The flight of a fly inspired Descartes to create the coordinates that bear his name. The antecedents go back to ancient Greece, since both Menaechmus, a disciple of Plato, and Apollonius of Perga, the Great Geometer, used mixed methods.

The clearest precursor was the distinguished Persian poet and mathematician Omar Jayam, whose Treatise on Demonstrations of Problems in Algebra can be considered the founding text of analytical geometry. The power of this simple idea lies in the fact that we can convert a line into an equation and vice versa.