The stepping stone from algebra to analysis

Algebra, as we know it today, was more or less first formalized by Mohammad al-Khwarizmi (circa 780 – 850), a Persian mathematician, whose published text (translated into Latin in the twelfth century), The Science of Reunion and Reduction, systematically worked through solutions of linear and quadratic equations.

Some eight or so centuries later, Rene Descartes (circa 1637) introduced, what I call, the x-factor into algebra by putting a grid onto what was previously the sand strewn abakon of the Ancient Greeks. In doing so, he revolutionized the study of geometry. Once drawn at random on a planar tablet, angles could then be given fixed standard positions and lines, parabolae, ellipses and other interesting planar curves could be described primarily by their equations in the variables x and y rather than by their descriptivegeometric properties. It was found that both planar curves and traces of paths in 3-dimensions were all expressible in terms of, what we now call, algebraic polynomial equations in one or more variables, thereby opening the door to the investigation of polynomials of varying degrees.

This ultimately led to a generalized definition of polynomials and the study of their properties as functions, a term first coined by one of the inventors of Calculus, Gottfried Leibniz, in 1673.

Last Updated by SAS October 07, 2026, 16:00:51