Maxwell's equations and the principles of quantum mechanics led to the idea of gauge invariance. Attempt to generalize this idea, motivated by physical concepts of phases, symmetry, and conservation laws, led to the theory of non-Abelian gauge fields. That non-Abelian gauge fields are conceptually identical to ideas in the beautiful theory of fiber bundles, developed by mathematicians without reference to the physical world, was a great marvel to me. In 1975 I discussed my feelings with Chern, and said "this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere." He immediately protested: "No, no. These concepts were not dreamed up. They were natural and real."
— C. N. Yang
#matematyka #fizyka #cytatywielkichludzi