The unreleased Claude model has successfully advanced the century-old "Riemann Hypothesis" research. The famous artificial intelligence research company Anthropic recently disclosed that its unreleased Claude research version model has made substantial progress in solving one of the most famous problems in mathematics - the "Riemann Hypothesis"

The unreleased Claude model has successfully advanced the century-old "Riemann Hypothesis" research. Anthropic, a well-known artificial intelligence research company, recently disclosed that its unreleased Claude research version model has made substantial progress in solving one of the most famous problems in mathematics - the "Riemann Hypothesis". In an autonomously run multi-day test cycle, the model successfully improved the known lower limit on the proportion of zeros on the critical line of the Riemannian zeta function from 41.6% to 67.2%. According to reports, the research model ran independently in the Claude Code environment, and the two phases of testing consumed a total of 31 million output tokens. Before finally finding a feasible solution, the model went through and discarded 650 failed ideas, executed 2,400 Shell instructions by coordinating 60 subagents, and wrote hundreds of Python scripts. The Anthropic team then invited its in-house mathematicians Levent Alpöge and Ralph Furman to rigorously verify the inference results, and presented the results to external number theorists such as Brian Conrey and Dan Goldston. In addition, team member Eric Easley helped formalize the proof in the Lean theorem prover. The Riemann Hypothesis was proposed by the German mathematician Bernhard Riemann in 1859. It has been included in the "Millennium Prize Problem" established by the Clay Mathematics Institute, with a reward of up to US$1 million. General-purpose AI assistants have long struggled to make original contributions to such deep, cutting-edge mathematical challenges. This time Claude successfully achieved this breakthrough in mathematical logic by integrating the existing research frameworks of many mathematicians such as Baluyot, Goldston, Suriajaya, Turnage-Butterbaugh and Bombieri, combined with the Weil-induced quadratic function space construction, through the simultaneous processing of positive definite and negative stator spaces and the reasonable use of non-diagonal quadratic forms. At present, Anthropic has publicly published papers with expert annotations, detailed process logs, and complete proofs that can be verified in Lean, but it has not mentioned whether such multi-agent collaboration mechanisms and advanced reasoning capabilities will be open to the public in the future. via cnBeta.COM - Chinese industry information station (author: source: cnBeta.COM)