Diffusion implies spreading, either observable (physical), or abstract and probabilistic (stochastic). At the beginning of the 19th century, the mathematics of both were established by Joseph Fourier and Pierre Simon Laplace. In 1807 Fourier submitted a monograph, Théorie de la propagation de la chaleur dans les solides (Theory of the propagation of heat in solids), to the French Academy of Sciences and introduced the partial differential equation describing heat flow. 1,2 The academy appointed Joseph Lagrange and Laplace as two of the four reviewers of the monograph; they questioned Fourier’s use of trigonometric series to solve the heat equation. Hence, the work was never approved.

At the time, Laplace was working on his theory of probability—in particular, estimating the probability that the sum of n random variables may be equal to or less than a certain value when n is very large. In 1809 he formulated a...

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