History

Abstract

The earliest works on algebra beginning with Al-jabr w’al muqâbala by Mohammed ben Musa Al-Khowârizmî (circa A.D. 825), from whence we get the word “algebra” (and the word “algorithm”), presented problems and solutions by numerical example. The notion of a “function,” whether explicit or implicit, would make no sense in such a context. It was not until about 1600 that the idea of using letters to denote both unknowns and coefficients was introduced by François Viéte (1540–1603). The algebraic methods of Viète were taken up by René Descartes (1596–1650) and combined with Descartes’s own coordinate system inspiration. That fundamental advance in 1637 finally brought mathematics to the point that the notion of a function could make sense.