Reading Mathematical Exposition

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Abstract
Reading mathematical exposition requires certain abilities due to the specific differences between natural language and the specialized language of mathematics. Also, a reader needs to contend with these differences in language and the nature of the subject itself. Mathematical language consists of at least two languages; namely, the object language and the metalanguage. Borrowed natural language words are used in a special sense in mathematics. In contrast to natural language, mathematical language is more precise, almost totally non‐redundant and relatively unambiguous. In mathematical language, quantification plays a more sophisticated and complex role. A reader of mathematical exposition needs to understand the use of variables, to recognize same form, to accommodate to the use of new terminology and notation, and to be able to deal with the, hierarchical development of definitions and the sequential organization of mathematics from definitions through to the proofs of theorems. He must work while reading and be prepared for the possibility that he may need the help of others. By noting the differences between mathematical and natural languages and the characteristics of a reader of mathematics, teachers will hopefully aid their students in improving their ability to read mathematics.

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