OpenAI announced on October 6, 2026, that its AI model successfully proved the quasi-Riemann hypothesis, a weaker version of the Riemann hypothesis. The proof relies on existing mathematical concepts rather than new ones, combining known ideas in an unexpected way.
The company released two versions of the proof. The first, dated September 30, 2026, spans 199 pages and claims that non-trivial zeros lie between 1/8 and 7/8. The second, shorter 49-page version, claims a range between 1/12 and 11/12.
Mathematicians are currently focusing on the 49-page version due to its accessibility. While the AI-generated text quality is considered poor by academic standards, experts generally agree the mathematical result is correct. The proof utilizes metaplectic forms, a niche area of number theory.
The breakthrough demonstrates that existing mathematical tools were sufficient to address the problem, contrary to previous expert beliefs. This result is expected to validate numerous other theorems in number theory, geometry, and theoretical computer science.
