Part IV — Chapter 11
Descartes & Fermat
The unification of algebra and geometry, and the birth of modern number theory
11.1 Descartes and Analytic Geometry
René Descartes (1596–1650) published La Géométrie in 1637, showing how geometric problems could be translated into algebraic equations and vice versa — creating analytic geometry. By introducing coordinate axes, he bridged the ancient geometric tradition and algebraic methods.
11.2 Fermat's Number Theory
Pierre de Fermat (1601–1665) discovered Fermat's little theorem, developed the method of infinite descent, and famously wrote in the margin of Diophantus: “I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.” His Last Theorem — that xn + yn = zn has no positive integer solutions for n > 2 — remained unproven for 358 years.