AI Proved the Quasi-Riemann Hypothesis. What Happens Now?

OpenAI announced a claimed proof of the quasi-Riemann hypothesis, a weaker but still powerful version of the Riemann hypothesis that only requires nontrivial zeros of the zeta function to lie inside a narrower vertical strip instead of precisely on the 1/2 line. Two AI-produced papers were released: a 199-page version asserting zeros lie between 1/8 and 7/8 that was formally verified in Lean, and a shorter 49-page version asserting a 1/12-11/12 strip that was the only one to receive human editing before publication. Experts have unpacked the shorter paper, generally agree the central arguments are correct, and have produced concise human write-ups; prominent number theorists are studying the proof in courses and private notes.

The proof did not introduce radically new mathematics but synthesized familiar tools and exposed an overlooked family of functions in the zeta/L-function landscape, realizing a program some researchers had advocated. Techniques pioneered by Radziwiłł and Dunn play a clear role, and the result immediately tightens theorems about prime distribution that follow from Riemann-type statements. The work’s uneven exposition and the fact that only one paper had human editorial input have provoked scrutiny about provenance and standards, but the mathematical content - if upheld under further verification and formalization - represents a major AI-for-math milestone with far-reaching consequences for analytic number theory.