Mathematics is the only science with a methodology based upon deductive logic, whereas physics is a quantitative science based upon experiment and observation in which trial and error are inherent. Physics uses the most relevant mathematics, for example using group theory to explain the theoretical basis for the crystalline structure of solids, an illustration of how, time and time again, a mathematical theorem perhaps developed by a Greek philosopher is relevant to today's newly developed physics proof.

Introduction. From Aristotle to the structure of glass. From Euclid to general relativity. From plucking strings to electrons in solids. The perception of number: from integers to quaternions. From tiling floors to quasicrystals. Determinism: from Newton to quantum chaos. Symmetry: from Galois to superstrings. From coin tossing to entropy. Topology: from the bridges of Konigsberg to polymers. From parabolas to fractons. Motion: from Zeno to Schrödinger. Appendices. Index.