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Mathematical notation

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 information on rendering mathematical formulae, see Help:Displaying a formula and Wikipedia:Manual of Style/Mathematics.

For example, Albert Einstein's equation 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.

International standard mathematical notation[edit]

The international standard ISO 80000-2 (previously, ISO 31-11) specifies symbols for use in mathematical equations. The standard requires use of italic fonts for variables (e.g., E=mc2) and roman (upright) fonts for mathematical constants (e.g., e or π).

Non-Latin-based mathematical notation[edit]

Modern Arabic mathematical notation is based mostly on the Arabic alphabet and is used widely in the Arab world, especially in pre-tertiary education.


(Western notation uses Arabic numerals, but the Arabic notation also replaces Latin letters and related symbols with Arabic script.)


In addition to Arabic notation, mathematics also makes use of Greek letters to denote a wide variety of mathematical objects and variables. On some occasions, certain Hebrew letters are also used (such as in the context of infinite cardinals).


Some mathematical notations are mostly diagrammatic, and so are almost entirely script independent. Examples are Penrose graphical notation and Coxeter–Dynkin diagrams.


Braille-based mathematical notations used by blind people include Nemeth Braille and GS8 Braille.

Abuse of notation

Begriffsschrift

Glossary of mathematical symbols

Bourbaki dangerous bend symbol

History of mathematical notation

ISO 31-11

ISO 80000-2

Knuth's up-arrow notation

Mathematical Alphanumeric Symbols

Mathematical formula

Notation in probability and statistics

Language of mathematics

Scientific notation

Semasiography

Table of mathematical symbols

Vector notation

Modern Arabic mathematical notation

A History of Mathematical Notations (1929), 2 volumes. ISBN 0-486-67766-4

Florian Cajori

Mazur, Joseph (2014), . Princeton, New Jersey: Princeton University Press. ISBN 978-0-691-15463-3

Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

Earliest Uses of Various Mathematical Symbols

how to type math notation in any text editor.

Mathematical ASCII Notation

at Cut-the-Knot

Mathematics as a Language

: Mathematical Notation: Past and Future. October 2000. Transcript of a keynote address presented at MathML and Math on the Web: MathML International Conference.

Stephen Wolfram