DNA self-assembly, as a method to construct nanostructures gave impetus to an emerging branch of mathematics, which we wish to coin as ‘DNA mathematics’. DNA mathematics models and analyzes structures obtained as bottom-up assembly, as well as the process of self-assembly. We present a range of topological questions associated with experimentally built assemblies. The questions vary from topological graph theory related to DNA strand routing a three-dimensional mesh, to questions in knot theory related to structural embeddings in 3D.