Differential geometry, fiber bundles and physical theories

Among intellectual disciplines, mathematics occupies a unique position. It is in many respects an art, but it is also the language of science. Although a great deal of mathematics can be traced directly to external influences, much of its creativity is motivated internally: “pour la gloire de l'esprit humain,” as Carl G. T. Jacobi put it. Often the mathematician lets the imagination soar, constrained only by logic, intrinsic structure, and a sense of historical continuity. Yet from time to time these abstract deliberations have important applications in other fields.