I shall describe two approaches to the study of self-assembly. The first approach involves experiments with DNA molecules. We use DNA like a construction material --- akin to the uses of brick, cement, glass, etc. --- to form nanostructures. The second approach involves a mathematical investigation of the law of mass action in chemistry. A major goal of our work is to solidify the mathematical foundations of mass action chemistry. In addition, we believe that the law of mass action is of intrinsic mathematical interest. We are led to a dynamical theory of sets of binomials over the complex numbers, with connections to number theory and toric varieties.
