Introduction Brownian motion is the random motion of particles suspended in a fluid (a liquid or a gas) resulting from their collision with the fast-moving atoms or molecules in the gas or liquid. This transport phenomenon is named after the botanist Robert Brown. In 1827, while looking through a microscope at particles trapped in cavities inside pollen grains in water, he noted that the particles moved through the water. Atoms and molecules had long been theorised as the constituents of matter, and Albert Einstein published a paper in 1905 that explained in precise detail how the motion that Brown had observed was a result of the pollen being moved by individual water molecules. This explanation of Brownian motion served as convincing evidence that atoms and molecules exist, and was further verified experimentally by Jean Perrin in 1908. Perrin was awarded the Nobel Prize in Physics in 1926 "for his work on the discontinuous structure of matter" (Einstein had received the award five years earlier "for his services to theoretical physics" with specific citation of different research). The direction of the force of atomic bombardment is constantly changing, and at different times the particle is hit more on one side than another, leading to the seemingly random nature of the motion. Brownian motion is among the simplest of the continuous-time stochastic (or probabilistic) processes, a big idea in physics.
Acknowledgement My sincere gratitude for the tireless contributions of Francisco Esquembre, Fu-Kwun Hwang, Wolfgang Christian, Félix Jesús Garcia Clemente, Anne Cox, Andrew Duffy, Todd Timberlake and many more in the Open Source Physics community.