This book collects some of the most interesting recent writings that are tackling, from various points of view, the problem of giving an accounting of the nature, purpose, and justification of real mathematical practicemathematics as actually done by real live mathematicians. What is the nature of the objects being studied? What determines the directions and styles in which mathematics progresses (or, perhaps, degenerates)? What certifies its claim to certainty, or to a priori status, to independence of experience? Why is mathematics the same for all times and places, or is it really the same, or in what senses is it the same and in what senses different? Many of these writings were read at conferences in Europe and America under the heading of 'history' or 'cultural studies' as well as 'philosophy.' It is the editors hope to help foster healthy interdisciplinary mutual aid in this young and fertile area. 'I was pleasantly surprised to find that this book does not treat mathematics as dessicated formal logic but as a living organism, immediately recognizable to any working mathematician.' - Sir Michael Atiyah, University of Edinburgh 'A wonderful collection of essays on the philosophy of mathematics, some by mathematicians, others by philosophers, and all having significant things to say. Most readers will be informed, some will be infuriated, but all will be stimulated.' - John H. Conway, John von Neumann Distinguished Professor of Mathematics, Princeton University

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