2 + 2 = 4
A well-known equality featuring the equal sign

The equals sign (British English) or equal sign (American English), also known as the equality sign, is the mathematical symbol =, which is used to indicate equality.[1] In an equation, it is placed between two expressions that have the same value, or for which one studies the conditions under which they have the same value.

In Unicode and ASCII it has the code point U+003D.[2] It was invented in 1557 by the Welsh mathematician Robert Recorde.

History

The first use of an equals sign, equivalent to 14x+15=71 in modern notation. From The Whetstone of Witte (1557) by Robert Recorde.
Recorde's introduction of "="

Prior to 16th century there was no common symbol for equality, and equality was usually expressed with a word, such as aequales, aequantur, esgale, faciunt, ghelijck or gleich, and sometimes by the abbreviated form aeq, or simply ⟨æ⟩ and ⟨œ⟩.[3] Diophantus's use of ⟨ἴσ⟩, short for ἴσος (ísos 'equals'), in Arithmetica (c. AD 250) is considered one of the first uses of an equals sign.[4]

The = symbol, now universally accepted in mathematics for equality, was first recorded by the Welsh mathematician Robert Recorde in The Whetstone of Witte (1557), just one year before his death.[5] The original form of the symbol was much wider than the present form. In his book Recorde explains his design of the "Gemowe lines" (meaning twin lines, from the Latin gemellus)[6]

Recorde, Robert (1557). The Whetstone of Witte. London: John Kyngstone. the third page of the chapter "The rule of equation, commonly called Algebers Rule."

The symbol = was not immediately popular. After its introduction by Recorde, it was not used again in print until 1618 (61 years later), in an anonymous Appendix in Edward Wright's English translation of Descriptio, by John Napier. It was not until 1631 that it received more than general recognition in England, being adopted as the symbol for equality in three influential works, Thomas Harriot's Artis analyticae praxis, William Oughtred's Clavis mathematicae and Richard Norwood's Trigonometria.[7] The sign was later used by John Wallis, Isaac Barrow and Isaac Newton, which helped it to spread to continental Europe.

Competing symbols

There were several other competing symbols for equality, especially outside of England around the 16th and 17th centuries, and Recorde's version made no significant influence in the European continent until 1650 or 1660. In 1559 the French monk Johannes Buteo published his Logistica using the symbol for equality. In 1571 Wilhelm Xylander published an edition of Diophantus' Arithmetica in which two parallel vertical lines || were used for equality.[a] This version was adopted by several prominent writers, including Giovanni Glorioso, Cardinal Michelangelo Ricci, and many French and Dutch mathematicians in the hundred years after, including René Descartes in 1621.

A major competitor to Recorde's sign was Descartes' own symbol (like a reversed U+221D ∝ PROPORTIONAL TO, from æquare[citation needed]), introduced in his La Géométrie (1637). In fact, Descartes himself used the sign = for equality in a letter in 1640. Descartes does not give any reason for introducing his new symbol; however, Florian Cajori suggests it is because = was also being used for a difference operation at the time. Due to the prominence of La Géométrie, by 1675, Descartes' symbol gained favour over Recorde's in Europe, and most 17th-century writers on the continent either used Descartes' notation for equality or none at all. Around the turn of the 18th century, Recorde's notation gained favour rapidly. The dominating trend in mathematics of the time was differential and integral calculus. The fact that both Newton and Gottfried Wilhelm Leibniz used Recorde's symbol led to its general adoption.