Rene Descartes. Artwork of the French philosopher and mathematician Rene Descartes (1596-1650), seen with some equations and lines. At top right is a cartesian equation describing a curved line called a parabola. The equations at lower right show the relationship between cartesian and polar coordinates. Polar coordinates give the position of a point by a distance and an angle, while cartesian coordinates describe the point using a vertical (y) and a horizontal (x) distance. Descartes created this coordinate, or cartesian, geometry in which geometrical problems are converted into algebraic forms so that algebraic techniques may be used to solve them.