In this insightful 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 - 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 uncovers the philosophical foundations on which the mathematical models of these phenomena are built. In so doing, he gives the reader a better feel not just for how physicists believe the natural world is structured, but also for how they have arrived at those conclusions.

Krieger's lucid discussions will help students of physics and applied mathematics appreciate the larger physical issues behind the mathematical details of modern physics. Historians and philosophers of science will gain deeper insights into how theoretical physicists do science, while technically advanced general readers will get a rare, behind-the-scenes glimpse into the world of modern physics.