Claude raises the lower bound on Riemann zeta zeros on the critical line
An unreleased Claude raised the proven fraction of Riemann zeta zeros on the critical line from 41.6% to 67.2% while attempting the Riemann hypothesis.
Claude failed at the hypothesis but combined work by Aryan, Baluyot-Goldston-Suriajaya-Turnage-Butterbaugh and a 2000 Bombieri paper into a new bound. Two Anthropic mathematicians validated it and wrote an expert note; Claude also produced a formally verifiable proof. Experts Brian Conrey and Dan Goldston reviewed it on short notice.
- Date
- Monday, 10 August 2026
- Lab
- Anthropic
- Kind
- paper
- Access
- paper only
Figures
| Measure | Value | Measured by |
|---|---|---|
| Proven lower bound on share of zeros on the critical line | 67.2% up from 41.6%; unreleased research model | company |
Anthropic does not expect the technique to prove the Riemann hypothesis. Validation was internal plus informal expert reading; no journal refereeing yet as of 2026-10-04 in the sources read.
Sources
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