67.2% Is Not 67.2% of the Riemann Hypothesis

67.2% does not mean that Claude solved 67.2% of the Riemann hypothesis.

Anthropic reports a narrower mathematical result. The proven lower bound on the fraction of Riemann zeta zeros on the critical line increased from 41.6% to 67.2%. The Riemann hypothesis says all non-trivial zeros lie there. This work does not prove that.

The research workflow is also notable. Anthropic reports about 31 million output tokens across two Claude Code sessions. The second run used roughly 60 subagents, executed about 2,400 shell commands, and wrote hundreds of Python scripts. The team then had mathematicians check the paper and released a Lean 4 formalization companion.

The boundaries matter. The model was an unreleased research version. Internal verification and short expert review are not formal peer review. Anthropic also says it does not expect these techniques to lead directly to a proof of the Riemann hypothesis.

This is a large research-agent workflow with a checkable mathematical result, not a solved millennium problem.

Research: https://www.anthropic.com/research/riemann-zeta

Lean companion: https://github.com/anthropics/zeta-23-lean