Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.
Vladimir ArnoldAll mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and other institutions dealing with missiles, such as NASA).
Vladimir ArnoldCryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.
Vladimir ArnoldCelestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.
Vladimir Arnold