The mathematician may be compared to the designer of garments, who is utterly oblivious of the creatures whom his garments may fit. To be sure, his art originated in the necessity for clothing such creatures, but this was long ago. To this day a shape will occasionally appear which will fit into the garment as if the garment had been made for it. Then there is no end of surprise and delight!
There have been quite a few such delightful surprises. The conic sections, invented in an attempt to solve the problem of doubling the alter of an oracle, ended by becoming the orbits followed by the planets in their couses about the sun. The imaginary magnitudes invented by Cardan and Bombelli describe in some strange way the characteristic features of aternating currents. The absolute differential calculus, which originated as a fantacy of Riemann, became the mathematical vehicle for the Theory of Relativity. And the matrices, which were a complete abstaction in the days of Cayley and Sylvester, appear admirably adapted to the exotic situation exhibited by the quantum theory of the atom.