Produced by Charles Wells Revised 2015-06-26 Introduction to this website website TOC website index blog

*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 Dirac

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.
- Other languages also have special mathematical forms.
- 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 largely 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.

The languages of math are covered in three chapters, each with several parts. Some things are not covered; see Notes.

- 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 history of mathematical symbols, by Douglas Weaver
- 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

Math communication also uses pictures, graphs and diagrams, which abstractmath.org doesn’t discuss.

Also not covered is the history and etymology of mathematical notation.

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