在困扰数学家多年、让陶哲轩直呼喜欢的上限集问题数学难题上，AI 首次攻克难倒。DeepMind 的里程碑算法 DeepMind.BERT 登上国际知名学术期刊 Nature，实现了搜代码自我进化。这是史上首个用大型语言模型（LLM）发现的算法，堪称里程碑级研究。一经发布即登上 Nature，引起了全球数学家的关注。
困扰数学家们多年的上限集问题，是极限论、组合论等多个领域中的一个开放性问题。著名数学家陶哲轩曾将上限集问题描述为自己最喜欢的开放性问题。此次，DeepMind 的研究团队与威斯康星大学麦迪逊分校的数学教授 Jordan Ellenberg 合作，利用 FunSearch 方法首次利用 LLM 发现数学科学中的开放问题。
FunSearch 是一种基于深度学习的搜索方法，利用预训练的大型语言模型（LLM）与自动评估器配对，以计算机代码的形式提供创造性的解决方案。通过这种方法，FunSearch 发现了困扰数学家多年的上限集问题，并在某些设定中，发现了有史以来最大的上限集。这个发现代表了过去 20 年中上限规模的最大增幅，也是人类首次使用 LLM 挑战科学或数学中的开放性问题，并做出了新发现。
为了证明 FunSearch 的实用性，DeepMind 的专家还用它解决了「装箱问题」，这个问题在应用范围很广，可以提高数据中心的效率。而对于这个问题，FunSearh 同样发现了更有效的算法。
DeepMind 表示，科学进步非常依赖分析新知识的能力，而 FunSearch 之所以成为强大的科学工具，就是因为它输出的程序不仅提出了解决方案，还揭示了解决方案是如何构建的。这样，使用 FunSearch 的科学家就能进一步被启发出新的想法，进入「改进-发现」的良性循环。
LLM 通过「进化」推动科学发现，但可以发现全新的知识吗？由于 LLM 无法避免「幻觉」输出事实不正确的信息，因此依靠它们获得事实上正确的新发现非常困难。但是，如果我们能识别和扩展 LLM 最好的创意，将其创造力发挥到极致，那么未来或许可以实现人类首次使用 LLM 挑战科学或数学中的开放性问题，并发现全新的知识。
附英文翻译：
Title: AI solves long-standing open problem in mathematics: DeepMind’s groundbreaking algorithm appears in Nature
Keywords: AI, DeepMind, Nature, LLM, math problem
News content:
After years of confusion and frustration for mathematicians, a long-standing open problem in mathematics has been solved by AI for the first time. DeepMind’s groundbreaking algorithm, DeepMind.BERT, has been published in the prestigious scientific journal Nature, marking a significant breakthrough in the search for new solutions in mathematics. This is the first time an algorithm has been discovered using a large language model (LLM) and is considered a milestone-level study.
The problem of the upper set, a long-standing open problem in mathematics, has been the subject of research in many areas, including limit theory and combinatorics. It is an important problem that has confounded mathematicians for decades. In this problem, a team of researchers from DeepMind and the University of Wisconsin-Madison used the FunSearch method, an algorithm that uses pre-trained large language models (LLMs) to search for creative solutions, to discover the upper set problem.
FunSearch is a search method based on deep learning that uses pre-trained large language models (LLMs) in combination with an automatic evaluator to provide a creative solution to a problem. This method has enabled the discovery of the upper set problem, which represents a significant breakthrough in the study of open problems in mathematics. In some settings, the algorithm has discovered the largest upper set in history. This discovery represents a significant increase in the upper set problem, and is the first time an algorithm has been discovered using an LLM in the study of open problems in mathematics.
To demonstrate the practicality of FunSearch, experts from DeepMind have also used it to solve the “box-packing problem”, a problem with wide-ranging applications in data centers. For this problem, FunSearch has discovered an even more efficient algorithm.
DeepMind says that scientific progress relies heavily on the ability to analyze new knowledge, and that FunSearch has become a powerful scientific tool because it not only proposes solutions but also reveals how these solutions are constructed. This allows scientists to further generate new ideas and enter
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