Direct discovery · Mathematics · Computer science
Claude raises a Riemann-zeta critical-line bound from 41.6% to 67.2%
A new unconditional lower bound showing that more than two thirds of the nontrivial zeros of the Riemann zeta function lie on the critical line, with a public Lean certificate.
Summary
Anthropic reports that an unreleased Claude model, initially asked to attack the Riemann hypothesis, instead combined prior analytic-number-theory results to raise a longstanding unconditional critical-line bound from 41.6% to 67.2%. Anthropic mathematicians studied the proof, outside experts examined it on short notice, and a public Lean 4 repository provides a machine-checkable formalization.
AI role
An unreleased Claude research model coordinated dozens of subagents to explore ideas, search literature, run numerical checks, develop the proof, and later help formalize it in Lean.
Narrative role
This adds an organization-independent counterpart to the OpenAI and DeepMind mathematics milestones: an unintended research result emerged from a broad exploratory agent workflow and was subsequently packaged as both an informal paper and a formal certificate.
Caveat
The result does not prove the Riemann hypothesis and relies heavily on combining earlier mathematical work. The paper is not peer reviewed, most human review described by Anthropic was internal or conducted on short notice, and the research model is unreleased.