Arthur Cayley wrote hundreds of maths papers while working as a London lawyer
For fourteen years Arthur Cayley earned his living drawing up property deeds, and in his spare hours produced between two and three hundred mathematics papers. He and his friend J. J. Sylvester used to talk through invariant theory while strolling around the courts of Lincoln's Inn.
Cayley was born in Richmond, London, on 16 August 1821, but spent his first eight years in Saint Petersburg, where his father traded as a merchant. The family settled at Blackheath in 1829. At King's College School his master spotted exceptional talent and persuaded his father to send him to Cambridge rather than into the family business. At Trinity College he excelled at four modern and ancient languages besides mathematics, published three papers by twenty, and finished as Senior Wrangler, taking the first Smith's Prize too.
A fellowship gave him four years in Cambridge, during which he wrote 28 memoirs for the Cambridge Mathematical Journal. When it lapsed he needed a profession, so in April 1846 he entered Lincoln's Inn and specialized in conveyancing. As a pupil he still found time to travel to Dublin for William Rowan Hamilton's lectures on quaternions. Around 1860 Cambridge created the Sadleirian chair of pure mathematics, and Cayley, then 42, became its first holder, trading a lucrative practice for a modest salary without regret. He married at once and enjoyed a contented home life that the unmarried Sylvester openly envied.
His mathematics was vast. He stated the Cayley-Hamilton theorem, that every square matrix satisfies its own characteristic polynomial, checking it for 2-by-2 and 3-by-3 cases. He was the first to define an abstract group as a set with an operation obeying certain rules, moving beyond Galois' permutation groups. With George Salmon he found the 27 straight lines lying on a cubic surface, and he counted the labelled trees on n points as n raised to the power n minus 2. His collected works fill thirteen quarto volumes containing 967 papers.
Cayley also backed university education for women, teaching at Girton in its early days and chairing Newnham's council for years. In 1882 he lectured at Johns Hopkins in Baltimore, where Sylvester was then professor, and in 1883 he presided over the British Association. He painted watercolours, which sometimes helped with diagrams, and loved novels and travel. He died on 26 January 1895, and a lunar crater now bears his name.
Source: Arthur Cayley
