Among 377 results announced by OpenAI on October 6, 2026, one stood out: a proof of the quasi-Riemann hypothesis, a weaker version of the Riemann hypothesis that has remained open for over 160 years. Unlike other recent AI proofs, this one has been unpacked by human experts. Mathematicians such as Jared Duker Lichtman of Stanford University called it "the most significant AI-for-math achievement so far, by quite a margin."
The proof came in two versions. The first, dated September 30, 2026, showed that all nontrivial zeros of the Riemann zeta function lie between 1/8 and 7/8, and was formally verified using the Lean programming language. A second version, completed about a week later and not yet formally verified, proved a weaker result: zeros must have a real part between 1/12 and 11/12. The first paper is 199 pages long; the second is 49 pages. Both, according to the source, are "horribly written" in a way typical of recent AI-generated results.
What surprised mathematicians is that the proof introduced no new concepts. Instead, it unearthed hidden connections between old ideas, relying in part on techniques pioneered by Maksym Radziwiłł of New York University and Alexander Dunn of the Georgia Institute of Technology. The implications, Radziwiłł said, are "staggering": in a sense, the vast majority of consequences of the Riemann hypothesis already follow from the quasi version. The result narrows the strip where nontrivial zeros can appear, which directly informs how primes are distributed along the number line.