OpenAI claims AI-generated proof of quasi‑Riemann hypothesis
OpenAI released a batch of 377 papers on October 6, 2026, among which a 199‑page manuscript claims to prove that all nontrivial zeros of the Riemann zeta function lie between 1/8 and 7/8. A second, shorter 49‑page version, dated about a week later, asserts a weaker bound of 1/12 to 11/12 and is the only paper in the set that received human editing.
Key points
- OpenAI posted 377 papers on Oct 6 2026, including a 199‑page proof placing zeros between 1/8 and 7/8.
- A 49‑page version proves zeros lie between 1/12 and 11/12 and is the only paper edited by a human.
- Top mathematicians deem the result likely correct but note it does not resolve the full Riemann hypothesis.
Mathematicians such as Jared Duker Lichtman (Stanford), Maksym Radziwiłł (NYU) and Alexander Dunn (Georgia Tech) describe the result as the most significant AI‑for‑math achievement to date, noting that it synthesizes existing ideas without introducing new concepts. Leading number theorists, including Peter Sarnak (Princeton) and Michael Rubinstein (Waterloo), say the proof appears correct but await full verification, and they stress that it does not settle the full Riemann hypothesis, which remains an open problem after 160 years.
The story so far
9 episodes →- OpenAI claims AI-generated proof of quasi‑Riemann hypothesisthis story
AI Proved the Quasi-Riemann Hypothesis. What Happens Now?
quantamagazine.org · 19 October 2026
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