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arXiv · 2509.26076

IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation

Johannes Schmitt·Gergely Bérczi·Jasper Dekoninck·Jeremy Feusi·Tim Gehrunger·Raphael Appenzeller·Pieter Belmans·Alessio Bottini·Jim Bryan·João Camarneiro·Ana Cannas da Silva·Niklas Canova·Ana-Maria Castravet·Timo de Wolff·Claudio Fontanari·Filippo Gaia·Baran Hashemi·Daniel Holmes·David Holmes·Aitor Iribar Lopez·Victor Jaeck·Martina Jørgensen·Steven Kelk·Martijn Kool·Stefan Kuhlmann·Adam Kurpisz·Johannes Lengler·Chiara Meroni·Ingmar Metzler·Martin Möller·Samuel Muñoz-Echániz·David Muñoz-Lahoz·Robert Nowak·Georg Oberdieck·Daniel Platt·Dylan Possamaï·Gabriel Ribeiro·Aluna Rizzoli·Daria Sakhanda·Raúl Sánchez Galán·Zheming Sun·Diaaeldin Taha·Josef Teichmann·Richard P. Thomas·Henk van der Pol·Michel van Garrel·Charles Vial·Ignacio Barros·Benjamin Doerr·Peter Grünwald·Henry Liu·David Martins·Aleksandar Mijatović·Sergej Monavari·Marc Roth·Patrick Schnider·Yannik Schuler·Pim Spelier·Yuuji Tanaka·Ronald van Luijk
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Abstract

As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of mathematical knowledge. However, existing benchmarks are limited, as they focus solely on final-answer questions or high-school competition problems. To address this gap, we introduce IMProofBench, a private benchmark consisting of 77 peer-reviewed problems developed by expert mathematicians. Each problem requires a detailed proof and is paired with subproblems that have final answers, supporting both an evaluation by human experts and a large-scale quantitative analysis through automated grading. Furthermore, unlike prior benchmarks, the evaluation setup simulates a realistic research environment: models operate in an agentic framework with tools like web search for literature review and mathematical software such as SageMath. Our results show that current LLMs can already solve a significant percentage of research-level questions. IMProofBench will continue to evolve as a dynamic benchmark in collaboration with the mathematical community, ensuring its relevance for evaluating the next generation of LLMs.

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Johannes Schmitt, Gergely Bérczi, Jasper Dekoninck, Jeremy Feusi, Tim Gehrunger, Raphael Appenzeller, Pieter Belmans, Alessio Bottini, Jim Bryan, João Camarneiro, Ana Cannas da Silva, Niklas Canova, Ana-Maria Castravet, Timo de Wolff, Claudio Fontanari, Filippo Gaia, Baran Hashemi, Daniel Holmes, David Holmes, Aitor Iribar Lopez, Victor Jaeck, Martina Jørgensen, Steven Kelk, Martijn Kool, Stefan Kuhlmann, Adam Kurpisz, Johannes Lengler, Chiara Meroni, Ingmar Metzler, Martin Möller, Samuel Muñoz-Echániz, David Muñoz-Lahoz, Robert Nowak, Georg Oberdieck, Daniel Platt, Dylan Possamaï, Gabriel Ribeiro, Aluna Rizzoli, Daria Sakhanda, Raúl Sánchez Galán, Zheming Sun, Diaaeldin Taha, Josef Teichmann, Richard P. Thomas, Henk van der Pol, Michel van Garrel, Charles Vial, Ignacio Barros, Benjamin Doerr, Peter Grünwald, Henry Liu, David Martins, Aleksandar Mijatović, Sergej Monavari, Marc Roth, Patrick Schnider, Yannik Schuler, Pim Spelier, Yuuji Tanaka, Ronald van Luijk. 2026-07-09. IMProofBench: Benchmarking AI on Research-Level Mathematical Proof Generation. https://arxiv.org/abs/2509.26076

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