I believe that mathematics and physics, alas science in general, are not the private property of scientists. Here are some of the ways I try to share their beauty and importance with a wider audience.
A book presenting the ergodic theorem, one of the most profound results in modern mathematics. The theorem says, in essence, that for many dynamical systems, time averages equal space averages: a gas in equilibrium eventually "visits" all its possible states proportionally. The book traces the theorem's history from Boltzmann's hypothesis to its rigorous proof by Birkhoff and von Neumann, and illuminates its deep connections to probability, physics, and our understanding of irreversibility and entropy. Accessible to a broad audience, the book requires only an introductory college-level foundation in mathematics and physics.