Large Language Models for Mathematicians

大型语言模型（LLMs）如ChatGPT因其通用语言理解能力，特别是生成高质量文本或计算机代码的能力，受到了极大的关注。对于许多职业来说，LLMs代表了一个宝贵的工具，可以加快和提高工作质量。在这篇文章中，我们讨论它们在多大程度上可以帮助专业数学家。我们首先提供了所有现代语言模型中使用的Transformer模型的数学描述。基于最近的研究，我们随后概述了最佳实践和潜在问题，并报告了语言模型的数学能力。最后，我们揭示了LLMs改变数学家工作方式的潜力。

Large language models (LLMs) such as ChatGPT have received immense interest for their general-purpose language understanding and, in particular, their ability to generate high-quality text or computer code. For many professions, LLMs represent an invaluable tool that can speed up and improve the quality of work. In this note, we discuss to what extent they can aid professional mathematicians. We first provide a mathematical description of the transformer model used in all modern language models. Based on recent studies, we then outline best practices and potential issues and report on the mathematical abilities of language models. Finally, we shed light on the potential of LMMs to change how mathematicians work.