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 practice - mathematics 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 editor's hope to help foster healthy interdisciplinary mutual aid in this young and fertile area.