Brownian motion
Albert Einstein (in one of his 1905 papers) and Marian Smoluchowski (1906) brought the solution of the problem to the attention of physicists, and presented it as a way to indirectly confirm the existence of atoms and molecules. Their equations describing Brownian motion were checked by the experimental work of Jean Baptiste Perrin in 1908.  Perrin was awarded the Nobel Prize in Physics in 1926 "for his work on the discontinuous structure of matter".