Arthur Cayley
| Arthur Cayley | |
|---|---|
Portrait in London by
Barraud & Jerrard |
|
| Born |
16 August 1821 Richmond, Surrey, UK |
| Died | 26 January 1895 (aged 73) Cambridge, England |
| Residence | England |
| Nationality | British |
| Fields | Mathematics |
| Institutions | Trinity College, Cambridge |
| Education | King's College School |
| Alma mater |
Trinity College, Cambridge (BA, 1842) |
| Academic advisors |
George Peacock William Hopkins |
| Notable students |
H. F. Baker Andrew Forsyth Charlotte Scott |
| Known for |
Algebraic geometry Group theory Cayley–Hamilton theorem Cayley–Dickson construction |
| Notable awards |
Smith's Prize (1842) De Morgan Medal (1884) Royal Medal (1859) Copley Medal (1882) |
Arthur Cayley F.R.S. (/ˈkeɪli/; 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. 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. Formerly, when mathematicians spoke of "groups", they had meant permutation groups. Cayley's theorem is named in honour of Cayley.
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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