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{{Short description|System of symbolic representation}}{{More citations needed|date=June 2022}}{{For|information on rendering mathematical formulae|Help:Displaying a formula|Wikipedia:Manual of Style/Mathematics}}{{Use dmy dates|date=November 2023|cs1-dates=y}}{{Use list-defined references|date=November 2023}}Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way.For example, Albert Einstein's equation E=mc^2 is the quantitative representation in mathematical notation of the mass–energy equivalence.Mathematical notation was first introduced by François Viète at the end of the 16th century and largely expanded during the 17th and 18th centuries by René Descartes, Isaac Newton, Gottfried Wilhelm Leibniz, and overall Leonhard Euler.

Symbols

The use of many symbols is the basis of mathematical notation. They play a similar role as words in natural languages. They may play different roles in mathematical notation similarly as verbs, adjective and nouns play different roles in a sentence.

Letters as symbols

Letters are typically used for naming—in mathematical jargon, one says representing—mathematical objects. The Latin and Greek alphabets are used extensively, but a few letters of other alphabets are also used sporadically, such as the Hebrew {{tmath|aleph}}, Cyrillic {{math|Ш}}, and Hiragana {{math|よ}}. Uppercase and lowercase letters are considered as different symbols. For Latin alphabet, different typefaces provide also different symbols. For example, r, R, R, mathcal R, mathfrak r, and mathfrak R could theoretically appear in the same mathematical text with six different meanings. Normally, roman upright typeface is not used for symbols, except for symbols representing a standard function, such as the symbol "sin" of the sine function.ISO 80000-2:2019In order to have more symbols, and for allowing related mathematical objects to be represented by related symbols, diacritics, subscripts and superscripts are often used. For example, hat {f'_1} may denote the Fourier transform of the derivative of a function called f_1.

Other symbols

Symbols are not only used for naming mathematical objects. They can be used for operations (+, -, /, oplus, ldots), for relations (=,