May 13, 2026
Benchmarks in Leipzig Challenge
A benchmark problem set of research-level mathematics problems,
written by 49 researchers to test the limits of frontier AI models.
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 Tier-4 Benchmark
Research-level problems to which we know the answers.
See the Leipzig Tier-4 Benchmark for the models' performance.
The Leipzig Challenge
A subset of the Leipzig Tier-4 Benchmark on which all our AI solution attempts failed.
This is work in progress and more problems will be added.
AI-Solved Leipzig Challenge Problems
0/ 2 solved
Solve History
| Date | Model | New problems solved |
|---|---|---|
| 2026-05-07 | none | no problem solved yet |
Problem Set (2 problems, more to be added)
Algebra
Let $KQ$ be the path algebra with $Q$ of linear oriented Dynkin type $A_3$ having 3 vertices. Let A be the total preprojective algebra of $KQ$. How many indecomposable non-zero $A$-modules are there up to isomorphism?
Combinatorics
Let $A$ be the set of signed permutations of length $12$, this is the set of permutations $\pi$ of the set $\{\pm 1, \dots, \pm 12\}$ for which $\pi(-i) = -\pi(i)$.
Consider the random variable $X$ that assigns to a uniformly drawn signed permutation $\pi \in A$ the number of indices $i \in \{-12,\dots,-1,1,\dots,7\}$ such that $\pi(i) > \pi(i+5)$ if $i,i+5$ have the same sign, or such that $\pi(i) > \pi(i+6)$ if $i,i+5$ do not have the same sign. (The sign of a negative number if $-1$, the sign of a positive number is $1$ and the sign of $0$ is $0$.)
What is the variance of this random variable?