OpenAI AI math and science claims tracker: what is checked, disputed or still pending

This is the running record of OpenAI's claimed AI-made breakthroughs in mathematics, computer science and physics since September 2026: what was claimed, what has been checked, and what has been disputed. It is a living page. We update it when the status of a claim changes, and we date every line. Status labels are ours, and they describe the evidence, not OpenAI's confidence.

How to read the status labels

• Claimed: announced by OpenAI, no independent check reported.
• Under examination: outside experts have been asked to check it, and no verdict is published.
• Disputed: named experts publicly challenge the result, its framing or its credit.
• Machine-checked: a Lean proof exists, which confirms the steps follow from the statement as written, not that the statement is the one that matters. Our piece on what a verified AI proof means covers the distinction.

Everything below comes from reporting we opened, linked in the sources. OpenAI's own posts are described through that reporting. Where outlets conflict, we say so.

The timeline

September 1, 2026. OpenAI said it had begun large-scale work on all of the Millennium Prize Problems, according to the Wikipedia article on the company's bulk release of mathematical papers.

September 8, 2026: Navier-Stokes. Status: disputed. OpenAI said an internal model, which it described as more capable than GPT-6 Astra, proved that three-dimensional Navier-Stokes can develop a singularity in finite time. The Next Web reported that the effort began September 1 and used about 10,000 concurrent agents over about 88 hours, at a cost OpenAI put in the millions of dollars. The proof had not been published when announced, and OpenAI said it does not intend to claim the $1 million Clay prize. Tristan Buckmaster of NYU, who with Levent Alpöge of Anthropic had posted preprints on related problems, said he had not seen OpenAI's proof and alleged his group's results had been shared with OpenAI days earlier. OpenAI disputes his account.

September 11, 2026. A declaration titled "A Severe Misalignment of AI in Mathematics," signed by 28 Fields Medalists, was published, per Wikipedia.

September 21, 2026: the wrong problem? Scientific American reported that the proof solves a variant with an external force acting on the fluid, which most experts studying the problem do not consider. Three mathematicians posted an arXiv preprint arguing OpenAI's method can never extend to the full problem. Luis Silvestre of the University of Chicago told the magazine: "The most important problem is unsolved." Diego Córdoba said: "All fluids we know of are under some kind of external force." The Clay problem statement written by Charles Fefferman includes an option that permits an external force, so the result arguably meets the official formulation, Scientific American noted. Same day, per Wikipedia, an OpenAI blog post said an internal model trained since August 28 had resolved more than 100 long-standing open problems.

September 29, 2026. A nine-member advisory group hosted at the Institute for Advanced Study in Princeton published recommendations, per Wikipedia.

October 6, 2026: 722 manuscripts. Status: mixed, partly machine-checked. OpenAI released 722 manuscripts organized into 372 topics on GitHub. About half have Lean machine-verified proofs, per Wikipedia. Three papers were retracted within a day and 14 were revised. Claims include a matrix multiplication exponent of O(n^2.25+ε) against a previous record of about 2.37, and an irrationality exponent of 2 for pi. A claim that Hilbert's tenth problem over the rationals is unsolvable came with no Lean formalization. Terence Tao and other mathematicians criticized the volume of claims released without structured verification, per OfficeChai.

October 26, 2026: three more claims. OpenAI announced:

• Exponential Time Hypothesis. Status: under examination, machine-checked. The model produced the disproof on October 16 and OpenAI checked it in Lean the next day. Russell Impagliazzo and Ramamohan Paturi of UC San Diego and Ryan Williams of MIT are organizing an open examination, and their letter says: "Our involvement should not be taken as certification of the claim." OpenAI agreed to release all raw data and fund a conference.
• Local smoothing conjecture, in all dimensions. Status: claimed, released for scrutiny. If correct it also settles the Kakeya and Stein restriction conjectures, per The Next Web. Local smoothing was proved in two dimensions in 2019 and Kakeya in three dimensions in 2025.
• Existence of certain four-dimensional quantum field theories, including QCD. Status: claimed, material withheld. A group led by Nobel laureate David Gross will write up the work and chose not to release the AI-produced material for now.

What the pattern shows

Three things recur across the entries. First, the verification layer is catching up unevenly. The ETH review has named, qualified reviewers and a data-release commitment. The Navier-Stokes record shows a result that can be formally correct and still contested on whether it answers the question people care about. Second, credit is unresolved: OpenAI says it does not seek academic credit and gave $5 million to the Simons Foundation for workshops on AI-produced results, while Buckmaster's dispute and the Fields Medalists' declaration show the field has not settled the norms. Third, volume is itself a problem, as Tao's criticism and the 17 corrections to the October 6 batch show.

What would change a status

A verdict from the ETH group moves that entry to confirmed or refuted. A published Clay Mathematics Institute decision, which we have not seen, would settle the prize question for Navier-Stokes, though not the dispute over the variant. A third-party Lean audit of the October 6 statements would tell us how many of the machine-checked papers prove what their titles say. Each of these would earn a dated update here.

Our take

Treat every entry as a claim from a lab with a commercial interest until independent experts say otherwise, and treat the experts' hedges as the signal. The most reliable sentence we can print today is that OpenAI has made a run of ambitious claims, some of them machine-checked, none yet confirmed by the communities that own the problems, and one publicly contested on the question of what was solved. We will update this page when that changes, and we will correct it in public if we get a line wrong.