Part III: The Age of Analysis
1800–1870
The 19th century saw mathematics leap beyond the calculus framework into bold new territories. Fourier showed that any function can be decomposed into sines and cosines. Gauss, Bolyai, and Lobachevsky proved that Euclid's geometry is not the only one. And Riemann created a geometry of curved spaces that would become Einstein's theory of gravity.
Ch 7
Fourier & the Mathematics of Heat
How the physics of heat conduction created one of the most powerful tools in all of mathematics.
Ch 8
Non-Euclidean Geometry
The 2,000-year quest to prove the parallel postulate ends by destroying it.
Ch 9
Riemann & the Geometry of Space
The lecture that changed everything: geometry in n dimensions with variable curvature.