Noesion Radarnoesion.ai
Research2026-08-10

Anthropic reported on August 10, 2026 that an unreleased research version of Claude improved a longstanding lower bound on the fraction of nontrivial zeros of the Riemann zeta function lying on the critical line, raising it from 41.6% to 67.2%. The result came from an attempt at the Riemann hypothesis itself, prompted by Anthropic staff member Jarred Sumner, and was produced across two Claude Code sessions using about 31 million output tokens, 650 discarded ideas, roughly 60 coordinated subagents, 2,400 shell commands and thousands of numerical checks. It builds on work by Baluyot, Goldston, Suriajaya and Turnage-Butterbaugh plus a 2000 paper by Bombieri. Anthropic mathematicians Levent Alpöge and Ralph Furman validated the proof, a Lean formalization was published on GitHub, and experts Brian Conrey and Dan Goldston reviewed the paper. Anthropic said it does not expect the techniques to resolve the hypothesis.

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