Part II: The Greek Revolution
The birth of deductive reasoning — how Greek thinkers transformed mathematics from practical computation into a rigorous logical discipline.
Overview
Between roughly 600 BCE and 300 CE, Greek mathematicians achieved something unprecedented: they insisted that mathematical statements be proved from axioms through logical deduction. Euclid's Elements became the model of rigorous argument for two millennia. Archimedes anticipated calculus. Diophantus pioneered the study of equations in integers. This tradition, transmitted through Arabic and Latin translations, became the foundation of all Western mathematics.
Chapters
Chapter 4: Pythagoras & Euclid
The Pythagorean brotherhood, the discovery of irrationals, and Euclid's Elements — the most influential mathematics book ever written.
Chapter 5: Archimedes & Apollonius
The method of exhaustion, the area of a parabola, the spiral of Archimedes, and Apollonius's masterful theory of conic sections.
Chapter 6: Diophantus & Late Antiquity
Diophantine equations, Hypatia of Alexandria, and the transmission of Greek knowledge to the medieval world.