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Benchmarks in Leipzig

Andrei Balakin Mikl\'os B\'ona Marie-Charlotte Brandenburg Clara Briand Veronica Calvo Cortes Shelby Cox Jesus A. De Loera Danai Deligeorgaki Hannah Friedman Tim Gehrunger Chiara Giardino Stephen Griffeth Baran Hashemi Elena Hoster Alexander Ivanov Nupur Jain Aryaman Jal Leonie Kayser Joris Koefler Kevin K\"uhn Mario Kummer Felix Lotter Ren\'e Marczinzik Victor S. Miller Alejandro Morales Greta Panova Gianni Petrella Nathan Pflueger Lakshmi Ramesh Nikolas Rieke Carlos Rodriguez Andrea Rosana Flavio Salizzoni Otto T. P. Schmidt Sven Ulf Schmitz Lina Maria Simbaqueba Marin Luca Sodomaco Christian Stump Bernd Sturmfels Alexander Taveira Blomenhofer Simon Telen Philipp Tuchel Emil Verkama Carl Felix Waller Julian Weigert Annette Werner Nathan Williams Claudius Zibrowius
Oct 2026
Artificial Intelligence

Abstract

Between April 1 and May 15, 2026, a group of 49 mathematicians compiled a dataset of research-level mathematics questions with known answers. Most of the work was done during the three-day workshop Benchmarks in Leipzig with 35 participants at the Max Planck Institute for Mathematics in the Sciences in Leipzig, Germany. We present the resulting collection of 100~questions. We evaluated these questions in three stages: a single attempt by five state-of-the-art LLMs and their predecessors, followed by a 20-runs-per-model evaluation with three of these models, and finally a 3-run attempt with two heavy-thinking models. After Stage 1, 41 questions remained completely unsolved; after Stage 2, this count dropped to 16; and we concluded Stage 3 with only 2 unsolved questions. This demonstrates that the mathematical reasoning capabilities of LLMs are becoming impressive. In September 2026, we added a fourth stage in which the next generation of models attempted all 100 questions once more, after which only 1 question remains unsolved.

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