OpenAI hands mathematicians 372 AI-generated proofs to check on GitHub
OpenAI posted 372 results from an internal model to GitHub, at about three hours of ChatGPT Pro compute each on average. Finding proofs is now cheap enough that the slow step is mathematicians checking and judging them.
The Engineer · Build desk
What happened
- OpenAI says nearly every result came from a single prompt to a single agent, though some took more than one attempt.
- Many of the proofs ship with Lean formalizations a machine can check, and OpenAI plans to formalize more.
- The Institute for Advanced Study advisory group OpenAI consulted could advise on how results are communicated, but not on whether or how fast they are produced.
- In an open letter, 25 Fields Medal winners warned that mass-producing true statements could damage mathematics, whose real goal is conceptual understanding.
Why it matters
- What it limits constraint Reviewers who trust the Lean files can skip the line-by-line logic check, but only for the formalized subset, and they still have to rule on originality themselves.
- What it costs cost OpenAI pays for generation in compute, while mathematicians pay for vetting in their own review time, and the volume could exceed their capacity for manual review.
- What it sets up precedent If a versioned GitHub release with Lean files is accepted as the record, other labs can circulate machine-generated results without waiting on journal referees.
- What doesn't add up contradiction A passing Lean check cannot settle the dispute between OpenAI and the Fields medalists over whether mass-produced results help mathematics or harm it.
Next story · Invest · Oct 8
Lean proof checks cover about 300 of the 722 math manuscripts OpenAI's unreleased model producedConfirmed3 publishers
Three hours is an average across 372 results [5][1]. OpenAI shared only averages, with no per-problem figures and no prompts [4]. Across the whole set that is roughly 1,116 hours of ChatGPT Pro Thinking compute [22]. Treat it as a number about OpenAI's problem list. For it to transfer to another group's list, their problems would have to resemble the ones this model was given, and failed attempts would have to be counted the same way. Some results took multiple attempts [13]. The Decoder's report does not say whether those retries are inside the average.
The Navier-Stokes run needed a 10,000-agent swarm and millions of dollars [6]. Next to that, one agent per result is a large drop in what a proof costs to find. Checking is slower. The Navier-Stokes solution has been under formal review for weeks, according to OpenAI [7].
Lean is aimed at that gap. It is a programming language built so a machine can check a proof [3]. When the checker accepts a formalized proof, the logic is correct [16]. No referee has to do the line-by-line pass. Lean cannot judge whether a result is relevant or original [16]. Each result is meant to solve or advance an open problem, some tied to the Riemann hypothesis [2]. Whether a given result is new and matters is still a mathematician's call. I think formalization is the right engineering choice for the half of review it covers. I'd want The Decoder's "many" formalized proofs [3] turned into a count before treating the bottleneck as cleared.
The packaging deserves credit. The repository keeps revision logs and citations [11]. OpenAI also published reasoning summaries, statistics on how many problems the model attempted, and compute estimates [8]. A versioned history suits results that will be corrected in public. OpenAI has said it wants to improve its citations and presentation [18]. The Decoder calls the choice of GitHub over journals a statement that the traditional process is too slow for this volume [17].
The doubts reach OpenAI's own advisers. The advisory group it consulted includes Fields Medal winner Timothy Gowers [19][4]. Gowers has warned that within one to two decades the mathematical literature could grow enormously while no human community remains that truly understands it [20]. Terence Tao has argued that training young mathematicians should emphasize the human side and tightly limit AI tool use [21].
OpenAI plans to fund workshops and conferences on understanding AI-produced results [10]. It says it is working on a responsible release of the model to "directly empower scientists with state-of-the-art capabilities" [12]. A wider release would put proof generation at roughly this cost in more hands, with the same human reviewers on the other end.
What to watch
- A count of how many of the 372 results carry Lean formalizations as the planned ones are added.
- The outcome of the formal review of OpenAI's Navier-Stokes solution.
- The terms of OpenAI's planned release of the model to scientists, and whether it comes with per-problem compute figures.
Clarity's read
What the record supports and how the coverage leans. The claims behind it follow.
Reality
- Evidence58
- Adoption10
- Hype gap+35
- Incentives72
- Confidence60
Perspective Coverage
6 publishers- Builder
- Builder 44%
- Operator
- Operator 31%
- Investor
- Investor 25%
Claim ledger
Ranked by verification strength, evidence, and original report placement.
- [1]
OpenAI published 372 new mathematical results generated by an internal frontier model.
- [2]
Each result is supposed to solve an open problem or make substantial progress toward one; the collection includes improvements to major computer algorithms and advances related to the Riemann hypothesis.
- [3]
Many of the proofs come with formalizations in Lean, a programming language built for machine-checkable mathematical proofs; more formalizations are planned.
- [4]
OpenAI consulted the Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study and loosely followed its public recommendations; the company did not publish any prompts and shared only average compute costs, not per-problem figures.
- [5]
On average, each result consumed roughly three hours of ChatGPT Pro Thinking compute.
- [6]
OpenAI's Navier-Stokes solution required a swarm of 10,000 agents and millions of dollars in compute.
- [7]
According to OpenAI, the same model produced a solution to a Navier-Stokes problem that has been under formal review for weeks.
- [8]
OpenAI published methodology details including summaries of the reasoning process, statistics on how many problems the model attempted, and estimates of compute costs.
- [9]
OpenAI set a boundary for the advisory group: the mathematicians can advise on how results get communicated, but not on whether or how fast they are produced.
- [10]
OpenAI plans to fund workshops and conferences focused on understanding AI-produced results.
- [11]
OpenAI hosts the results in a GitHub repository with revision logs and citations, instead of publishing in academic journals.
- [12]
OpenAI says it is working on a responsible release of the model to "directly empower scientists with state-of-the-art capabilities."
- [13]
Nearly every result came from a single prompt to a single AI agent, OpenAI says, though some took multiple attempts.
- [14]
In an open letter titled "A Severe Misalignment of AI in Mathematics," 25 Fields Medal winners warned of a deep disconnect between the AI industry's goals and those of mathematics, arguing problem-solving is a tool and proxy for conceptual understanding and that mass-producing true statements could destroy fertile ground.
- [15]
The reason for formalization is that the volume of AI-generated results could overwhelm the math community's capacity for manual review.
- [16]
Lean formalizations can verify logical correctness but cannot judge whether a result is mathematically relevant or original.
- [17]
The Decoder describes publishing on GitHub instead of in journals as a statement move implying the traditional process of doing science is too slow for this volume.
- [18]
OpenAI acknowledged it wants to improve the quality of its citations and presentation.
- [19]
The advisory group includes Fields Medal winner Timothy Gowers among other mathematicians.
- [20]
Gowers has warned that within one to two decades mathematical literature could grow enormously while no human community remains that truly understands it.
- [21]
Fields Medal winner Terence Tao has said training young mathematicians needs to emphasize the human side and tightly limit AI tool use.
- [22]
The 372 results used roughly 1,116 hours of ChatGPT Pro Thinking compute in total.
Sources
6 independent publishers whose own reporting we read for this story.
- dev.toWhat Agent Builders Can Borrow from OpenAI's Math Research
1 article · October 7, 2026
- qz.comOpenAI's AI solved one famous math problem. Then it cracked hundreds more
1 article · October 7, 2026
- runtimewire.comOpenAI publishes 722 math manuscripts generated by an unreleased model
1 article · October 6, 2026
- techspot.comOpenAI publishes 722 AI-generated math papers as researchers challenge its closed model
1 article · October 7, 2026
- the-decoder.comOpenAI dumps 372 AI-generated math proofs on GitHub, telling the academic world to keep up
2 articles · October 7, 2026
- theneuron.ai😺 OpenAI’s AI produced 722 math manuscripts
1 article · October 7, 2026
Topics and entities
Topics
- Formal Verification
- Scholarly publishing
- AI for Mathematics