Part IV: Early Modern Transformation
Renaissance breakthroughs, the invention of analytic geometry, probability theory, and the epoch-making creation of calculus.
Overview
The 16th and 17th centuries witnessed an explosion of mathematical creativity. Italian algebraists solved cubic and quartic equations. Descartes married algebra and geometry. Pascal and Fermat founded probability theory through a famous exchange of letters. And Newton and Leibniz, working independently, invented calculus — the mathematical language of change that would transform physics, engineering, and every quantitative science.
Chapters
Chapter 10: Cardano & Renaissance Algebra
The dramatic story of the cubic formula — Tartaglia's secret, Cardano's publication, and Ferrari's quartic solution.
Chapter 11: Descartes & Fermat
La Géométrie and the unification of algebra and geometry. Fermat's little theorem, his last theorem, and his correspondence on probability.
Chapter 12: Newton & Leibniz — The Calculus
Two independent inventions, one bitter priority dispute, and the mathematical revolution that changed science forever.
Chapter 13: Pascal & the Birth of Probability
Pascal's triangle, the problem of points, the Pascaline calculator, and the philosophical wager.