AI and humans collaborate to make major advances in mathematics

On September 7, 2026, Anthropic's AI model Claude achieved a major breakthrough by proving that over 67.25% of the zeta zeros lie on the critical line, significantly advancing the Riemann Hypothesis. This progress marks a shift from the previous 0.8% advancement over 37 years, bringing the solution closer by 32.75%. The proof, however, was complex and lacked intuitiveness, making it difficult for mathematicians to grasp. Youness Lamzouri, a mathematician, simplified Claude's proof using a concise Hilbert space inequality, transforming the problem into an estimation of correlations. This elegant approach was quickly verified by AxiomProver, an AI tool from the Axiom team, within hours of its release. The verification process marked a milestone in mathematics, demonstrating the power of machine verification. Building on this success, the Axiom team and other mathematicians made progress on the Twin Prime Conjecture, further narrowing the gap between prime numbers. This collaboration signals the dawn of a new era where human insight and machine computation work together to redefine mathematical discovery.