To assess the ability of current AI systems to correctly solve research-level mathematics problems, we tested several AI systems on a set of ten problems in a broad range of mathematical fields; these problems arose naturally in the research process of the contributors. This document includes the problems, our methodology, and the results of our testing. We provide links to supplementary documents including the human solutions, the AI-generated solutions, and the referee reports and logs for the AI-generated solutions. The ten problems were contributed by the following mathematicians: (1) Dariusz Kalociński and Theodore A. Slaman, (2) Richard Schwartz, (3) Aleksa Milojevic and Benny Sudakov, (4) Larry Guth, (5) Oleg Butkovsky, Jonathan Mattingly, and Lorenzo Zambotti, (6) Joshua Evan Greene and Duncan McCoy, (7) Sucharit Sarkar, (8) Sam Payne and Jidong (Jayden) Wang, (9) Sylvie Corteel and John Lentfer, (10) Srivatsav Kunnawalkam Elayavalli.
翻译:为了评估当前人工智能系统正确解决研究级数学问题的能力,我们在一组涵盖广泛数学领域的十个问题上测试了若干 AI 系统;这些问题自然产生于贡献者的研究过程中。本文档包含这些问题、我们的方法论以及测试结果。我们提供了辅助文档的链接,包括人工解法、AI 生成解法,以及针对 AI 生成解法的审稿报告和日志。这十个问题由以下数学家贡献:(1)Dariusz Kalociński 和 Theodore A. Slaman,(2)Richard Schwartz,(3)Aleksa Milojevic 和 Benny Sudakov,(4)Larry Guth,(5)Oleg Butkovsky、Jonathan Mattingly 和 Lorenzo Zambotti,(6)Joshua Evan Greene 和 Duncan McCoy,(7)Sucharit Sarkar,(8)Sam Payne 和 Jidong (Jayden) Wang,(9)Sylvie Corteel 和 John Lentfer,(10)Srivatsav Kunnawalkam Elayavalli。