用生成式AI辅助数学研究，提升猜想生成与验证效率。
Advancing mathematics research with generative AI
- 将生成式AI作为交互助手，处理编码、验算等重复任务。
- 结合神经符号求解器与形式化证明系统，增强推理能力。
- 适合数学研究者探索新猜想或自动化验证复杂问题。
生成式AI模型在高级数学研究中的主要局限在于其非逻辑推理本质。然而，大型语言模型及其改进版本能够捕捉人类难以察觉的高等数学模式。通过合理设计，这些模型可作为强大的交互式助手，协助完成编码、调试、验证实例、提出猜想等繁琐工作。本文探讨了生成式AI如何推动数学研究进展，并讨论其与神经符号求解器、计算机代数系统及形式化证明工具（如Lean）的集成应用。
原文摘要 · Abstract (English)
The main drawback of using generative AI models for advanced mathematics is that these models are not primarily logical reasoning engines. However, Large Language Models, and their refinements, can pick up on patterns in higher mathematics that are difficult for humans to see. By putting the design of generative AI models to their advantage, mathematicians may use them as powerful interactive assistants that can carry out laborious tasks, generate and debug code, check examples, formulate conjectures and more. We discuss how generative AI models can be used to advance mathematics research. We also discuss their integration with neuro-symbolic solvers, Computer Algebra Systems and formal proof assistants such as Lean.
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