Anthropic’s Claude AI model attempted to solve the 167-year-old Riemann Hypothesis after a massive 36-hour computational run. While falling short of a complete proof, an experimental swarm of 60 subagentes successfully pushed a key mathematical limit from 41.6% to 67.2%.
A 167-year-old mathematical enigma known as the Riemann Hypothesis has drawn a fresh attempt at proof from artificial intelligence.
The 60-Subagent Swarm and the 31-Million-Token Run
The attempt began when Xataka reported that Jarred Sumner, an employee at Anthropic without a background in advanced mathematics, asked a specialized variant of Claude to tackle the Riemann Hypothesis. What followed was far from a standard chat interaction. The model deployed an orchestration of 60 subagents working in parallel over the course of a day and a half.
During this 36-hour session, the system consumed 31 million output tokens across two Claude Code sessions. The AI wrote hundreds of Python scripts and ran continuous numerical checks. After cycling through and discarding 650 failing ideas, the agent swarm hit on a novel path by connecting recent theories from mathematicians such as Bombieri and Baluyot in a way researchers had not previously combined.
Pushing the Critical Line Boundary From 41.6% to 67.2%
Formulated in 1859 by Bernhard Riemann, the hypothesis concerns the distribution of prime numbers and examines the non-trivial zeros of the zeta function. Riemann posited that all these infinite zeros lie on a specific vertical line known as the critical line. While proving the entire hypothesis remains elusive, mathematicians historically focused on determining what proportion of those zeros actually sit on that line.
Before this experiment, researchers had rigorously established that 41.6% of the zeros satisfied the rule. This marks the first time in history that more than half—specifically two-thirds—of the zeros have been proven to sit where Riemann predicted.
Validation Protocols and the Limits of Statistical Proof
After finding the result, the AI agents attempted to dismantle their own work by searching for counterexamples. They downloaded 54 related studies from arXiv to ensure the idea had not been published previously, and then re-proved the result from scratch. Two mathematicians at Anthropic subsequently studied the resulting proof using the Lean platform and validated it.
Despite this milestone, the company acknowledges that the statistical technique deployed here has a hard ceiling. Proving that a majority of zeros fall on the line is fundamentally different from proving that every single one of the infinite zeros does. Anthropic confirmed that this method is unlikely to determine the remaining 32.8% of prime number zeros.
During the process, human intervention was minimal. Sumner repeatedly prompted the system with phrases like sigue adelante
and cree en ti mismo
—instructions that effectively granted the model permission to consume vast amounts of computing power despite repeated failures. Researchers emphasize that while models like Claude are not generating entirely new foundational theories from scratch, they are proving exceptionally adept at trawling vast libraries of human literature to find hidden connections.
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