Stephen G. Brush

“The suggestion that eternal recurrence might be proved as a theorem of physics, rather than as a religious or philosophical doctrine, seems to have occurred at about the same time to the German philosopher Friedrich Nietzsche and the French mathematician Henri Poincaré. Nietzsche encountered the idea of recurrence on his studies of classical philology, and again in a book by Heine. It was not until 1881 that he began to take it seriously, however, and then he devoted several years to studying physics in order to find a scientific-sounding formulation of it. Poincaré on the other hand, was led to the subject by his attempts to complete Poisson's proof of the stability of the solar system, though he was also concerned with the difficulty of explaining irreversibility by mechanical models such as Helmholtz's monocyclic systems. Poincaré's theorem belongs to the history of theoretical physics, Nietzsche's speculations to the history of philosophical culture, and they are not usually discussed in the same context. Yet I find it necessary to consider them together since it was just at the end of the 19th century that developments in science were strongly coupled to the philosophical-cultural background. Both Nietzsche and Poincaré were trying, though in very different ways, to attack the "materialist" or "mechanist" view of the universe.”
― Stephen G. Brush, The kind of motion we call heat: A history of the kinetic theory of gases in the 19th century