OpenAI Claims 100-Plus Open Math Problems Solved: The Verification Is Still Underway

An OpenAI internal model deployed as roughly 10,000 concurrent AI agents has produced a machine-verified proof of a fundamental fluid dynamics problem — one of mathematics' seven Millennium Prize Problems — and the company says the same system has resolved more than 100 other open mathematical questions. But the Clay Mathematics Institute has not awarded the $1 million prize. No list of the other claimed problems and no corresponding proofs have been made public as of October 8. The mathematics community's response ranges from qualified engagement to pointed skepticism, and a live attribution dispute adds a contested dimension to the announcement.

What 10,000 Agents Did for 88 Hours

On September 8, OpenAI announced it had produced a Lean-verified proof showing that the three-dimensional Navier-Stokes equations can develop a singularity in finite time. The proof was produced by an unnamed internal model described as "significantly more capable than GPT-6 Astra," the company's publicly released flagship. The model had begun training on August 28 and was not publicly available at announcement time. OpenAI stated explicitly that it does not intend to claim the Millennium Prize for the result.

The Navier-Stokes computation ran for 88 hours. Approximately 10,000 model instances operated concurrently, exchanging roughly 2.7 million messages and generating approximately 130 billion output tokens — all figures from OpenAI, not independently verified. After completing the proof, OpenAI used GPT-6 Astra to formalize the result in Lean, a formal proof-verification language in which every logical step is checked against mathematical axioms — a process that took an additional 17 hours. The Lean proof files are publicly available alongside a 166-page analytical paper submitted for peer review.

Blowup, Not Regularity — and Not the Full Clay Problem

The Navier-Stokes Millennium Prize concerns whether smooth solutions to the 3D incompressible equations can develop a finite-time singularity. The Clay formulation includes four variants (A–D): statements A and B cover the unforced Cauchy problem; statements C and D add a smooth external forcing term. OpenAI's proof demonstrates that with such a smooth external force, a vortex can spiral inward, elongate, and develop a singularity — resolving the question for variants C and D by showing blowup does occur.

This is technically meaningful: no prior formal proof of the forced-case result existed. But resolving C and D is not the same as resolving A or B, which most working mathematicians consider the harder and more physically significant case. The Clay Prize does not separately recognize forced-case results, and as of October 8 the Clay Institute still lists Navier-Stokes as active and pending community review. Even if the proof passes peer review and is broadly accepted, Clay's rules additionally require two years of public availability before a prize can be awarded — placing eligibility no earlier than approximately late 2028.

The mathematical strategy OpenAI's agents exploited was developed over years by Diego Córdoba of the Institute for Mathematical Sciences in Madrid and Luis Martínez-Zoroa of CUNEF University, who pioneered analytic techniques for constructing fluid singularities. Princeton's Charles Fefferman, who wrote the Clay Institute's official description of the Navier-Stokes problem, said the intellectual heroes of the story are Córdoba and Martínez-Zoroa.

A Governance Panel and an Unverified Problem List

On September 21, OpenAI introduced AGMAI — the Advisory Group on Mathematics and Artificial Intelligence — and announced that the same internal model had resolved more than 100 additional open mathematical problems. The nine-member panel, hosted at Princeton's Institute for Advanced Study, includes Fields Medalists Timothy Gowers and Martin Hairer alongside mathematical physicist Edward Witten, and operates independently of OpenAI with members receiving no payment. The panel is advisory only; it has no authority over OpenAI's publication schedule.

AGMAI's stated current task is advising OpenAI on how to coordinate the release of the claimed additional results. As of this writing, no public list of the 100-plus problems and no corresponding proofs have appeared. The claims rest entirely on OpenAI's September 21 announcement.

Read more: OpenAI flags progress on a second Millennium Prize Problem before the first is verified

The mathematical community's organized response predated the AGMAI announcement. On September 11, twenty-five Fields Medalists published "A Severe Misalignment of AI in Mathematics" at mathandai.org, warning of rushed verification and the risk that AI-generated proofs could contaminate mathematical literature. Signatories include Terence Tao, Peter Scholze, Maryna Viazovska, Manjul Bhargava, and James Maynard. Only one AGMAI member — Camillo De Lellis — also signed the letter, reflecting a divided rather than uniformly hostile expert community.

An Attribution Dispute OpenAI Has Partially Acknowledged

The night before OpenAI's announcement, NYU mathematician Tristan Buckmaster published a statement saying he and Levent Alpöge — a mathematician at Anthropic — had spent nearly a year developing proofs for forced blowup in the three-dimensional Euler equations and related fluid systems using a combination of Anthropic's and OpenAI's own tools, including Codex. Their Lean-verified results appeared September 7.

OpenAI's announcement acknowledged the context: the company said it began work on September 1 after hearing "rumors" that Alpöge and Buckmaster had solved a Millennium Prize problem. OpenAI credited them with priority on the Euler result and said it reached out on September 6 to propose a concurrent release, at which point it learned they had resolved the forced Euler problem rather than Navier-Stokes. OpenAI stated that its agents did not see any of Buckmaster and Alpöge's work before it was made public, and that a subsequent investigation confirmed Buckmaster's Codex prompts "could not have influenced the system in any way, including through training."

Buckmaster has contested aspects of this account, describing the circumstances of the September 6 call and alleging pressure from OpenAI researcher Sébastien Bubeck; Bubeck denied that characterization. OpenAI has not published its investigation records, and no external audit mechanism exists to verify the conclusion independently. Per Quanta Magazine's reporting, different parties are presenting different versions and the details remain murky. The dispute represents the first high-profile attribution conflict in Millennium Prize-adjacent AI research, where the boundary between tool use and co-discovery has no established precedent.

Read more: Google internal math AI targeted an unsolved number theory problem

The FrontierMath Trajectory and Competitive Context

The September 8 result reflects a measurable capability curve. On Epoch AI's FrontierMath Tier 4 benchmark — which tests research-level mathematical reasoning — GPT-4-era models scored roughly 5 percent in 2024. By mid-2026, GPT-5.6 Sol had reached 83 percent. The unnamed model used for the September work sits above GPT-6 Astra on OpenAI's internal capability scale. All FrontierMath figures are from Epoch AI and OpenAI reporting.

No other lab has published comparable research-math results. Google DeepMind's AlphaProof, combined with AlphaGeometry 2, solved four of six IMO 2024 problems at silver-medal level — meaningful for competition mathematics but structurally different from tackling unsolved research problems.

OpenAI's multi-agent reinforcement learning approach differs architecturally from AlphaProof's game-tree search. Whether orchestrating thousands of model instances generalizes across mathematical domains, or whether it was particularly suited to the structure of forced Navier-Stokes, cannot be determined from currently public information.

The infrastructure requirements are significant. Generating 300 billion tokens across 4.9 million agent-to-agent messages over a multi-day run demands a level of compute that no individual research group or university math department could independently replicate — OpenAI put the total cost in the millions of dollars. This creates an asymmetry: the Lean proof files are public, but the research process that generated them is not reproducible outside a handful of frontier labs. That asymmetry is part of what the open letter signatories identified as a structural concern — mathematical progress that depends on concentrated computational resources produces results the community can verify but not independently generate.

What the AGMAI Timeline Actually Determines

AGMAI's role means any proof releases should follow a structured schedule. Peer review of the 166-page paper will provide the first independent technical assessment of the core Navier-Stokes result. For the Clay Prize, the two-year public availability requirement means the earliest possible eligibility window is approximately late 2028 — contingent on successful peer review, public acceptance, and the Clay Institute initiating its formal review process.

What OpenAI has demonstrated is that a large multi-agent reinforcement learning system, running for days rather than minutes, can produce Lean-verified mathematics at a level no prior AI result has reached. Whether that capability extends to the full unforced Navier-Stokes problem, or to the more than 100 other claimed open problems, will be answered by what AGMAI coordinates for release — and when the broader community has the chance to assess it.