Abstract

The development of modern mathematics has depended considerably upon the concept of functionality. Modern mathematicians have used it as the framework for much of their theory in the advanced fields of analysis and higher algebra. Descartes in the seventeenth century founded Cartesianism, an ingenious system whereby geometric loci can be represented algebraically. In this system, known as analytical geometry, any algebraic function corresponds to a geometric locus, and conversely. This algebraic representation of a curve or surface in space laid the ground work for higher geometry, —the analytical treatment of spacial elements. The paramont importance of functionality is thus evident in the entire field of modem mathematics.

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