Mathematical notation

Mathematical notation is a symbol or sign used to write a mathematical idea, number, operation, or relationship. For example, + represents addition, and = represents equality. Notation makes it possible to compress lengthy discussion into brief, calculable text.

Most mathematical notation is a matter of convention rather than natural law. Its meaning depends on the branch of mathematics and the author. The same symbol can have two meanings in different places, so most scientific textbooks include a notation list at the beginning to define how symbols are used.

Common types

Mathematical notation can be divided into several categories. Operator symbols such as +, −, × and ÷ indicate operations performed on numbers. Relation symbols such as =, <, > compare two quantities. Structural symbols such as parentheses () and commas organize the order of reading. There are also symbols representing fixed numbers, such as π and e.

Brief history

Early mathematics in Babylon, Egypt, and Greece was generally written out in words rather than short symbols. The use of modern notation grew gradually over several centuries in Europe beginning in the late medieval period, as printed mathematics textbooks spread the practice. Some symbols derive from abbreviations of Latin words.

Writing and technology

With computers and the internet, mathematical symbols have been added to character encoding systems such as Unicode, making it possible to write them in ordinary text. Text formatting systems such as LaTeX have special commands that produce mathematical symbols; for example, a short command produces the square root symbol. Learning websites and encyclopedias often include a notation list so readers can look up the meaning of any symbol they encounter.