The History of Equality Symbols in Math

Close-up of equal sign equation on chalkboard.
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Imagine trying to write out a math equation in words. For lower level computation problems this would be difficult enough, but for longer algebra and calculus problems, writing out an equation in words could take multiple pages. Using mathematical symbols consumes less time and space. Furthermore, math symbols are international, allowing individuals to share information through symbolism that they could not share in words.

Equal Sign

Before the equal sign came into popular use, equality was expressed in words. According to Lankham, Nachtergaele, and Schilling at University of California-Davis, the first use of the equal sign (=) came in 1557. Robert Recorde, circa 1510 to 1558, was the first to use the symbol in his work, “The Whetstone of Witte.” Recorde, a Welsh physician and mathematician, used two parallel lines to represent equality because he believed they were the most equal things in existence.

Inequalities

The signs for greater than (>) and less than (<) were introduced in 1631 in “Artis Analyticae Praxis ad Aequationes Algebraicas Resolvendas.” The book was the work of British mathematician, Thomas Harriot, and was published 10 years after his death in 1621. The symbols actually were invented by the book’s editor. Harriot initially used triangular symbols which the editor altered to resemble the modern less/greater than symbols. Interestingly, Harriot also used parallel lines to denote equality. However, Harriot’s equal sign was vertical (II) rather than horizontal (=).

Less/Greater Than or Equal To

The symbols for less/greater than or equal to (< and >) with one line of an equal sign below them, were first used in 1734 by French mathematician, Pierre Bouguer. John Wallis, a British logician and mathematician, used similar symbols in 1670. Wallis used the greater than/less than symbols with a single horizontal line above them.

Equal by Definition

There are several symbols used in algebra to denote “equal by definition.” The modern symbols are (:=), (?), and (≡). Equal by definition first appeared in “Logica Matematica” by Cesare Burali-Forti, an Italian mathematician who lived from 1861–1931. Burali-Forti actually used the symbol (=Def).

Not Equal To

The modern sign for "not equal to" is an equal sign with a slash through it. This symbol is attributed to Leonhard Euler, a Swiss mathematician who lived from 1707 to 1783.

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