Boltzmann’s collective work was a mathemetical tour de force. Building on Clausius and Maxwell, he demonstrated that the distribution of gas phase atoms and molecules follows from probability theory. Atoms and molecules distribute themselves in space and momentum to the most probable distribution. Boltzmann used probability theory to quantify the most probable state and then demonstrated the connection between this state and its entropy. This novel approach, later validated by Sackur–Tetrode, led to the creation of statistical mechanics.