In this work, Martin H. Krieger shows what physicists are really doing behind the nearly impenetrable cloud of mathematical models they use as research tools. He argues that the technical details of these complex calculations serve not only as a means to an end, but also reveal key aspects of the physical properties they model. Using two "tours de force" of modern physics as case studies, as proofs that ordinary matter is stable, and solutions to the Ising model of a phase transition (how a liquid freezes to a solid, for instance), Krieger seeks to uncover the philosophical foundations on which the mathematical models of these phenomena are built.