He was a pioneer of statistical physics and made significant contributions to the theory of Brownian motion and stochastic processes.

He was born in 1872 into an upper-class family in Vorder-Brühl, near Vienna, to father Wilhelm and mother Teofila (née Szczepanowska).

[6] When World War I began the following year, the work conditions became unusually difficult, as the spacious and modern Physics Department building, built by Witkowski a short time before, was turned into a military hospital.

Smoluchowski lectured in experimental physics; his students included Józef Patkowski, Stanisław Loria and Wacław Dziewulski.

Professor Władysław Natanson wrote in an obituary of Smoluchowski: "With great pleasure I recall the charm of his life, his noble cordiality, combined with exquisite kindness.

I wish I could render the curious appeal of his personality, recall how temperate he was, how modest and elegantly diffident, yet always full of a pure, spontaneous joy.

It describes the time evolution of the probability density function for a particle undergoing Brownian motion under the influence of external forces and diffusion.

Roman became a notable physicist who worked in Poland, and after World War II settled in the United States (the Institute for Advanced Study at Princeton).

[17] Streets in several Polish cities bear the name of Smoluchowski including in Gdańsk, Lublin, Malbork, Kraków, Poznań and Wrocław.