The Promise of Quantum Field Theory

For mathematicians, QFT is as rich a type of object as they could hope for. Defining the characteristic properties shared by all quantum field theories will almost certainly require merging two of the pillars of mathematics. If mathematicians can understand QFT, there's no telling what mathematical discovery is a weight in its unlocking. For physicists, a complete mathematical description of QFT is the flip side of their field's overriding goal, a complete description of physical reality.