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help with abstract math

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.
• 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.