arXiv 2412.165432026-02-13cs.AI

数学与人工智能：连接数学与AI的综述

Mathematics and Machine Creativity: A Survey on Bridging Mathematics with AI

Shizhe Liang, Wei Zhang, Tianyang Zhong, Tianming Liu

备注：: This article is withdrawn due to internal authorship and supervisory considerations that require clarification before the work can proceed in its current form. After further review, I believe it is appropriate to pause and formally resolve these matters to ensure full compliance with institutional and collaborative research policies

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AI总结：

本文综述了AI在数学研究中的应用，探讨了AI通过提供灵活框架和归纳推理能力，如何支持数学研究，并促进数学与AI的跨学科理解。

摘要：

本文全面概述了人工智能（AI）在数学研究中的应用，突显AI在该领域开始发挥的变革性作用。传统上，AI的进步严重依赖数学和统计学提供的理论基础。然而，近年来AI，特别是强化学习（RL）和大语言模型（LLMs）的发展，展示了AI能够通过提供灵活的算法框架和强大的归纳推理能力，回馈数学研究的潜力。本文旨在建立AI与数学之间的桥梁，提供关于相互利益的见解，并促进更深入的跨学科理解。特别是，我们认为尽管当前的AI和LLMs在复杂演绎推理上可能存在问题，但它们的“固有创造力”，即基于对浅层模式识别生成高吞吐量输出的能力，对支持和启发数学研究具有重要潜力。这种创造力，往往被忽视，可能是解锁数学新视角和方法的钥匙。此外，我们还解决了跨学科交流的不足：数学家可能不完全理解AI的最新进展，而AI研究人员经常优先考虑基准性能而非前沿数学研究中的实际应用。本文旨在弥合这一差距，详细探讨AI的基础、其优势及其在数学科学中的新兴应用。

英文摘要：

This paper presents a comprehensive overview on the applications of artificial intelligence (AI) in mathematical research, highlighting the transformative role AI has begun to play in this domain. Traditionally, AI advancements have heavily relied on theoretical foundations provided by mathematics and statistics. However, recent developments in AI, particularly in reinforcement learning (RL) and large language models (LLMs), have demonstrated the potential for AI to contribute back to mathematics by offering flexible algorithmic frameworks and powerful inductive reasoning capabilities that support various aspects of mathematical research. This survey aims to establish a bridge between AI and mathematics, providing insights into the mutual benefits and fostering deeper interdisciplinary understanding. In particular, we argue that while current AI and LLMs may struggle with complex deductive reasoning, their "inherent creativity", the ability to generate outputs at high throughput based on recognition of shallow patterns, holds significant potential to support and inspire mathematical research. This creative capability, often overlooked, could be the key to unlocking new perspectives and methodologies in mathematics. Furthermore, we address the lack of cross-disciplinary communication: mathematicians may not fully comprehend the latest advances in AI, while AI researchers frequently prioritize benchmark performance over real-world applications in frontier mathematical research. This paper seeks to close that gap, offering a detailed exploration of AI fundamentals, its strengths, and its emerging applications in the mathematical sciences.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。