ABSTRACT
If one defines algebra as a set of problems that include establishing basic algebraic identities and formulating and solving quadratic and cubic equations, then its beginnings go back four thousand years, and ancient mathematics is rife with the geometrical treatment of algebraic problems. But the modern origins of analytic geometry, which combines algebra and geometry by formulating certain correspondences between curves and equations, are generally assigned to the work of François Viète (1540-1603), René Descartes (1596-1650), and Pierre de Fermat (1601-1665). In general, geometry, rather than an abstract symbolic structure, was the universal language of antiquity, and the domains of geometry and number were segregated. Viète, Descartes, and Fermat introduced an essentially modern form of mathematics, in which the domains of geometry and number could be deeply and fruitfully integrated under the aegis of an abstract symbolic structure.
