OpenAI dumps 372 AI-generated math results on GitHub, from the 4D Kakeya conjecture to the Riemann hypothesis

On 6 October 2026 OpenAI posted a large batch of mathematical results to a GitHub repository (at 6 p.m. EDT, i.e. 3 p.m. PT). According to The Verge, it contains 722 manuscripts grouped into 372 result families, all produced by an unreleased frontier model.

What is claimed

• Each result, OpenAI says, resolves or substantially advances an open question in mathematics or theoretical computer science.
• Highlights reported by Scientific American include a claimed solution of the four-dimensional Kakeya conjecture, improvements to important computer algorithms and progress towards the Riemann hypothesis.
• Many of the proofs have already been checked in Lean, a proof-verification language, which makes them very likely correct; others will take mathematicians months to assess.
• An OpenAI spokesperson told Scientific American that almost all results came from a single prompt given to a single AI agent (while adding that some may have needed several attempts). The earlier Navier–Stokes result, by contrast, was produced by a swarm of 10,000 agents costing millions in compute. The Verge reports OpenAI’s claim that the “average result” used compute equivalent to about three hours of ChatGPT Pro thinking.

Criticism

An independent advisory group of mathematicians that OpenAI convened in September recommends publishing the model, the exact prompt and the compute time for every result. OpenAI is releasing only the average compute plus some statistics — no prompts — and says it is not bound by the recommendations. “We should ask for receipts,” MIT mathematician Andrew Sutherland told Scientific American. Daniel Litt (University of Toronto) welcomed the release, while Terence Tao has criticised the “insane” pace of AI labs’ results.

Caveat: the claims come from OpenAI; independent verification of the non-Lean results is only beginning.