For Sir Arthur Cayley, Baronet, see Cayley baronets.
Arthur Cayley
FRS
Born
(1821-08-16)16 August 1821
Richmond, Surrey, England
Died
26 January 1895(1895-01-26) (aged 73)
Cambridge, England
Education
King's College School
Alma mater
Trinity College, Cambridge (BA, 1842)
Known for
Algebraic geometry
Group theory
Cayley–Hamilton theorem
Cayley–Dickson construction
Awards
Smith's Prize (1842)
De Morgan Medal (1884)
Royal Medal (1859)
Copley Medal (1882)
Scientific career
Fields
Mathematics
Institutions
Trinity College, Cambridge
Academic advisors
George Peacock
William Hopkins
Notable students
H. F. Baker
Andrew Forsyth
Charlotte Scott
Arthur CayleyFRS (/ˈkeɪli/; 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.
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 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 a group in the modern way—as a set with a binary operation satisfying certain laws.[2] Formerly, when mathematicians spoke of "groups", they had meant permutation groups. Cayley tables and Cayley graphs as well as Cayley's theorem are named in honour of Cayley.
^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."
^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.
ArthurCayley FRS (/ˈkeɪli/; 16 August 1821 – 26 January 1895) was a British mathematician who worked mostly on algebra. He helped found the modern British...
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S2CID 199546746; reprinted as article 52 in Cayley, Arthur (1889), The collected mathematical papers of ArthurCayley, vol. I (1841–1853), Cambridge University...
first was discovered by ArthurCayley in 1843 presented to the Cambridge Philosophical Society. It is in two parts and Cayley's first hyperdeterminant...
foundation was used to establish the professorship. On 10 June 1863 ArthurCayley was elected with the statutory duty "to explain and teach the principles...
ArthurCayley Headlam CH (2 August 1862 – 17 January 1947) was an English theologian who served as Bishop of Gloucester from 1923 to 1945. Headlam was...
Airy, Jacob Bronowski, Christopher Budd, Kevin Buzzard, ArthurCayley, Donald Coxeter, Arthur Eddington, Ben Green, John Herschel, James Inman, J. E....
constructed using similar triangles and parallelograms, and the Cayley diagram (named after ArthurCayley). Overconstrained mechanisms can be obtained by connecting...
1st century AD. The modern theory began in 19th century with work by ArthurCayley, followed by more extensive developments in the 20th century by Karl...
obtain substantial information about their homology. Before Morse, ArthurCayley and James Clerk Maxwell had developed some of the ideas of Morse theory...
1933 by Ruth Moufang, and is named after ArthurCayley for his 1845 paper describing the octonions. In the Cayley plane, lines and points may be defined...
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