Explore a comprehensive lecture on the intersection of smooth invariants in four-dimensional manifolds and quantum field theory. Delve into topics such as nuclear force, Yang-Mills theory, instantons, topological invariants, and supersymmetric Yang-Mills theory. Discover Witten's theory, low-energy effective theory, and Donaldson invariance. Examine future research directions, generalized monopole equations, path integrals, and Class S theories. Gain insights from Gregory W. Moore's AMS Invited Address at the 2020 Joint Mathematics Meetings, offering a deep dive into advanced mathematical concepts and their applications in quantum physics.