用AI演化搜索自动发现数学新构造，部分成果超越已有最优解。
Mathematical exploration and discovery at scale
- 结合大模型生成与自动化评估，迭代优化数学算法解决方案。
- 在67个数学问题中复现多数最优解，多个问题找到更优解。
- 可将有限结果推广为普适公式，适合数学研究者与AI协作探索。
AlphaEvolve（Novikov等，2025）是一种通用的进化式编程代理，将大语言模型的生成能力与自动化评估相结合，在迭代演化框架中提出、测试并优化算法解法，以应对复杂科学与实际问题。本文展示其作为自主发现数学新构造、推进长期开放问题理解的工具潜力。我们选取涵盖数学分析、组合数学、几何学与数论的67个问题进行验证，系统在多数案例中复现了现有最优解，并在若干问题中发现了改进解。在某些情况下，AlphaEvolve能将有限输入值的结果归纳为适用于所有输入的通用公式。此外，该方法可与Deep Think和AlphaProof结合，构建更广泛的框架，实现自动证明生成与进一步数学洞察。结果表明，大语言模型引导的演化搜索可自主发现补充人类直觉的数学构造，有时达到甚至超越已有最佳成果，凸显人机协同在数学发现中的巨大潜力。我们提出AlphaEvolve是一种强大的新型数学发现工具，能够大规模探索广阔搜索空间，高效求解复杂优化问题，显著降低准备与计算时间成本。
原文摘要 · Abstract (English)
AlphaEvolve (Novikov et al., 2025) is a generic evolutionary coding agent that combines the generative capabilities of LLMs with automated evaluation in an iterative evolutionary framework that proposes, tests, and refines algorithmic solutions to challenging scientific and practical problems. In this paper we showcase AlphaEvolve as a tool for autonomously discovering novel mathematical constructions and advancing our understanding of long-standing open problems. To demonstrate its breadth, we considered a list of 67 problems spanning mathematical analysis, combinatorics, geometry, and number theory. The system rediscovered the best known solutions in most of the cases and discovered improved solutions in several. In some instances, AlphaEvolve is also able to generalize results for a finite number of input values into a formula valid for all input values. Furthermore, we are able to combine this methodology with Deep Think and AlphaProof in a broader framework where the additional proof-assistants and reasoning systems provide automated proof generation and further mathematical insights. These results demonstrate that large language model-guided evolutionary search can autonomously discover mathematical constructions that complement human intuition, at times matching or even improving the best known results, highlighting the potential for significant new ways of interaction between mathematicians and AI systems. We present AlphaEvolve as a powerful new tool for mathematical discovery, capable of exploring vast search spaces to solve complex optimization problems at scale, often with significantly reduced requirements on preparation and computation time.
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