The language of mathematics is the system used by mathematicians to communicate mathematical ideas among themselves. This language consists of a substrate of some natural language (for example English) using technical terms and grammatical conventions that are peculiar to mathematical discourse (see Mathematical jargon), supplemented by a highly specialized symbolic notation for mathematical formulas.
Like natural languages in general, discourse using the language of mathematics can employ a scala of registers. Research articles in academic journals use a more formal tone than oral exchanges over a scribbled-upon napkin in the university cafeteria.
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“Theoretically, I grant you, there is no possibility of error in necessary reasoning. But to speak thus “theoretically,” is to use language in a Pickwickian sense. In practice, and in fact, mathematics is not exempt from that liability to error that affects everything that man does.”
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