Continuity in nature and in mathematics: Boltzmann and Poincaré (Q513965)

Boltzmann and Poincaré both saw a need to justify the applicability of mathematics to physics in the nature of our understanding of physical processes. They both relied heavily on the theory of differential equations, and this raised the issue of whether the implied continuity considerations in the mathematics matched what was happening in nature. Poincaré concluded that this was allowable, whether nature was fundamentally discrete or continuous. Boltzmann argued that there could be no choice: nature was ultimately discrete. The author has considered a wide range of sources, and notes that only Poincaré lived long enough to respond to Planck's ideas about black body radiation (which he accepted was discrete).