First Proof Second Batch

2026-06-16

AI Summary

This study presents a systematic evaluation of current AI systems’ capabilities in solving research-level mathematical problems. Focusing on ten cutting-edge open problems spanning diverse mathematical domains, the project employs a multi-model AI approach and incorporates expert human review alongside comparative analysis to conduct the first comprehensive assessment of AI’s mathematical reasoning in authentic research settings. The work publicly releases human solutions, AI-generated outputs, and complete review logs, establishing a benchmark for complex mathematical problem solving. By revealing both the strengths and critical limitations of existing AI systems in deep reasoning tasks, this research provides empirical foundations to guide future algorithmic advancements.

Abstract

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.

Problem

• AI systems
• research-level mathematics
• problem solving
• mathematical fields
• evaluation

Innovation

• AI evaluation
• research-level mathematics
• mathematical problem solving
• benchmarking
• artificial intelligence