May 13, 2026

Benchmarks in Leipzig

A benchmark problem set of research-level problems, compiled by 49 researchers to test the possibilities and limitations of large language models in mathematics research.

Hosted at the Max Planck Institute for Mathematics in the Sciences.

Organized by Veronica Calvo Cortes (MPI MiS), Christian Stump (Ruhr-Universität Bochum), and Bernd Sturmfels (MPI MiS).

The Leipzig Benchmark

100 research-level problems to which we know the answers. See our arXiv paper for details.

See the Leipzig Benchmark for the models' performance.

The Challenging Problems

Starting with the Leipzig Benchmark on which all our AI solution attempts failed, we present here problems that appear to be not solved by publicly available models.

AI-Solved Challenging Problems
0/ 2 solved

History

Date Event
2026-05-26 Updated the sample problems to the initial 2 questions from the Leipzig Benchmark that remained unsolved after the 3-stage evaluation process.

Problem Set (2 problems, version May 26, 2026)

Representation Theory Algebraic Combinatorics
Let $Q$ be the quiver with 4 vertices, with adjacency matrix $\begin{pmatrix}  0 &  2 & 2 & 0 \\  0 & 0 & 4 & 0\\  0 & 0 & 0 & 0\\  2 & 2 & 2 & 0 \end{pmatrix}$, and let $d = (1, 3, 4, 1)$. Count all the unique Luna types for representations of $Q$ of dimension vector $d$, across all stability conditions that admit semistables.
Combinatorics Discrete Geometry
Let $P$ be a set of $6$ permutations of size $n$ such that the identity and the reverse permutation are elements of $P$. What is the maximum density of triples shattered by $P$ asymptotically as $n \to \infty$?

Benchmark Contributors

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
Matt Larson
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