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Produced by Charles Wells     Revised 2017-01-20
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THE LANGUAGES OF MATHEMATICS

In science one tries to tell people, in such a way as to be understood by every­one, something that no one ever knew before. But in poetry, it's the exact opposite. --Paul Dirasc

Mathematics in the English-speaking world is communicated using two languages:

Mathematical English is a special form of English.

• It uses ordinary words with special meanings.
• Some of its structural words (“if”, “or”) have different meanings from those of ordinary English.
• It is both written and spoken.
• The symbolic language of math is a distinct, special-purpose language.
• It has its own symbols and rules that are rather different from spoken languages.
• It is not a dialect of English.
• It is mostly a written language.
• Simple expressions can be pronounced, but complicated expressions may only be pointed to or referred to.
• It is used by all mathematicians, not just those who write math in English.
• Math in writing and in lectures involve both mathematical English and the symbolic language, embedded in each other and referring back and forth to each other.

Contents

The languages of math are covered in three chapters, each with several parts.

• Mathematical English
• The symbolic language of math
• More about math languages

Some things are not covered; see Notes.

Links

• Communicating mathematics: useful ideas from computer science, by Charles Wells.
• Earliest Known Uses of Some of the Words of mathe­matics, by Jeff Miller
• Gyre&Gimble, a blog about math and language by Charles Wells
• The Handbook of Mathematical Discourse, by Charles Wells
• The Language of mathe­matics, by Mohan Ganesalingam. Not available on the internet.
• The language and grammar of mathe­matics, by Timothy Gowers
• On the communication of mathematical reasoning, by Atish Bagchi and Charles Wells.
• On-line etymological dictionary
• Varieties of mathematical prose, by Atish Bagchi and Charles Wells

Notes

Math communication also uses pictures, graphs and diagrams, which are discussed in the chapters Images and Metaphors and Images and Metaphors for Functions.

Abstractmath.org does not cover the history and etymology of mathematical notation.

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