René Descartes (31 March 1596 — 11 February 1650) is decidedly a mixed blessing to humanity. His mind/body duality idea has confused generations upon generations of thinkers. His distillation of the (reductionist) scientific method is arguably naïve and misleading. It came to him, by the way, in a dream as he was sleeping in a stove, on a famous night in November 1619 in the city of Ulm. Don’t try this at home.
Born in France, he studied law in Poitiers, fought all over Europe in the Thirty Years War, lived in almost every city in Holland, studied mathematics and astronomy at Leiden, planned a Treatise on the World, corresponded with royalty, and died in mysterious circumstances in Sweden, perhaps from having to get up early in the morning. He was buried in a graveyard for unbaptized children, but the grateful French have moved his remains to the Abbey of Saint-Germain-des-Prés. His works were once on the Index of Prohibited Books, but now no-one studying philosophy can escape reading either the Discourse on Method, or the Meditations on the First Philosophy, or the Principles of Philosophy of “cogito ergo sum” fame.
All in all a seminal figure in many areas including optics, his contribution to mathematics is prodigious. Perhaps he is best remembered for introducing coherent mathematical notation (powers as superscripts, x for an unknown, the Cartesian plane), and for the absolutely revolutionary idea that geometric problems can be solved by algebraic methods; the latter gave an important impetus to the development of calculus a generation later. To these may be added many results in geometry, fundamental, for example, in proving that certain problems, such as trisecting an angle, cannot be solved with compass and straightedge, and the forever useful Descartes’ rule of signs in polynomial equations.