roughly three-quarters of the research goals in a prestigious European grant he had received that June ^[21]. "So we've had whole research programs wiped out on Tuesday by their dump," Tristan Buckmaster, a mathematics professor at New York University, said on CNBC ^[22]. Hugo Duminil-Copin, a 2022 Fields Medalist, wrote that OpenAI claimed results on every major unsolved problem he had publicly discussed over his career. "The shock is immense. I am paralysed," he wrote ^[23]. In a seminar, he said his PhD students and postdocs were "in a state of total panic" ^[24].

Credit is the second grievance. "You have to understand, they have access to all our research proposals," Buckmaster said, according to Business Insider, describing grant panelists who put summaries of proposals into a language model ^[25]. Speaking to The New York Times about an earlier development, he said: "There's likely to be a bunch of results where they take someone's work and then take it to completion." ^[26] Kra worries that researchers who fear their unfinished ideas could be absorbed by AI before publication will become more secretive ^[27]. That is a change in user behavior, and it runs against the open seminar culture the release depends on. A new group calling itself the Association for Human Mathematics has called on mathematicians to stop working with OpenAI ^[28]. Alex Kontorovich, a distinguished professor at Rutgers who sees reasons for optimism, said: "I don't think we have any interest in giving prizes to someone who pressed the button." ^[29]

In our view, full Lean coverage would have solved Buzzard's problem and left Green's untouched. The grievances in this section concern careers and credit ^[21][25].

The crypto scare had no artifact to check

Peter Scholze carried the worry into security. He raised the possibility that these systems could find ways to break widely used encryption, writing that the difficulty of finding such algorithms "does, to my non-expert eyes, not significantly exceed what these systems are now capable of." ^[30]

On October 7, Ethereum Foundation researcher Justin Drake warned that powerful AI systems might eventually find attacks on the elliptic-curve cryptography that authorizes blockchain transactions ^[32]. Exponential View reported he urged preparation for "bunker mode," warning AI could undermine those signatures before quantum computers do, and that Meltem Demirors called it a "sobering moment" for the industry ^[31]. Vitalik Buterin backed taking the possibility seriously but discouraged users from rushing to move funds into new wallets ^[32]. Buterin also warned that AI could find shortcuts against lattice-based cryptography, comparing the risk to the history of integer factorization ^[33]. As an illustration, he floated multiplying key sizes by ten, and said Ethereum's long-term roadmap has moved toward hash-based signatures and proofs ^[34].

Charles Hoskinson, Cardano's founder, answered on October 9. "The factoring analogy is wrong," he wrote, arguing that Buterin had not identified a credible new attack ^[35]. "The case against lattices is the GNFS story, a.k.a. a hunch about 'structure,' and a multiplier pulled out of thin air," Hoskinson wrote ^[36]. He called the ten-times idea "numerology" and said security parameters must move with measurable improvements in attack algorithms ^[34]. The lattice schemes at issue, ML-KEM and ML-DSA, were approved by the U.S. National Institute of Standards and Technology in August 2024 as FIPS 203 and FIPS 204 ^[37]. Steering developers away from them, Hoskinson warned, could slow protections already being deployed and leave systems exposed to future quantum attacks ^[38].

The two men disagree on how to act on a warning. Neither, in these reports, points to an AI-found attack on any of the schemes they are arguing about ^[35]. Hoskinson is applying Buzzard's standard to security: change parameters when there is a measured result ^[34]. We think Buterin's own advice to users, not to rush their funds into new wallets, sits closer to that standard than the public exchange suggests ^[32].

A 2x2 for Monday

For a team shipping AI output to expert users, two questions sort it. The first is whether the person receiving the output can verify it at a cost they will actually pay, including confirming that the check matches the claim ^[12]. The second is whether a named person can answer questions about it ^[16].

- Checkable, with an owner. Experts adopt it. Nothing in this release fully fits yet; a Lean-verified result plus the workshops OpenAI has promised would come closest ^[11][19]. - Checkable, no owner. Trusted but undigested. This is Tao's "fruitful once digested" case, and Agol's Perelman comparison puts the digestion in years ^[15][17]. - Owned, not checkable. Argued over and not acted on. Buterin and Hoskinson have put their names to opposite positions, and the decision waits on a measured attack ^[34][35]. - Neither. Buzzard's pile. Users wait for someone else to read it ^[3].

We think teams should ship the checkable-and-owned quadrant first and hold the rest until it qualifies. The tradeoff is a smaller launch: on OpenAI's own count, leading with formalized work would have meant 300 results instead of a 719-manuscript repository ^[11]. We would track two numbers for the rollout: the share of outputs whose check has been matched to the claim, and how long it takes an outside expert to cite or build on a result.

One question sits outside the grid. It asks whether the output finishes work that a user was paid to do. For Green's grant and the research programs Buckmaster described, the answer was yes ^[21][22].