Coordinates

Abstract

The most important step in geometry since ancient times was the introduction of coordinates by Descartes in his Geometry of 1637. Coordinates are a simple idea, but not much use without algebra and a symbolic notation, which is probably why the idea did not take off earlier. The time was ripe for coordinates in 1637, because algebra and its notation had matured over the preceding century, to a level similar to high school algebra today. In fact, Fermat in 1629 hit on the same idea as Descartes, and he illustrated it with similar results, but they were not published at the time.