Conformal field theories are characterized by structure constants (3-point correlation functions). In order for the theory to be consistent, the structure constants must satisfy the “bootstrap equation”, which is useful to numerically solve, for example, for the critical exponent of the 3d Ising model. From a mathematical point of view, the bootstrap equation arises from the operad structure of spacetime, and such mathematics may be useful to find (as yet undiscovered) constraints on quantum field theory. In this talk, we will introduce the notion of operad and discuss the relation between operads and operator product expansions based on mathematical studies of conformal field theories in two dimensions.