Christopher Pincock's book has two parts. Part I provides Pincock's analytical framework (Chapter 2), chapter-length discussions (supported by detailed analysis of a host of examples) of different types of scientific representation and the epistemic benefits (Chapters 3–6) and risks (Chapter 7) associated with their mathematics. Its principal thesis is that mathematics primarily contributes to scientific representations by promoting scientists' epistemic goals. Part II explores the consequences of the foregoing for philosophy of mathematics. It covers Steiner-Wigner puzzles about the unreasonable effectiveness of mathematics (Chapter 8), indispensability arguments, mathematical explanation, and lessons from the mathematics of rainbows (Chapters 9–11), mathematical fictionalism (Chapter 12), and the proper treatment of content (Chapter 13). Chapter 14 draws conclusions: mathematics has objective, non-fictional truth conditions, but their ontological basis is an open question; central parts of mathematics require a priori justification, but no adequate standard epistemology renders them a priori. *** The success of...