Quantum field theory is the unification of quantum theory and special　theory of relativity. It provides the framework for the standard model, a theory of all the observed forces (except gravity) of nature. String theory is the leading candidate for a unified theory of all the four forces. It yields a consistent theory of quantum gravity, at least in the perturbative, weak field domain. For several decades, quantum field theory and string theory have been the major sources of inspirations formathematics. There have been deep interactions between them with mathematics through algebra and geometry.