OpenAI says its next model solved ten open math problems. Mathematicians say two recycle earlier work without credit.

What happened

On August 1, OpenAI published ten results that it said resolve or make substantial progress on long-standing open problems across high-dimensional geometry, coding theory, group theory, complexity and lattice cryptography. The company said the proofs were generated by an internal version of Astra, described as its next major model, and that the tokens needed to find them "would cost roughly $2,000 at Sol API rates." Humans then prepared the manuscripts, and the model formalised each argument as a machine-checkable Lean certificate.

Within days, working mathematicians disputed how two of the headline results were presented. Reporting in Scientific American quoted Steven Miller, a mathematician at Yeshiva University, who said the sphere-packing result reuses an argument from his own 2016 paper without credit, and that the pattern "points to research misconduct." Francesco Fournier-Facio, a group theorist at the University of Cambridge, said the non-sofic groups result combined ideas from existing 2016 and 2019 papers, and framed the issue as overstatement rather than fraud, pointing at "the big PR machine that wants to sound as impressive as possible." According to that reporting, OpenAI had initially described some of the problems as having seen no progress for around a decade, then softened the language after the criticism. An OpenAI spokesperson told the magazine the company takes responsibility for the correctness of the results and planned minor updates.

The attribution question OpenAI raised itself

The announcement is notable for how directly it addresses credit. In a section titled "Responsibility to the mathematical community," OpenAI cites the Leiden Declaration on AI and Mathematics and argues that "claiming human authorship for a proof generated entirely by an AI system would misrepresent both the system's contribution and the nature of genuine human intellectual work." The dispute reported by Scientific American is about a different kind of attribution: not who among the humans deserves credit, but whether earlier published work by other mathematicians was acknowledged at all. A machine-checkable Lean certificate can establish that a proof is correct. It cannot establish that the proof is new, or that its ingredients were credited.

Analysis

This is the second time in under a year that an OpenAI mathematics claim has drawn a public correction from the people who work in the field. In October 2025, a company executive said GPT-5 had found solutions to ten previously unsolved Erdős problems; mathematician Thomas Bloom, who maintains the relevant problem list, called that "a dramatic misrepresentation," because the problems were open to him, not open to the field. The recurring shape matters more than any single result: a striking headline number, a very low quoted cost, and a verification story that arrives days or weeks later from independent specialists rather than before publication.

Two cautions are worth keeping separate from the integrity question. First, the widely shared "$2,000 in compute" figure describes only the successful runs, and says nothing about how many problems were attempted, or the cost of the mathematicians who selected the problems and wrote the manuscripts. Without the denominator, the figure is not yet an efficiency claim that can be evaluated. Second, the results were released through a company blog post and a long manuscript that, as critics including Gary Marcus noted, contains little about how the system works or what role humans played. Correctness that can be checked in Lean and provenance that can be checked by peer review are different properties, and only one of them was supplied on release.

None of this means the underlying results are worthless. It means the interesting claim, that a model is doing genuinely new mathematics, is exactly the claim the release did not make easy to verify. The useful development here is not the ten proofs. It is that specialists audited them in public within days, which is roughly what a healthy response to an "AI solved X" announcement should look like.

What to watch

Whether OpenAI's promised updates add the missing citations and, more importantly, whether future announcements from any lab arrive with the methodology, the attempt-count and the prior-work review attached, rather than left for the field to reconstruct afterward.

Fact is drawn from OpenAI's own announcement and paper; the misconduct allegations and the quoted mathematicians are as reported by Scientific American.