OverviewWhy is there a material world? Why is it fundamentally mathematical? Matter Matters explores a seventeenth-century answer to these questions as it emerged from the works of Descartes and Leibniz. The 'mathematization' of the physics is shown to have been conceptually underwritten by two methods of philosophizing, namely, analysis and synthesis. The connection between these things--mathematics, matter, and the methods of analysis and synthesis--has thus far gone unexplored by scholars. This book works out the context in which the theory of modern matter arose, and shows how the method of analysis aligns with Descartes's famous doctrine of clear and distinct ideas. Kurt Smith develops the method of synthesis, focusing primarily on Leibniz, and argues that both analysis and synthesis establish isomorphic conceptual systems--which turn out to be isomorphic to what mathematicians today call a group. He reconciles realist and idealist readings of Descartes, and reveals a richer picture of Descartes's position on the reality of matter. Matter Matters establishes the claim that mathematics is intelligible if, and only if, matter exists.