Every time I see a question like this I am reminded of something V.I. Arnold wrote, which I take the liberty of quoting here: > 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 by other > institutions dealing with missiles, > such as NASA.). > > Cryptography has generated number > theory, algebraic geometry over finite > fields, algebra \footnote{The creator > of modern algebra, Vi\`ete, was the > cryptographer of King Henry~I\/V of > France.}, combinatorics and computers. > > Hydrodynamics procreated complex > analysis, partial derivative > equations, Lie groups and algebra > theory, cohomology theory and > scientific computing. > > 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).