Overview
- Anthropic announced on Monday that an unreleased research version of its Claude model increased the proven lower bound for nontrivial Riemann zeta zeros on the critical line from 41.6% to 67.2%.
- The company says the result emerged over two Claude Code sessions that used about 31 million output tokens, tested roughly 650 ideas, coordinated around 60 subagents, and ran thousands of computational checks.
- Anthropic reports that two of its mathematicians reviewed Claude’s paper, external experts Brian Conrey and Dan Goldston examined it on short notice, and the argument was formalized in the Lean proof assistant.
- The claim does not prove the Riemann Hypothesis, and independent reviewers and analysts note that full public disclosure of primary proofs, data, and broader peer review are still needed to corroborate the result.
- The episode highlights that large language models can generate substantial, verifiable steps in hard math while raising questions about verification, reproducibility, and how the field should credit AI versus human contributors.