Claude and a New Result in a Classic Mathematics Problem
Anthropic reports that an unreleased research version of Claude made progress on a longstanding problem connected to the Riemann hypothesis. The model did not prove the hypothesis itself, but it did improve a lower bound related to the zeros of the Riemann zeta function, raising it from 41.6% to 67.2%. The result is presented as an example of how AI can extend mathematical work in ways that contribute to science even when it does not solve the original open problem.
The Riemann zeta function is tied to the distribution of prime numbers, and the Riemann hypothesis is one of the central conjectures in mathematics. The hypothesis says that the zeros that determine the primes all lie on a particular vertical line. Mathematicians have not proved or disproved it, but they have developed related results over time, including estimates for how many zeros are on that line. Anthropic’s post places Claude’s finding in that broader research history.
Claude’s result builds on prior work by several mathematicians. The post says it draws especially on research by Baluyot, Goldston, Suriajaya, and Turnage-Butterbaugh, as well as a 2000 paper by Bombieri. By combining these ideas, Claude identified a way to surpass the previous best known lower-bound proportion. Anthropic says the result was validated by two mathematicians on staff and also formalized in Lean so it could pass standard verification tools.
The post also describes how the work unfolded. A staff member prompted Claude to take a real attempt at the Riemann hypothesis, and the model first generated many ideas that did not work. It then coordinated a larger set of subagents, which ran shell commands, wrote Python scripts, checked numerical data against known zeros, and reviewed one another’s work. Claude later re-checked the proof, searched for counterexamples, downloaded papers from arXiv to see whether the result was already known, and independently re-proved its finding.
Anthropic frames the episode as evidence of progress in AI’s mathematical abilities. The model did not solve the famous open problem, but it produced a new, valid result while trying. In that sense, the post presents AI not as a replacement for mathematicians, but as a tool that can help extend their ideas and contribute to scientific progress through careful computation, validation, and collaboration with human experts.
Sources:
