Anthropic said Monday that an unreleased research version of Claude produced an unconditional proof lifting a longstanding lower bound on the fraction of Riemann zeta zeros lying on the critical line from 41.6% to 67.2% (rendered as 67.25% in some accounts). The company published a 35-page paper and a Lean 4 formalization alongside the announcement. It doesn’t resolve the Riemann hypothesis, conjectured in 1859 and still carrying the Clay Mathematics Institute’s $1 million bounty; Anthropic notes the proof method can’t determine the status of the remaining zeros.

The framing matters as much as the number. This wasn’t a mathematician’s careful prompt. Jarred Sumner, an Anthropic staffer described as a non-mathematician, simply asked the model to “take a real stab” at the problem. Claude generated 650 unsuccessful ideas, then spent roughly 36 hours across two Claude Code sessions coordinating about 60 subagents that ran 2,400 shell commands and produced 31 million output tokens. Two subagents developed the key mathematical ideas; 13 contributed supporting ideas; 13 acted as validators.

The argument itself is genuinely classical in shape. It combines methods from Enrico Bombieri’s 2000 paper with more recent work by Siegfred Baluyot, Daniel Goldston, Ade Irma Suriajaya, and Caroline Turnage-Butterbaugh removing a Riemann-hypothesis assumption from Hugh Montgomery’s 1973 framework. Anthropic mathematicians Levent Alpöge and Ralph Furman validated the paper internally; number theorists Brian Conrey and Daniel Goldston examined it on short notice.

No referee reports have been published and no peer-reviewed journal has accepted the result as of August 11. Anthropic hasn’t disclosed which Claude variant produced it, or whether that variant will ever ship.

The interesting move is releasing the Lean 4 formalization. It reframes the announcement as an artifact machines can check, not a claim awaiting the profession’s slow verdict.

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