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.
All 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).
Celestial mechanics is the origin of dynamical systems, linear algebra, topology, variational calculus and symplectic geometry.
The existence of mysterious relations between all these different domains is the most striking and delightful feature of mathematics (having no rational explanation).
Hydrodynamics procreated complex analysis, partial differential equations, Lie groups and algebra theory, cohomology theory and scientific computing.
Cryptography has generated number theory, algebraic geometry over finite fields, algebra, combinatorics and computers.
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