James Robert Brown is Professor of Philosophy at the University of Toronto, Canada.

"Extraordinary! A brilliant, important book. Summing up: Highly recommended." —M. Schiff, CHOICE"…The book has been written in a very clear, lively way, it is a pleasure to read. It is very accessible, even entertaining, and the author is very good in explaining issues without technicalities. … Summarizing: a very elegant, accessible and up-to-date book on the philosophy of mathematics, not only very appropriate for beginners, but also a must for experts."—H.C.M. de Swart, Zentralblatt MATH 1171Praise for the First Edition:"This book is a breath of fresh air for undergraduate philosophy of mathematics. Very accessible and even entertaining, Brown explains most of the issues without technicalities. "—Janet Folina, Macalester College"A wonderful introduction to the philosophy of mathematics. It's lively, accessible, and, above all, a terrific read. It would make an ideal text for an undergraduate course on the philosophy of mathematics; indeed, I recommend it to anyone interested in the philosophy of mathematics — even specialists in the area can learn from this book."—Mark Colyvan, University of Sydney

• Preface and Acknowledgements 1. Introduction: The Mathematical Image 2. Platonism 3. Picture-Proofs and Platonism 4. What is Applied Mathematics? 5. Hilbert and Gödel 6. Knots and Notation 7. What is a Definition? 8. Constructive Approaches 9. Proofs, Pictures and Procedures in Wittgenstein 10. Computation, Proof and Conjecture 11. How to Refute the Continuum Hypothesis 12. Calling the Bluff. Notes. Bibliography. Index