Recently, the global mathematics and artificial intelligence communities have witnessed a moment of breakthrough that redefines cognition. The AI model Claude, developed by Anthropic, has made a significant breakthrough in proving the Riemann Hypothesis, known as the "Holy Grail of Mathematics," successfully confirming that more than 2/3 (67.25%) of the zeta zeros lie on the critical line and are simple zeros. This astonishing achievement not only broke the long-standing stagnation of only advancing the boundary by 0.8% over the past 37 years but also directly pushed humanity's journey to fully solve the Riemann Hypothesis to just the remaining 32.75%.

As a core barrier in modern analytic number theory, the Riemann Hypothesis is directly related to the deep laws of prime distribution and forms the load-bearing wall for thousands of advanced mathematical theorems. Faced with this extremely complex century-old problem, Claude chose a highly "aesthetic" technical approach. It calculated large matrices that grow with variables, using the trace of the matrix, the Hilbert–Schmidt norm, and a complex rank-trace inequality to push the lower bound of zeros up to 67.25%. However, because this proof is filled with obscure matrix transformations and lengthy and complicated tool combinations, it appears very cumbersome and lacks intuitiveness, making it difficult for top mathematicians to digest even after obtaining the results.

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While the academic community was struggling with the "non-human" feel of the AI proof, mathematician Youness Lamzouri demonstrated the exquisite taste of human wisdom. He used refined intuition and Occam's Razor principle to cut out redundant parts from Claude's proof, completing a reduction with an extremely concise and elegant Hilbert space inequality. This transformed the complex lower bound problem into an estimation of correlations and directly applied the unconditional version of Montgomery's theorem to provide a more elegant and concise new proof.

Even more astonishingly, this transformation did not slow down during the lengthy peer review process. Within a few hours after Youness published the preprint draft, Axiom team's AI tool AxiomProver automatically launched, seamlessly verifying the proof in the formal verification language Lean. This means that major breakthroughs like the Riemann Hypothesis were completely verified at the machine level on the very day the paper was released.

Building on this foundation, the Axiom team and related mathematical forces seized the momentum and achieved significant progress on the Twin Prime Conjecture, further narrowing the gap between primes. As machine verification tools like AxiomProver become deeply integrated with AI frontiers, the classical era of traditional mathematics relying on long manual reviews is being completely ended, and a new future of mathematics woven by human insight and machine computing power is rapidly taking shape.