From Molecules to Mathematics

To celebrate the 40th anniversary of bottom-up DNA nanotechnology we highlight the interaction of the field with mathematics. DNA self-assembly as a method to construct nanostructures gave impetus to an emerging branch of mathematics, called here ‘DNA mathematics’. DNA mathematics models and analyzes structures obtained as bottom-up assembly, as well as the process of self-assembly. Here we survey some of the new tools from DNA mathematics that can help advance the science of DNA self-assembly. The theory needed to develop these tools is now driving the field of mathematics in new and exciting directions. We describe some of these rich questions, focusing particularly on those related to knot theory, graph theory, and algebra.