Claude pushed a Riemann zeta bound from 41.6% to 67.2%

An unreleased research version of Claude raised the proven lower bound on the share of Riemann zeta zeros lying on the critical line from 41.6% to 67.2%, Anthropic says. The Riemann hypothesis itself is still standing.

Anthropic’s Jarred Sumner asked Claude to take a serious run at the problem. The first 650 ideas went nowhere. After he asked again, the model spent a day and a half coordinating roughly 60 subagents that ran 2,400 shell commands and wrote hundreds of Python scripts. All of it fit into two Claude Code sessions and 31 million output tokens.

Anthropic mathematicians Levent Alpöge and Ralph Furman went through the work, and at the company’s request Brian Conrey and Dan Goldston reviewed the paper. Claude wrote up the proof in Lean, and it passed standard verification.