# Arthur Cayley

Arthur Cayley (Mathematics) (16 August 1821 – 26 January 1895) was a prolific British mathematician who worked mostly on algebra. He helped found the modern British school of pure mathematics.

He postulated the Cayley–Hamilton theorem —that every square matrix is a root of its own characteristic polynomial, and verified it for matrices of order 2 and 3.(1) He was the first to define the concept of a group in the modern way—as a set with a binary operation satisfying certain laws.(2) Formerly, when mathematicians spoke of “groups”, they had meant permutation groups. Cayley tables and Cayley graphs as well as Cayley’s theorem are named in honour of Cayley.

He was the first to coin the mathematical idea of 1/ “finite group” (1854) and 2/ “tree” (1857).

Name “tree” for the data structure in Math/CS was coined by Arthur Cayley in 1857 (Tree (graph theory) - Wikipedia) - A History of Abstract Algebra | Israel Kleiner | Springer

Cayley was into representing mathematical forms graphically. On-the-Theory-of-Groups Desiderata-and-suggestions

He was also perhaps the first to perform diagrammatic algebra [1]. He performed a graphical tree algebra on the very first paper he introduced the concept of “trees” in 1857. - ho.history overview - Who invented diagrammatic algebra? - MathOverflow

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