An unreleased Claude research version improved a Riemann zeta zero lower bound from 41.6% to 67.2%

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An Anthropic staffer asked Claude to 'take a real stab at the Riemann hypothesis.' It didn't solve it, but an unreleased research version pushed the known lower bound for zeros of the Riemann zeta function on the critical line from 41.6% to 67.2%. Claude worked across two Claude Code sessions, generating 31M output tokens, coordinating ~60 subagents, running 2,400 shell commands, and writing hundreds of Python scripts for numerical checks and peer review among subagents. The result combines recent work by Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh (which removes the Riemann hypothesis assumption from Montgomery's techniques) with Bombieri's 2000 paper. A paper, an informal expert note, and a Lean formalization (passing the comparator tool) are provided. External mathematicians Brian Conrey and Dan Goldston reviewed the paper on short notice; Anthropic's own mathematicians validated it. The post does not disclose the model version, parameter count, or release timeline. Worth a look as an unintended mathematical side effect, not a proof of the Riemann hypothesis.

Why it matters: Anthropic's official blog discloses that an unreleased Claude version produced a verifiable math advance on a Riemann-related problem, lifting the zero-ratio lower bound from 41.6% to 67.2%, with a paper and internal mathematician validation. All three HKR axes hit, and this i...