History of Brownian motion

The study of the history of sciences, through its breakthroughs and failures, its debates and oppositions, helps us understand how and why the theories we know today are shaped the way they are, how and why models, concepts and vocabulary emerged, and ultimately offers a deeper intuition of the scientific knowledge accumulated over the years.

Brownian motion is a particularly rich subject for historians because of its life span (~1827 - today), its relevance in almost all natural sciences as well as in mathematics, and its deciding role in the debates of the XXth century, such as the acceptance of the atomic hypothesis.
Observed and described by the botanist Robert Brown in 1827, Brownian motion was then theorised by physicists in the 1900s, and eventually modelled by mathematicians from the 1920s, while still evolving as a physical theory, as depicted in the very naive timeline. Consequently, Brownian motion now refers to the natural phenomenon but also to the theories, both mathematical and physical, accounting for it.

Although Brownian motion is well documented in the literature, its history is often split into parts either from 1827 to Perrin’s experiments in the late 1900s, from a physicist’s point of view; or from the 1920s from a mathematician’s point of view. In this work, I tackled the period straddling the two ‘half-histories’ just mentioned, in order to appreciate continuity, and I used the concept of Brownian velocity as a leading thread because of the key role it played in the divergence between mathematicians' and physicists' theories of Brownian motion.

The topics covered involve the domain-shift from physics to mathematics, the reasons why the young mathematician Wiener studied Brownian motion, the enhancements of the physical theory by Ornstein and Uhlenbeck, the comparison between physicists' and mathematicians' Brownian motion, in particular concerning the existence of Brownian velocities, and the (missing) communication between two communities working on the same subject in parallel but with different goals, thus leading to contradictory theories.