# History behind the heat equation

Who was the first mathematician/physicist to derive the heat equation $$u_t=\Delta u$$ and when? Was it already known to explain most diffusion phenomena? How much time passed between the first appearance of the heat equation and Fourier's solution? What were the previous attempts?

I'm not looking for a very detailed monograph of this part of history but rather a short account that may be condensed in an answer.

• Heat equation was first formulated by Fourier in a manuscript presented to Institut de France in 1807, followed by his book Theorie de la Propagation de la Chaleur dans les Solides the same year, see Narasimhan, Fourier’s heat conduction equation: History, influence, and connections. In the book he presented a solution in terms of trigonometric series. There was nothing previous to attempt, "diffusion phenomena" were not studied until much later, when atomic theory was accepted. Sep 29, 2020 at 23:04