Laplace, Fourier, and stochastic diffusion

TL;DR

This paper explores the historical development and interconnections of Laplace's, Fourier's, and stochastic diffusion, highlighting their influence on mathematical physics, probability, and analysis.

Contribution

It provides a historical analysis of how Laplace, Fourier, and stochastic diffusion concepts influenced each other and shaped modern mathematical physics and probability theory.

Findings

Laplace's early formulation of stochastic diffusion predates Einstein.

Fourier's heat diffusion work was influenced by Laplace's probability concepts.

The interaction between these mathematicians significantly impacted subsequent scientific developments.

Abstract

Stochastic diffusion equation, which attained prominence with Einstein's work on Brownian motion at the beginning of the twentieth century, was first formulated by Laplace a century earlier as part of his work on Central Limit Theorem. Between 1807 and 1811, Fourier's work on heat diffusion, and Laplace'swork on probability influenced and inspired each other. This brief period of interaction between these two illustrious figures must be considered remarkable for its profound impact on subsequent developments in mathematical physics, probability theory and pure analysis.