Advancing mathematics research with generative AI
Lisa Carbone
使用生成式AI模型进行高级数学的主要缺点是,这些模型不是逻辑推理引擎。 然而,大型语言模型及其改进可以在高等数学中选择人类难以看到的模式。 通过将生成式AI模型的设计发挥优势,数学家可以将它们用作强大的交互助手,可以执行繁琐的任务,生成和调试代码,检查示例,制定猜想等等。 我们讨论了如何利用生成式AI模型推进数学研究。 我们还讨论了他们与计算机代数系统和Lean等正式证明助手的集成。
The main drawback of using generative AI models for advanced mathematics is that these models are not 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 ...