Oliver Penrose’s work focused on the mathematical basis of statistical mechanics. Oliver has worked on many problems in statistical physics. A notable early success was his estimate (with Lars Onsager) of the proportion of condensate in liquid helium, but his later interests moved to the rigorous derivation of statistical mechanics and ergodic behaviour, where he enjoys an international reputation. Particularly noticeable was his vigorous resolution of the conditions under which the Van der Waals equation holds.