Claude Research Model Raises Riemann Zeta Zero Lower Bound from 41.6% to 67.2%
Anthropic
An unreleased Anthropic research version of Claude, working across two Claude Code sessions with about 60 sub-agents and 31M output tokens, improved a decades-old lower bound on the fraction of Riemann zeta zeros satisfying the Riemann hypothesis, combining recent number-theory results with Bombieri's 2000 work into a new Weil-quadratic-form argument. Two Anthropic mathematicians and outside experts (Brian Conrey, Dan Goldston) reviewed the result, and Claude also produced a Lean-verifiable version of the proof.
Why it matters
It does not prove the Riemann hypothesis and Anthropic does not expect the technique to lead there, but it is a rare case of a frontier model producing an expert-reviewed advance on an open problem in pure mathematics, illustrating both the promise and current limits of agentic AI-assisted research.
Importance: 3/5
Notable, expert-reviewed research result from a frontier lab with independent media pickup.