Arthur Cayley

Arthur Cayley (1821–1895) was a British mathematician and one of the central figures of 19th-century mathematics. After studying at Cambridge, he practised as a lawyer for fourteen years while publishing approximately 250 mathematical articles. In 1863, he accepted a chair in pure mathematics at Cambridge, less lucrative than his legal career but allowing him to devote most of his time to mathematics. He is regarded as one of the inventors of matrix algebra and the founder of matrix theory as an independent discipline. From 1854 onwards, he laid the foundations of abstract group theory, going beyond the permutation groups then known, and introduced the concept of a vector space. His work in n-dimensional geometry, non-Euclidean geometry and projective geometry opened up perspectives that would permanently shape the development of mathematics and physics. His name is attached to numerous objects and results: the algebra of octonions, or Cayley octaves; the Cayley graph of a group; the Cayley surface (a ruled cubic surface); Cayley's theorem, according to which every group is isomorphic to a subgroup of a symmetric group; and the Cayley–Hamilton theorem, according to which every square matrix satisfies its characteristic polynomial. A member of the Royal Society from 1852, he was one of the founders of the modern British school of pure mathematics.