Einstein’s 1905 paper on Brownian motion1 convinced the scientific community of the existence of atoms. Einstein used Brownian Motion to explain the apparently random motion of pollen particles suspended in still water.
Brownian Motion as we know it, was developed by Norbert Weiner in the 1920s. Weiner constructed Brownian motion as a probability measure on continuous path space. See this paper “Weiner and Integration in Function spaces” by Mark Kac2.
Yes, that Kac in the Feynman-Kac forumla. He won the Chauvenet Prize for his 1947 expository paper “Random walk and the theory of Brownian motion”. He won another chauvenet for his 1966 paper “Can one hear the shape of a drum?”. ↩