Cayleys

Cayleys is primarily a surname of English origin. In modern usage, Cayleys can function as the plural or possessive form of Cayley when referring to more than one person bearing the surname or to things associated with a Cayley family. The usual form for a single individual is Cayley; Cayleys appears mainly in genealogical, archival, or biographical writing when a collective reference is intended.

The surname derives from English place-names and has variants such as Cayley and Cayl(e)y; populations bearing the name are dispersed in the United Kingdom and other English-speaking regions, often reflecting historical landholding or settlement patterns.

There is no standard mathematical or scientific concept called Cayleys. In reference works, terms named after the mathematician Arthur Cayley use the singular form Cayley (for example Cayley’s theorem, Cayley graphs, and the Cayley–Hamilton theorem). The plural Cayleys does not denote a distinct mathematical object.

Notable people with the surname Cayley include Arthur Cayley, a 19th-century British mathematician known for foundational contributions to algebra and geometry; other individuals with the surname Cayley have appeared in various fields, though none are as widely cited.

See also: Cayley, Cayley graphs, Cayley–Hamilton theorem, Cayley’s theorem.