Arthur Cayley

Arthur Cayley
Born(1821-08-16)16 August 1821
Richmond, Surrey, England
Died26 January 1895(1895-01-26) (aged 73)
Cambridge, England
EducationKing's College School
Alma materTrinity College, Cambridge (BA, 1842)
Known for
Awards
Scientific career
FieldsMathematics
InstitutionsTrinity College, Cambridge
Academic advisors
Notable students

Arthur Cayley FRS (/ˈkli/; 16 August 1821 – 26 January 1895) was a British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics, and was a professor at Trinity College, Cambridge for 35 years.

He postulated what is now known as the Cayley–Hamilton theorem—that every square matrix is a root of its own characteristic polynomial, and verified it for matrices of order 2 and 3.[1] He was the first to define the concept of an abstract group, a set with a binary operation satisfying certain laws,[2] as opposed to Évariste Galois' concept of permutation groups. In group theory, Cayley tables, Cayley graphs, and Cayley's theorem are named in his honour, as well as Cayley's formula in combinatorics.

  1. ^ See Cayley (1858) "A Memoir on the Theory of Matrices", Philosophical Transactions of the Royal Society of London, 148 : 24 : "I have verified the theorem, in the next simplest case, of a matrix of the order 3, ... but I have not thought it necessary to undertake the labour of a formal proof of the theorem in the general case of a matrix of any degree."
  2. ^ Cayley (1854) "On the theory of groups, as depending on the symbolic equation θn = 1," Philosophical Magazine, 4th series, 7 (42) : 40–47. However, see also the criticism of this definition in: MacTutor: The abstract group concept.