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

OpenAI’s October 6, 2026 announcement had 377 results in it, but one drew the attention. The company said it had settled a weaker form of the Riemann hypothesis, the quasi-Riemann hypothesis. To mathematicians, that is not a footnote. Jared Duker Lichtman of Stanford called it the most significant AI-for-math result so far, by quite a margin.

The Riemann hypothesis has been open for more than 160 years, and its appeal is simple to state even if the details are not. It asks where the nontrivial zeros of the zeta function live. Those zeros are tied to the way prime numbers are distributed, and primes are the basic atoms of arithmetic. Bernhard Riemann first made the connection in 1859, and the field has been circling it ever since.

The classic conjecture says every nontrivial zero sits on the vertical line where the real part is 1/2. The quasi version asks for something weaker: prove that the zeros stay inside a narrower vertical strip than the one already known between 0 and 1. That still matters a lot. As Maksym Radziwiłł put it, the consequences are staggering, because the vast majority of what follows from RH already follows from quasi-RH.

OpenAI described two versions of the proof. One, dated September 30, claimed a strip from 1/8 to 7/8 and was formally verified in Lean. The other, completed almost a week later, claimed a weaker 1/12 to 11/12 strip and has not yet been formally verified. The 7/8 paper is 199 pages long. The 11/12 version is 49 pages, and that shorter draft is the one most mathematicians are focusing on.

And the proof did something else that surprised people. It did not invent a new theory from scratch. Alexander Dunn of the Georgia Institute of Technology called it a surprising synthesis of well-known ideas. Radziwiłł and Dunn helped pioneer some of the techniques involved, and other number theorists are now working through what the result really means.