Anthropic宣布其一款尚未正式发布的AI模型在数学领域取得进展，显著提高了黎曼猜想成立的下界[1]。黎曼猜想悬赏金额达100万美元，已有150多年未被解决[1]。该模型通过协调60个子代理、测试650个不同想法，在一天半的时间内完成了这项工作，消耗31百万tokens[1]。
在这个分布式研究架构中，60个子代理分别承担不同职责：2个专注开发关键数学思想，13个贡献想法，30个尝试但最终未能开发新想法，13个作为验证者，2个协助撰写论文[1]。Anthropic公司内部的两位数学家对研究结果进行了确认，并使用开源证明助手Lean将其形式化[1]。
这一成果是2024年AI在数学领域多个突破之一，其他包括解决Erdos问题和Jacobian猜想的否证[1]。然而，这些进展也引起了数学界的反思。Fields奖得主Timothy Gowers表示："如果我们进入一个数学定理不再与数学家相关联的世界，这也许不会比恒星不以天文学家命名、大多数恒星根本没有名字这一事实更成问题。"[1]
Anthropic has announced that one of its yet-to-be-released AI models has made significant progress on the Riemann Hypothesis, substantially raising the lower bound for which the conjecture holds true [1]. The achievement was accomplished in just one and a half days through a coordinated effort involving 60 sub-agents that tested 650 different mathematical ideas [1].
The Riemann Hypothesis, which carries a one-million-dollar bounty and has remained unsolved for over 150 years, represents one of mathematics' most challenging open problems [1]. To complete this work, the model consumed 31 million tokens while orchestrating its distributed approach [1]. Among the 60 sub-agents, two focused on developing key mathematical concepts, thirteen contributed ideas, thirty attempted but failed to develop novel approaches, thirteen served as verifiers, and two assisted in writing the paper [1]. The results were subsequently confirmed by two in-house mathematicians at Anthropic and formalized using Lean, an open-source proof assistant [1].
This breakthrough is part of a broader wave of AI-driven mathematical advances in 2024, with models also resolving the Erdős problem and disproving the Jacobian conjecture [1]. However, the achievement has sparked discussion within the mathematics community about potential shifts in how mathematical theorems are attributed. Mathematician Timothy Gowers reflected on this concern, stating: "If we arrive at a world where mathematical theorems are no longer associated with mathematicians, maybe that won't be any more problematic than the fact that stars aren't named after astronomers and most aren't named at all." [1]