Benchmarks in Leipzig

arXiv:2606.05818v2 Announce Type: replace-cross 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.

Authors:Andrei Balakin, Miklós Bóna, 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 Kühn, Mario Kummer, Felix Lotter, René 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

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.

9 pages including 11 tables + 20 pages appendix containing the 100 Leipzig Benchmark questions. v2: adds the September 2026 re-run (Stage 4) with nine model configurations using web search and code execution

History and Overview (math.HO); Artificial Intelligence (cs.AI); Algebraic Geometry (math.AG); Combinatorics (math.CO); Representation Theory (math.RT)

arXiv:2606.05818 [math.HO]

(or arXiv:2606.05818v2 [math.HO] for this version)

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Benchmarks in Leipzig

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