Part V — Chapter 17
Riemann & Fourier
Reshaping geometry, decomposing functions, and the mystery of prime numbers
17.1 Joseph Fourier
Joseph Fourier (1768–1830) claimed that any function could be expressed as an infinite sum of sines and cosines — a Fourier series. This became one of the most powerful tools in mathematics, physics, and engineering — essential in signal processing, quantum mechanics, and data compression.
17.2 Bernhard Riemann
Bernhard Riemann (1826–1866) introduced Riemannian geometry, which became the mathematical language of Einstein's general relativity. In a single eight-page paper (1859), he connected prime distribution to the Riemann zeta function. His hypothesis about its zeros remains the most famous unsolved problem in mathematics.