  All physical systems in equilibrium obey the laws of thermodynamics. In other
words, whatever the precise nature of the interaction between the atoms and
molecules at the microscopic level, at the macroscopic level, physical systems
exhibit universal behavior in the sense that they are all governed by the same
laws and formulae of thermodynamics. In this paper we describe some recent
history of universality ideas in physics starting with Wigner's model for the
scattering of neutrons off large nuclei and show how these ideas have led
mathematicians to investigate universal behavior for a variety of mathematical
systems. This is true not only for systems which have a physical origin, but
also for systems which arise in a purely mathematical context such as the
Riemann hypothesis, and a version of the card game solitaire called patience
sorting.
