From AMS Glossary
(Also called Brownian movement.) The rapid and chaotic motion of particles suspended in a fluid at rest as a consequence of fluctuations in the rate at which fluid molecules collide with the particles.
On average, the particles experience zero net force, but deviations from this average give rise to Brownian motion, so named because it reputedly was observed first in pollen grains by the botanist Robert Brown. Whether Brown actually observed what we now call Brownian motion has been questioned on the grounds that his grains were so large that their fluctuating motion would have been imperceptible. But even if Brownian motion can ever be shown not to have been observed by Brown, his name is likely to be forever attached to this motion, especially since mathematicians have generalized this term to a broad class of stochastic processes. Brownian motion is more than just a scientific curiosity, having played a key role in establishing the reality of molecules and in presenting a convincing argument for the kinetic theory of gases.
Boorse, H. A., and L. Motz 1966. The World of the Atom. Vol. I, . 206–212.