Arthur Cayley | |
|---|---|
 | |
| Born | (1821-08-16)16 August 1821 |
| 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 | |
| Awards |
|
| Scientific career | |
| Fields | Mathematics |
| Institutions | Trinity College, Cambridge |
| Academic advisors | |
| Notable students | |
Arthur CayleyFRS (/ˈkeɪli/; 16 August 1821 – 26 January 1895) was an English mathematician who worked mostly on algebra. He helped found the modern British school ofpure mathematics, and was a professor atTrinity College, Cambridge for 35 years.
He postulated what is now known as theCayley–Hamilton theorem—that everysquare matrix is a root of its owncharacteristic polynomial, and verified it for matrices of order 2 and 3.[1] He was the first to define the concept of an abstractgroup, a set with abinary operation satisfying certain laws,[2] as opposed toÉvariste Galois' concept ofpermutation groups. In group theory,Cayley tables,Cayley graphs, andCayley's theorem are named in his honour, as well asCayley's formula in combinatorics.
Arthur Cayley was born inRichmond, London, England, on 16 August 1821. His father, Henry Cayley, was a distant cousin ofGeorge Cayley, theaeronautics engineer innovator, and descended from an ancientYorkshire family. He settled inSaint Petersburg, Russia, as amerchant. 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 linguistCharles Bagot Cayley. Arthur spent his first eight years in Saint Petersburg. In 1829 his parents were settled permanently atBlackheath, London, where Arthur attended a private school.
At age 14, he was sent toKing's College School. The young Cayley enjoyed complex maths problems, and the school's master observed indications of his mathematical genius. He advised the father to educate his son not for his own business, as he had intended, but at theUniversity of Cambridge.
At the age of 17 Cayley began residence atTrinity College, Cambridge, where he excelled in Greek, French, German, and Italian, as well asmathematics. The cause of theAnalytical Society had now triumphed, and theCambridge Mathematical Journal had been instituted by Gregory andRobert Leslie Ellis. To this journal, at the age of twenty, Cayley contributed three papers, on subjects that had been suggested by reading theMécanique analytique ofJoseph Louis Lagrange and some of the works ofLaplace.
Cayley's tutor at Cambridge wasGeorge Peacock and his private coach wasWilliam Hopkins. He finished his undergraduate course by winning the place ofSenior Wrangler, and the firstSmith's prize.[3] His next step was to take the M.A. degree, and win a Fellowship by competitive examination. He continued to reside at Cambridge University for four years; during which time he took some pupils, but his main work was the preparation of 28 memoirs to the Mathematical Journal.
Because of the limited tenure of his fellowship it was necessary to choose a profession; likeDe Morgan, Cayley chose law, and was admitted toLincoln's Inn, London on 20 April 1846 at the age of 24.[4] He made a specialty ofconveyancing. It was while he was a pupil at thebar examination that he went toDublin to hearWilliam Rowan Hamilton's lectures onquaternions.[5]
His friendJ. J. Sylvester, his senior by five years at Cambridge, was then anactuary, resident in London; they used to walk together round the courts ofLincoln's Inn, discussing thetheory of invariants and covariants. During these fourteen years, Cayley produced between two and three hundred papers.[5]
Around 1860, Cambridge University'sLucasian Professor of Mathematics (Newton's chair) was supplemented by the newSadleirian professorship, using funds bequeathed by Lady Sadleir, with the 42-year-old Cayley as its first holder. His duties were"to explain and teach the principles of pure mathematics and to apply himself to the advancement of that science." He gave up a lucrative legal practice for a modest salary, but never regretted the exchange, since it allowed him to devote his energies to the pursuit that he liked best. He at once married and settled down in Cambridge, and (unlike Hamilton) enjoyed a home life of great happiness. Sylvester, his friend from his bachelor days, once expressed his envy of Cayley's peaceful family life, whereas the unmarried Sylvester had to fight the world all his days.
At first the Sadleirian professor was paid to lecture over one of the terms of the academic year, but the university financial reform of 1886 freed funds to extend his lectures to two terms. For many years his courses were attended only by a few students who had finished their examination preparation, but after the reform the attendance numbered about fifteen. He generally lectured on his current research topic.
As for his duty to the advancement of mathematical science, he published a long and fruitful series of memoirs ranging over all of pure mathematics. He also became the standing referee on the merits of mathematical papers to many societies both at home and abroad.
In 1872, he was made an honorary fellow of Trinity College, and three years later an ordinary fellow, a paid position. About this time his friends subscribed for a presentation portrait.Maxwell wrote an address praising Cayley's principal works, including his Chapters on the Analytical Geometry of dimensions; On the theory ofDeterminants; Memoir on the theory of Matrices; Memoirs on skew surfaces, otherwise Scrolls; and On the delineation of a Cubic Scroll.[6]
In addition to his work onalgebra, Cayley made fundamental contributions toalgebraic geometry. Cayley andSalmon discovered the 27 lines on acubic surface. Cayley constructed theChow variety of all curves in projective 3-space.[7] He founded the algebro-geometric theory ofruled surfaces. His contributions tocombinatorics include counting thenn−2trees onn labeled vertices by the pioneering use ofgenerating functions.
In 1876, he published aTreatise onElliptic Functions. He took great interest in the movement for the university education of women. At Cambridge the first women's colleges were Girton and Newnham. In the early days ofGirton College he gave direct help in teaching, and for some years he was chairman of the council ofNewnham College, in the progress of which he took the keenest interest to the last.
In 1881, he received from theJohns Hopkins University,Baltimore, where Sylvester was then professor of mathematics, an invitation to deliver a course of lectures. He accepted the invitation, and lectured at Baltimore during the first five months of 1882 on the subject of theAbelian and Theta Functions.
He was awarded honorary membership of theManchester Literary and Philosophical Society in 1859.[8] and in 1893, Cayley became a foreign member of theRoyal Netherlands Academy of Arts and Sciences.[9]
In 1883, Cayley was President of theBritish Association for the Advancement of Science. The meeting was held at Southport, in the north of England. As the President's address is one of the great popular events of the meeting, and brings out an audience of general culture, it is usually made as little technical as possible.Cayley (1996) took for his subject the Progress of Pure Mathematics.
In 1889, theCambridge University Press began the publication of his collected papers, which he appreciated very much. He edited seven of the quarto volumes himself, though suffering from a painful internal malady. He died 26 January 1895 at age 73. His funeral at Trinity Chapel was attended by the leading scientists of Britain, with official representatives from as far as Russia and America.
The remainder of his papers were edited byAndrew Forsyth, his successor as Sadleirian professor, in total thirteen quarto volumes and 967 papers. His work continues in frequent use, cited in more than 200 mathematical papers in the 21st century alone.
Cayley retained to the last his fondness for novel-reading and for travelling. He also took special pleasure in paintings and architecture, and he practicedwater-colour painting, which he found useful sometimes in making mathematical diagrams.
Cayley is buried in theMill Road cemetery, Cambridge.
An 1874 portrait of Cayley byLowes Cato Dickinson and an 1884 portrait byWilliam Longmaid are in the collection ofTrinity College, Cambridge.[10]
A number of mathematical terms are named after him:
| International | |
|---|---|
| National | |
| Academics | |
| People | |
| Other | |
This article incorporates text from the 1916Lectures on Ten British Mathematicians of the Nineteenth Century byAlexander Macfarlane, which is in thepublic domain.
