阿瑟·凯莱1821—1895

生平

凯莱自小即喜欢解决复杂的数学问题。后来进入剑桥大学三一学院，在希腊语、法语、德语、意大利语以及数学方面成绩优异。

凯莱就读大学时已发表了3篇论文。为了谋生，他在1849年起正式执业为律师。到了1863年，他才正式进入学术圈，成为剑桥大学的教授。在他当律师的14年间，他发表了约二百五十篇论文。他一生发表了过九百篇论文，包括关于非欧几何、线性代数、群论和高维几何。

荣誉

• 数学上以凯莱命名的有：
• 八元数，又称Cayley数
• 凯莱定理
• 凯莱表
• 凯莱图
• 凯莱公式
• 凯莱-哈密顿定理
• Grassmann-凯莱代数

Arthur Cayley (; 16 August 1821 – 26 January 1895) was an English 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. He was the first to define the concept of an abstract group, a set with a binary operation satisfying certain laws, 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.

Early life

Arthur Cayley was born in Richmond, London, England, on 16 August 1821. His father, Henry Cayley, was a distant cousin of 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.

Education

At the age of 17 Cayley began residence at Trinity College, Cambridge, where he excelled in Greek, French, German, and Italian, as well as mathematics. The cause of the Analytical Society had now triumphed, and the Cambridge Mathematical Journal had been instituted by Gregory and Robert Leslie Ellis. To this journal, at the age of twenty, Cayley contributed three papers, on subjects that had been suggested by reading the Mécanique analytique of Joseph Louis Lagrange and some of the works of Laplace.

Law career

Because of the limited tenure of his fellowship it was necessary to choose a profession; like De Morgan, Cayley chose law, and was admitted to Lincoln's Inn, London on 20 April 1846 at the age of 24. He made a specialty of conveyancing. It was while he was a pupil at the bar examination that he went to Dublin to hear William Rowan Hamilton's lectures on quaternions.

His friend J. J. Sylvester, his senior by five years at Cambridge, was then an actuary, resident in London; they used to walk together round the courts of Lincoln's Inn, discussing the theory of invariants and covariants.

Professorship

Around 1860, Cambridge University's Lucasian Professor of Mathematics (Newton's chair) was supplemented by the new Sadleirian 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.

British Association presidency

In 1883, Cayley was President of the British 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.

The Collected Papers

In 1889, the Cambridge 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 by Andrew Forsyth, his successor as Sadleirian professor, in total thirteen quarto volumes and 967 papers.

Legacy

Cayley is buried in the Mill Road cemetery, Cambridge.

An 1874 portrait of Cayley by Lowes Cato Dickinson and an 1884 portrait by William Longmaid are in the collection of Trinity College, Cambridge.

A number of mathematical terms are named after him:

The crater Cayley on the Moon (and consequently the Cayley Formation, a geological unit named after the crater) is named after him.