We evaluate language models as both authors and solvers of mathematical problems. The benchmark evolves as new models contribute harder problems, revealing differences between problem-posing and problem-solving abilities.

We develop a type theory with semantics in categories enriched in categories of fuzzy sets, in analogy with Martin-Löf type theory and its interpretation in categories.

We introduce Torsor CNNs, a framework connecting discrete gauge theory to group synchronization for learning on graphs with local symmetries.

We develop a functorial framework for approximating the persistent homology transform using Kan extensions.

We compute the (4,2)-Gromov–Wasserstein distance between unit spheres of different dimensions with Euclidean metrics and uniform measures.

We construct a homotopy sheaf that organizes persistent homology transforms into a shape space and establish gluing and approximation results.

We decompose degree-zero persistent homology transforms of planar star-shaped objects into sectors and give conditions under which their diagram bundles have trivial geometric monodromy.

We show that dimensionality reduction via random projections preserves k-distance and thus persistent homology.