Arthur Cayley (
August 16 1821 -
January 26 1895) was a British
mathematician. He helped found the modern British school of
pure mathematics. As a child, Cayley enjoyed solving complex math problems for amusement. At eighteen, he entered
Trinity College, Cambridge, where he excelled in Greek, French, German, and Italian, as well as
mathematics. He worked as a
lawyer for 14 years.He was consequently able to prove the
Cayley-Hamilton theorem -- that every square matrix is a root of its own characteristic polynomial. 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. Formerly, when mathematicians spoke of "groups", they had meant
permutation groups.
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