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Arthur Cayley
Arthur Cayley F.R.S. (; 16 August 1821 – 26 January 1895) was a British mathematician. He helped found the modern British school of pure mathematics.
As a child, Cayley enjoyed solving complex maths problems for amusement. He entered Trinity College, Cambridge, where he excelled in Greek, French, German, and Italian, as well as mathematics. He worked as a lawyer for 14 years.
He postulated 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.〔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."〕 He was the first to define the concept of a group in the modern way—as a set with a binary operation satisfying certain laws.〔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 ).〕 Formerly, when mathematicians spoke of "groups", they had meant permutation groups. Cayley's theorem is named in honour of Cayley.
==Early years==
Arthur Cayley was born in Richmond, London, England, on 16 August 1821. His father, Henry Cayley, was a distant cousin of Sir George Cayley the aeronautics engineer innovator, and descended from an ancient Yorkshire family. He settled in Saint Petersburg, Russia, as a merchant. His mother was Maria Antonia Doughty, daughter of William Doughty. According to some writers she was Russian, but her father's name indicates an English origin. His brother was the linguist Charles Bagot Cayley. Arthur spent his first eight years in Saint Petersburg. In 1829 his parents were settled permanently at Blackheath, near London. Arthur was sent to a private school. At age 14 he was sent to King's College School. The school's master observed indications of mathematical genius and advised the father to educate his son not for his own business, as he had intended, but to enter the University of Cambridge.
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