Contributions of René Descartes in Mathematics René Descartes (1596–1650) made remarkable contributions that transformed mathematics and provided the basis for many modern branches of the subject. 1. Founder of Analytical Geometry Descartes introduced Analytical Geometry , which links algebra and geometry . He showed that geometric shapes can be represented by algebraic equations . This made it possible to study curves, lines, and figures using numbers and symbols. 2. Cartesian Coordinate System He developed the Cartesian coordinate system , using two perpendicular axes (x and y) to locate points in a plane. This system allows us to graph equations and visualize mathematical relationships easily. It is the foundation of graphing in algebra, geometry, and calculus. 3. Advancement in Algebraic Notation Descartes introduced modern algebraic symbols and conventions : Used letters (x, y, z) for unknowns. Used letters (a, b, c) for known constants. This simplified m...