Portrait of Cayley by Barraud & Jerrard. Now in London.
School period
Gallery of Arthur Cayley
Southside, Wimbledon Common, Wimbledon, London SW19 4TT, UK
From a small private school in London, Cayley moved, at fourteen, to King’s College School there.
College/University
Gallery of Arthur Cayley
Cambridge CB2 1TQ, UK
At seventeen Cayley entered Trinity College, Cambridge, as a pensioner, becoming a scholar in 1840. In 1842 he graduated as senior wrangler and took the first Smith’s prize.
At seventeen Cayley entered Trinity College, Cambridge, as a pensioner, becoming a scholar in 1840. In 1842 he graduated as senior wrangler and took the first Smith’s prize.
Arthur Cayley was a British mathematician. He helped found the modern school of pure mathematics in Great Britain.
Background
Ethnicity:
According to some accounts, Cayley's parents were Russian, but his grandfather's name indicates an English origin of Cayley's mother.
Cayley was born on August 16, 1821, at Richmond, England, the second son of Henry Cayley, a Russian merchant, and Maria Antonia Doughty. He was born during a short visit by his parents to England, and most of his first eight years were spent in Russia. His brother was the linguist Charles Bagot Cayley.
Education
From a small private school in London Cayley moved, at fourteen, to King’s College School there. At seventeen he entered Trinity College, Cambridge, as a pensioner, becoming a scholar in 1840. In 1842 Cayley graduated as senior wrangler and took the first Smith’s prize. In October 1842 he was elected a fellow of his college at the earliest age of any man of that century.
Cayley was tutor there for three years, spending most of his time in research. Rather than wait for his fellowship to expire (1852) unless he entered holy orders or took a vacant leaching post, he entered the law, studying at Lincoln’s Inn. He was called to the bar in 1849.
During the fourteen years, Cayley was at the bar, he wrote something approaching 300 mathematical papers, incorporating some of his best and most original work. It was during this period that he first met the mathematician J. J. Sylvester, who from 1846 read for the bar and, like Cayley, divided his time between law and mathematics. In 1852 Sylvester said of Cayley that he “habitually discourses pearls and rubies,” and after 1851 each often expressed gratitude to the other in print for a point made in conversation. That the two men profited greatly by their acquaintance is only too obvious when one considers the algebraic theory of invariants, of which they may not unreasonably be considered joint founders. They drifted apart professionally when Cayley left London to take up the Sadlerian professorship but drew together again when, in 1881-1882, Cayley accepted Sylvester’s invitation to lecture at Johns Hopkins University.
In 1863 Cayley was elected to the new Sadlerian chair of pure mathematics at Cambridge, which he held until his death. As a professor, his legal knowledge and administrative ability were in great demand in such matters as the drafting of college and university statutes. For most of his life, Cayley worked incessantly at mathematics, theoretical dynamics, and mathematical astronomy. He published only one full-length book, Treatise on Elliptic Functions (1876); but his output of papers and memoirs was prodigious, numbering nearly a thousand, the bulk of them since republished in thirteen large quarto volumes. His work was greatly appreciated from the time of its publication, and he did not have to wait for mathematical fame.
Cayley was above all a pure mathematician, taking little if any inspiration from the physical sciences when at his most original. His mathematical style was terse and even severe, in contrast with that of most of his contemporaries. He was rarely obscure, and yet in the absence of peripheral explanation, it is often impossible to deduce his original path of discovery. His habit was to write out his findings and publish without delay and consequently without the advantage of second thoughts or minor revision. There were very few occasions on which he had cause to regret his haste.
Cayley is remembered above all else for his contributions to invariant theory. Following Meyer (1890-1891), the theory may be taken to begin with a paper by Boole, published in 1841, hints of the central idea being found earlier in Lagrange’s investigation of binary quadratic forms (1773) and Gauss’s similar considerations of binary and ternary forms (1801). Cayley may be regarded as the first mathematician to have stated the problem of algebraic invariance in general terms. His work drew the attention of many mathematicians, particularly Boole, Salmon, and Sylvester in England and Aronhold, Clebsch, and, later, Gordan in Germany.
Beginning with an introductory memoir in 1854, Cayley composed a series of ten “Memoirs on Quantics,” the last published in 1878, which for mathematicians at large constituted a brilliant and influential account of the theory as he and others were developing it. The results Cayley was obtaining impressed mathematicians by their unexpectedness and elegance.
Achievements
Cayley is remembered as the leader of the British school of pure mathematics that emerged in the 19th century. He made important contributions to the algebraic theory of curves and surfaces, group theory, linear algebra, graph theory, combinatorics, and elliptic functions. He formalized the theory of matrices.
Royal Netherlands Academy of Arts and Sciences
,
Netherlands
1893
Prussian Academy of Sciences
,
Germany
Hungarian Academy of Sciences
,
Hungary
Personality
Cayley was the sort of courteous and unassuming person about whom few personal anecdotes are told; but he was not so narrow in outlook as his prolific mathematical output might suggest. He was a good linguist; was very widely read in the more romantic literature of his century; traveled extensively, especially on walking tours; mountaineered; painted in watercolors throughout his life; and took a great interest in architecture and architectural drawing.
Hermite compared him with Cauchy because of his immense capacity for work and the clarity and elegance of his analysis. Bertrand, Darboux, and Glaisher all compared him with Euler for his range, his analytical power, and the great extent of his writings.
Connections
In September 1863 Cayley married Susan Moline, of Greenwich; he was survived by his wife, son, and daughter.
