René Descartes (1596–1650) was one of the leading mathematicians, philosophers, and scientists of his day. He was a contemporary of Pascal and Fermat.

Descartes was born in 1596 in France in the village now named after him. His mother died at an early age, and Descartes got into the habit of rising very late in the morning. When he grew up, he became a mercenary soldier. The Thirty Years War was raging at the time, and Descartes would end up fighting for both sides. While serving in the Bavarian army in 1619, he had a vision that pointed him towards the invention of analytic geometry. He moved to Holland in 1628 and over the next 20 years would write several revolutionary works about mathematics and philosophy.

Among his many contributions to mathematics, the most significant is the invention of analytic geometry, also known as coordinate geometry or Cartesian geometry. This he published in La géométrie, which was published in 1637 as an appendix to his magnum opus, Discours de la méthode pour bien conduire sa raison et chercher la vérité dans les sciences.

Analytic geometry is geometry that uses a coordinate system and allows lines, curves, and other geometric objects to be treated algebraically. Thus, it provides a mapping, a link, between algebra and geometry. This often allows an insight into geometric problems that is not available geometrically. For example, Descartes was able to suggest that two of the three construction problems of antiquity—those of duplicating the cube and trisecting the angle—were impossible, an insight not possible by treating the problems geometrically.

One of the interesting things about La géométrie is that it is the first mathematical work that a modern mathematician would be able to understand without difficulty. Most of the symbols in it are the same as those used today, except for the equals sign that Descartes used.

Sources used (see bibliography page for titles corresponding to numbers): 38.