This distinctive anthology includes many of the most important recent contributions to the philosophy of mathematics. The featured papers are organized thematically, rather than chronologically, to provide the best overview of philosophical issues connected with mathematics and the development of mathematical knowledge. Coverage ranges from general topics in mathematical explanation and the concept of number, to specialized investigations of the ontology of mathematical entities and the nature of mathematical truth, models and methods of mathematical proof, intuitionistic mathematics, and philosophical foundations of set theory. This volume explores the central problems and exposes intriguing new directions in the philosophy of mathematics, making it an essential teaching resource, reference work, and research guide. The book complements Philosophy of Logic: An Anthology and A Companion to Philosophical Logic, also edited by Dale Jacquette (Blackwell 2001).