FEATUREDHacker News Frontpage· rssEN17:41 · 08·10
→An unreleased Claude research version improved a Riemann zeta zero lower bound from 41.6% to 67.2%
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.
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Featured · importance 88 · hook + knowledge + resonance
editor take
Claude didn't prove the Riemann hypothesis, but it pushed the lower bound for zeros on the critical line from 41.6% to 67.2% by combining two existing mathematical frameworks.
sharp
This one's worth opening because the math result is real—Anthropic had external mathematicians Brian Conrey and Dan Goldston review the paper on short notice, and they released a Lean formalization that passes the comparator tool. Claude's approach combined recent work by Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh (which removes the Riemann hypothesis assumption from Montgomery's techniques) with Bombieri's 2000 paper. It constructed a quadratic form with positive- and negative-definite subspaces, then used a rank inequality to derive the new 67.2% bound.
I'd discount this in two ways. First, Anthropic didn't disclose the model version, parameter count, or release timeline—this reads more like an internal capability probe than a product announcement. Second, the post itself says this technique probably won't lead to proving the Riemann hypothesis; it's more like pushing forward on an existing line of attack. But flip it around: a non-mathematician staffer gave a vague prompt, and the model found combinable pieces in the literature, coordinated ~60 subagents, ran 2,400 shell commands, and wrote hundreds of Python scripts for numerical checks and peer review among subagents—all across two Claude Code sessions spitting out 31M tokens. That agent workflow completeness is more interesting than the bound itself.
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