Claude pushed the zeta-zero lower bound from 41.6% to 67.2%

An unpublished research version of Claude raised the lower bound on the fraction of Riemann zeta function zeros lying on the critical line from 41.6% to 67.2%, Anthropic said in a research post. The Riemann hypothesis itself is still unproven.

The result came out of two Claude Code sessions and 31 million output tokens. Jarred Sumner, an Anthropic employee who isn’t a mathematician, asked Claude to “really go for” the hypothesis. The first 650 ideas went nowhere; after a second prompt, the model spent a day and a half coordinating roughly 60 subagents, running 2,400 shell commands and thousands of numerical checks.

Anthropic mathematicians Levent Alpöge and Ralph Furman went through the proof, and Eric Easley helped assemble a Lean formalization. Brian Conrey and Dan Goldston also reviewed the paper.