ScienceWeek

ARTHUR CAYLEY (1821-1895) AND THE THRORY OF INVARIANTS

Arthur Cayley (1821-1895), English mathematician, was educated at Cambridge University, becoming a fellow of Trinity College in 1845 but leaving after three years because he did not wish to take holy orders. He then spent 15 years as a lawyer before being appointed the first Sadleirian Professor of Mathematics at Cambridge in 1863. Apart from half a year spent at Johns Hopkins University in the US (1881-1882), he remained at Cambridge until his death.

Cayley is best known for his work with James Joseph Sylvester (1814-1897) on invariants, algebraic expressions that remain unchanged when their variables are transformed. The theory of invariants, generalized to differentials of the variables, formed the mathematical basis of Albert Einstein's General Theory of Relativity -- the idea that gravity is a manifestation of the curvature of a 4-dimensional space-time.

Cayley was also responsible for matrix algebra, which is now widely used in all branches of pure and applied mathematics: A matrix is a rectangular table of numbers and represents a transformation of variables.

Cayley was also one of the creators of higher-dimensional geometry, beginning with a paper of 1845 on spaces of (n) dimensions. The main founder of this theory was the German mathematician Hermann Grassmann (1809-1877), in his /Ausdehnungslehre/ (Theory of Extension) of 1844, but Cayley's early work was done independently.

Adapted from: E.A. Abbot and I. Stewart: The Annotated Flatland: A Romance of Many Dimensions. Perseus Publishing 2002, p.9. More information at: http://www.amazon.com/exec/obidos/ASIN/0738205419/scienceweek