Cayley, Arthur (1821–1895)

English mathematician who developed matrix algebra, used by Werner Heisenberg in his elucidation of quantum mechanics. He also developed the study of n-dimensional geometry, introducing the concept of the ‘absolute’, and formulated the theory of algebraic invariants.

Cayley was born in Richmond, Surrey, and studied mathematics at Cambridge before becoming a barrister. In 1863 he became professor of pure mathematics at Cambridge.

Cayley published about 900 mathematical notes and papers on nearly every pure mathematical subject, as well as on theoretical dynamics and astronomy. Some 300 of these papers were published during his 14 years at the Bar, and for part of that time he worked in collaboration with James Joseph Sylvester, another lawyer. Together they founded the algebraic theory of invariants in 1843. Cayley clarified many of the theorems of algebraic geometry that had previously been only hinted at, and he was one of the first to realize how many different areas of mathematics were drawn together by the theory of groups.