Mathematics as a language
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 are sources for detailed theoretical discussions about ideas concerning mathematics and its implications for society.
Here are some definitions of language:
These definitions describe language in terms of the following components:
Each of these components is also found in the language of mathematics.
Mathematical notation has assimilated symbols from many different alphabets and typefaces. It also includes symbols that are specific to mathematics, such as
Mathematical notation is central to the power of modern mathematics. Though the algebra of Al-Khwārizmī did not use such symbols, it solved equations using many more rules than are used today with symbolic notation, and had great difficulty working with multiple variables (which using symbolic notation can simply be called , etc.). Sometimes formulas cannot be understood without a written or spoken explanation, but often they are sufficient by themselves, and sometimes they are difficult to read aloud or information is lost in the translation to words, as when several parenthetical factors are involved or when a complex structure like a matrix is manipulated.
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