Anthropic's Claude Pushes Riemann Zeta Zero Bound Past Two Thirds
The result shows an AI model advancing an open mathematics problem largely through human encouragement rather than mathematical guidance, with the operator providing almost no technical input.
Reporting from 1 source: GIGAZINE.
Anthropic released results from an unreleased research version of Claude attempting the Riemann hypothesis. Claude failed to prove the conjecture itself but derived a new lower bound: at least two thirds of the zeta function's nontrivial zeros lie on the critical line, with an optimized figure around 67.25 percent. The previous bound stood at roughly 41.7 percent. The human operator mainly encouraged Claude with phrases like "keep going" and "believe in yourself".
Anthropic's unreleased research version of Claude tackled the Riemann hypothesis and came away with a partial result. The model failed to prove the conjecture, but it established that at least two thirds of the nontrivial zeros of the Riemann zeta function lie on the critical line, with an optimized bound of about 67.25 percent. The prior proven figure was roughly 41.7 percent, from 2020.
The unusual part is the division of labor. Jared Sumner, an Anthropic staff member, reported that his input consisted almost entirely of variations on "keep going" and "believe in yourself." Claude initially doubted it could make meaningful progress, rejecting its own candidates before Sumner pushed it to continue. The model ran about 60 subagents over roughly a day and a half, executing 2,400 shell commands and writing hundreds of Python scripts.
Anthropic noted that the foundation came from recent human mathematical research, with Claude's contribution being the recognition that those pieces could be combined. The result is formalized in the Lean 4 proof assistant, and the repository is public on GitHub.
Synthesized by Yomimono from the 1 cited source below, including Japanese-language reporting where cited, then editorially reviewed before publishing.