Language of Mathematics - The Grammar of Mathematics

The Grammar of Mathematics

The grammar used for mathematical discourse is essentially the grammar of the natural language used as substrate, but with several mathematics-specific peculiarities.

Most notably, the mathematical notation used for formulas has its own grammar, not dependent on a specific natural language, but shared internationally by mathematicians regardless of their mother tongues. This includes the conventions that the formulas are written predominantly left to right, also when the writing system of the substrate language is right-to-left, and that the Latin alphabet is commonly used for simple variables and parameters. A formula such as

is understood by Chinese and Israeli mathematicians alike.

Such mathematical formulas can be a part of speech in a natural-language phrase, or even assume the role of a full-fledged sentence. For example, the formula above, an equation, can be considered a sentence or sentential phrase in which the greater than or equal to symbol has the role of a verb. In careful speech, this can be made clear by pronouncing "≥" as "is greater than or equal to", but in an informal context mathematicians may shorten this to "greater or equal" and yet handle this grammatically like a verb. A good example is the book title Why does E = mc2?; here, the equals sign has the role of an infinitive.

Mathematical formulas can be vocalized (spoken aloud). The vocalization system for formulas has to be learned, and is dependent on the underlying natural language. For example, when using English, the expression "ƒ (x)" is conventionally pronounced "eff of eks", where the insertion of the preposition "of" is not suggested by the notation per se. The expression "", on the other hand, is vocalized like "dee-why-dee-eks", with complete omission of the fraction bar, in other contexts often pronounced "over". The book title Why does E = mc2? is said aloud as Why does ee equal em see-squared?.

Characteristic for mathematical discourse – both formal and informal – is the use of the inclusive first person plural "we" to mean: "the audience (or reader) together with the speaker (or author)".