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

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I.2 The Language and Grammar of Mathematics

1 Introduction

It is a remarkable phenomenon that children can learn to speak without ever being consciously aware of the sophisticated grammar they are using. Indeed, adults too can live a perfectly satisfactory life without ever thinking about ideas such as parts of speech, subjects, predicates, or subordinate clauses. Both children and adults can easily recognize ungrammatical sentences, at least if the mistake is not too subtle, and to do this it is not necessary to be able to explain the rules that have been violated. Nevertheless, there is no doubt that one’s understanding of language is hugely enhanced by a knowledge of basic grammar, and this understanding is essential for anybody who wants ...

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