Born in Richmond, Cayley studied mathematics at Cambridge University, but before becoming a professional mathematician spent 14 years working as a barrister. He was forced to do this since he was unwilling to take holy orders – which at that time was a necessary condition of continuing his mathematical career at Cambridge. When this requirement was dropped, Cayley was able to return to Cambridge and in 1863 became Sadlerian Professor there.

Cayley was an extremely prolific mathematician. His greatest work was the creation of the theory of invariants, in which he worked closely with his friend James Joseph Sylvester. Cayley developed this theory as a branch of pure mathematics but it turned out to play a crucial role in the theory of relativity, as it is important in the calculation of space–time relationships in physics. He also developed the theory of matrices and made major contributions to the study of n-dimensional geometry. He went a considerable way toward unifying the study of geometry. Cayley also did important work in the theory of elliptic functions.

One of Cayley's notable nonmathematical achievements was playing a large role in persuading the University of Cambridge to admit women as students.