This is a talk about the history of the mathematical modelling of noise.
The story starts with one of Einstein’s world changing papers of 1905: his mathematical description of Brownian motion, meant as a contribution to the scientific debate about the existence of atoms. It takes us on the path of Boltzmann and Langevin, and from physics to finance, where we meet Bachelier, a student of Poincare who saw an analogy between the motion of particles, and the evolution of stock market prices. It also takes us towards engineering, and electronics in particular. The story, however, is told from the point of view of a deeply biased mathematician, so it emphasises the beautiful ideas in partial differential equations and probability that other kind of storytellers would probably hide. In particular, the talk’s mathematical aim is to introduce, in a highly informal way, stochastic partial differential equations.