I will discuss some old and new relations between the characters, modular data and braiding and fusing matrices of rational conformal field theories and their associated modular tensor categories. These relations involve concepts from number theory which I will explain in the talk.

I will review the connection between the elliptic genus of K3 surfaces and the representation theory of the Mathieu group M_{24} and then discuss a proposed extension of this connection that applies to a larger set of groups and Jacobi forms.