The equals sign sat unused for sixty years after invention
Mathematical equality states two quantities share the same value, written A = B. Robert Recorde invented the twin parallel lines in 1557, calling them gemowe lines because nothing could be more equal. The symbol then vanished from print until 1618 and only spread widely with Newton and Leibniz.
Equality relates two quantities or expressions of the same value, written A = B and read A equals B. Unequal objects are distinct. The concept is often treated as primitive—each thing bears the relation to itself alone—yet fully defining it has proved circular and difficult since ancient times.
Before the 16th century, equality appeared as words like aequales or gleich, or abbreviations aeq. Diophantus used ἴσ in the 3rd century AD. Welsh mathematician Robert Recorde recorded = in The Whetstone of Witte (1557), explaining twin lines as gemowe from Latin gemellus. He published it a year before he died, in a much longer form than today's, and it did not reappear in print until 1618, in an anonymous appendix to Edward Wright's English translation of John Napier's Descriptio and gained English recognition around 1631.
Giuseppe Peano explicitly stated reflexivity, symmetry, and transitivity in 1889, though Euclid's common notions anticipated them. Gottfried Leibniz around 1686 formulated substitution: if a = b, a may replace b without changing meaning. In set theory, Zermelo–Fraenkel's axiom of extensionality defines equal sets as those sharing all members.
Equations connect expressions with =; identities hold for all variable values, conditional equations only for some. Bernhard Riemann introduced the triple-bar ≡ notation in 1857 lectures. Education uses balance scales: unknown weights stay balanced as objects are added or removed from both pans until the unknown alone remains. Gottlob Frege's 1879 Begriffsschrift helped axiomatize equality through logic rather than geometry alone. Aristotle in his Categories around 350 BC treated equality as the distinctive mark that distinguishes quantities from qualities. The word itself descends from Latin aequalis, built on aequus, meaning level or just, and reached Middle English through Old French around the fourteenth century.
Source: Equality (mathematics)
