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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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I.1 What Is Mathematics About?

It is notoriously hard to give a satisfactory answer to the question, “What is mathematics?” The approach of this book is not to try. Rather than giving a definition of mathematics, the intention is to give a good idea of what mathematics is by describing many of its most important concepts, theorems, and applications. Nevertheless, to make sense of all this information it is useful to be able to classify it somehow.

The most obvious way of classifying mathematics is by its subject matter, and that will be the approach of this brief introductory section and the longer section entitled SOME FUNDAMENTAL MATHEMATICAL DEFINITIONS [I.3]. However, it is not the only way, and not even obviously the best way. Another ...

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