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Concise, accessible sketches of the views of Plato, Aristotle, Leibniz, and Kant highlight this study of the general structure and foundation of pure and applied mathematics. Author Stephan Körner dedicates two chapters apiece -- one expository and one critical -- to each of the three main modern schools of thought on mathematical philosophy: the formalists, the logicists, and the intuitionists. After critically examining the propositions and theories of each philosophy, Körner presents a new position concerning the relation between mathematical theories, empirical data, and philosophical presuppositions.  The Review of Metaphysics praised this volume as "a lucid and stimulating essay which combines accuracy and sophistication with a minimum of technical language." Compact but comprehensive, this nontechnical introduction will appeal to professionals, students, and other readers interested in the intersection of philosophical problems with pure and applied mathematics.