IV.

Mathematics

The most notable contribution that Descartes made to mathematics was the systematization of analytic geometry (see Geometry: Analytic Geometry). He was the first mathematician to attempt to classify curves according to the types of equations that produce them. He also made contributions to the theory of equations. Descartes was the first to use the last letters of the alphabet to designate unknown quantities and the first letters to designate known ones. He also invented the method of indices (as in x²) to express the powers of numbers. In addition, he formulated the rule, which is known as Descartes's rule of signs, for finding the number of positive and negative roots for any algebraic equation.