Arthur Cayley

Arthur Cayley was product the theory of matrices through unique partnership with James Sylvester. They met in their twenties and were friends, colleagues, and co-authors for the rest of their lives.

Cayley's mathematical ability was recognized at an early age and he was encouraged to study the subject. He graduated from Cambridge University at the top of his class. After graduation, Cayley was awarded a three-year fellowship that allowed him to do as he pleased. During this time, he made several trips to Europe, where he spent his time taking walking tours, mountaineering, painting, reading novels, and studying architecture, as well as reading and writing mathematics. He wrote twenty five papers in mathematics, papers that were well received by the mathematical community.



When Cayley fellowship expired, he found that no problem as a mathematician was open to him unless he entered the clergy, so he left mathematics and prepare for legal career. When he was admitted to the bar, he met James Joseph Sylvester.

Cayley and Sylvester revived and intensified each other's interest in mathematics and each started to write mathematics again. During his fourteen year spent practicing law, Cayley wrote almost 300 papers. Each frequently expressed gratitude to the other for assistance and inspiration. In one of his paper, Sylvester wrote that "the theorem above enunciated was in part suggested in the course of a Conversation with Mr Cayley (to whom I am indebted for my restoration to the enjoyment of mathematical life)." In another, he said, "Mr Cayley habitually discourse pearls and rubies."

Cayley joyfully departed from the legal profession when Cambridge offered him a professorship in mathematics, even though his income suffered as a result. He was finally able to spend his life studying, teaching, and writing mathematics. He became quite famous as mathematician, writing almost 1,000 papers in algebra and geometry, often in collaboration with Sylvester. Many of this papers are pioneering work of scholarship. Cayley also played important role in changing Cambridge's policy that had prohibited the admission of women as students.

With Sylvester, he responsible for the theory of matrices, including the operation of matrices multiplication. Sixty-seven years after the invention of matrix theory, Heisenberg recognized it as the perfect tools for his revolutionary work in quantum mechanics. The work of Cayley and Sylvester in algebra become quite important for modern physics, particulary in the theory of relativity. Cayley also wrote on non-euclidean geometry.

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