Arthur Cayley

On 8 September 1863, Arthur Cayley married Susan Moline from Greenwich. Her father, Robert Moline, was a country banker. They eventually settled down to a quiet and happy life in Cambridge.

The couple had two children: a son Henry and a daughter, Mary. Henry Cayley studied mathematics at Cambridge, but realizing that he could never live up to his father’s reputation, decided to give it up and became an architect.

Towards the end of his life Cayley suffered from a painful abdominal ailment and died from it on 26 January 1895. He was then 73 years old and survived by his wife and children. He is buried at the Mill Road cemetery, Cambridge.

Arthur Cayley was born on 16 August 1821 in Richmond, Surrey, England. His father, Henry Cayley, came from an ancient Yorkshire family. At the time of Arthur’s birth, he was employed as a commercial agent in St. Petersburg, Russia, but had come to England on a short visit.

According to many biographers, his mother, Maria Antonia nee Doughty, was of Russian origin. But her father’s name, William Doughty, indicates she might have been of English descent. Arthur was born third of the couple’s five children.

He had two sisters, Sophia and Henrietta-Caroline and two brothers, William Henry and Charles Bagot. While Sophia and William Henry were elder to him, Charles Bagot and Henrietta-Caroline were younger. He never saw William, who died in infancy. Charles Bagot grew up to a noted linguist

Arthur spent the first eight years of his life in Petersburg where he came in contact with several languages like English, Russian and French. In 1829, the family permanently returned to England, settling at Blackheath, now a part of South East London.

In England, Arthur was admitted to a private school, where he studied till the age of fourteen. Thereafter in 1835, he started going to King's College School. In both the schools, young Arthur showed great skills in mathematics. In addition, he did well in science, winning prizes in chemistry.

In 1842, Arthur Cayley graduated as a Senior Wrangler from Cambridge, winning the Smith's Prize. He then received a fellowship and began his career at the same university. Although he left the position after only four years, the period had been academically very productive.

During this period, he worked on a large variety of topics such as algebraic curves and surfaces, elliptic functions, determinants, the theory of integration etc. Moreover, he had twenty-eight of his papers published in ‘Cambridge Mathematical Journal’ alone.

Among them, his 1843 paper, titled ‘On a theory of determinants’ is especially significant. In this paper, he extended the concept of two-dimensional determinant to multidimensional arrays. However, he did not limit himself to publishing in local journals alone.

In 1844, he made a visit to the Swiss Alps and Italy. As a result of this, he started taking an international approach and subsequently published a number of papers in ‘Journal de Mathématiques Pures et Appliquées’ (France) and ‘Journal für die reine und angewandte Mathematik’ (Germany).

In 1845, he wrote ‘On the Theory of Linear Transformations’, which laid the foundations for invariant theory. Despite such success, he decided to opt out of his academic career the very next year.

At that time, if one wanted to join the faculty of the Cambridge University, one had to join the Holy Order, a step Cayley was not ready to take. As his fellowship would have expired in 1852, he thought it prudent to take up another career and he chose law.

In April 1846, he entered Lincoln’s Inn, London, where he specialized in conveyancing. However, he did not abandon mathematics all together, but maintained contact with scholars at the Cambridge University.

He also attended a number of conferences, in the course of which, he met many renowned mathematicians, developing close bonds with them. In the year he took his bar examination, he went to Dublin to hear William Rowan Hamilton's lectures on quaternions, eventually developing a friendship with him.

This was also the time he developed a close bond with the mathematician James Joseph Sylvester. Sylvester was five years his senior at Cambridge, but was now studying law, later becoming an actuary.

Walking together round the courts of Lincoln's Inn, they discussed the theory of invariants and covariants. Later the two worked together, making major contributions to invariant as well as matrix theory.