For almost two thousand years, geometry and algebra lived apart. Greek geometry worked with ruler, compass and figures. Algebra, which reached Europe through the Arabs, worked with equations. At the start of the 17th century, two people had, at the same time and without consulting each other, the idea of joining them: René Descartes and Pierre de Fermat. A sentence that created a field Around 1636 Fermat wrote a short Latin text, Introduction to plane and solid loci. “Locus” was the Greek name for a set of points satisfying a condition, like the circle, the locus of points at a fixed distance from the centre. Right at the start, Fermat wrote: