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Cayley, Arthur

geometry theory college trinity

(1821–95) British mathematician: developed n-dimensional geometry, and the theory of matrices and algebraic invariants.

Cayley, the son of an English merchant, spent his first 8 years in Russia, where his father was then working. He was educated at King’s College School, London and Trinity College, Cambridge. Reluctant to be ordained, which was a necessary condition to remain a Fellow of Trinity College, he became a barrister. For 14 years he practised law, and only accepted the Sadlerian Chair of Pure Mathematics in Cambridge in 1863 when the requirement concerning religious orders was dropped.

He managed to publish over 300 papers while a barrister and by his death he had published over 900, covering all areas of pure mathematics, theoretical dynamics and astronomy. While they were both lawyers Cayley and his friend established the theory of algebraic invariants.

Cayley also developed a theory of metrical geometry, linking together projective geometry and non-Euclidean geometry. Together with he classified geometries as elliptic or hyperbolic depending on the curvature of space upon which the geometry was drawn (that is, whether a surface is saddle-like or dome-like).

The theory of matrices was an invention of Cayley’s and allowed compact manipulation of the many components of a geometrical system. The movement of a vector (directed line) when the space in which it is embedded is distorted can be described by this theory.

Cayley was a prolific mathematician with a strong and dependable character, much in demand both as a lawyer and administrator.

Cayley, Sir George [next] [back] Caxton, William (1422/1423–1491) - BIOGRAPHY, MAJOR WORKS AND THEMES, CRITICAL RECEPTION

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