Nepedia
Back to Discover
Advanced Reader
🔢

Arthur Cayley

math Maturity 7-9 death dying politics supernatural Next article →

This article covers sensitive topics: death_dying, politics, supernatural. Parents can manage visibility in Parental Controls.

Arthur Cayley was a foundational figure in modern mathematics. He was an English mathematician who specialized in algebra. His work helped establish the modern British school of pure mathematics. He spent 35 years as a professor at Trinity College, Cambridge. Cayley's influence is visible in many different branches of math today. His research covered algebra, geometry, and combinatorics.

Cayley made significant breakthroughs in several mathematical areas. In linear algebra, he postulated the Cayley–Hamilton theorem. This theorem states that every square matrix is a root of its own characteristic polynomial. He verified this for matrices of order 2 and 3. In group theory, he was the first to define an abstract group. He described it as a set with a binary operation that follows specific laws. This was a different approach than the permutation groups studied by Évariste Galois.

His work in algebraic geometry was also quite important. Cayley and a mathematician named Salmon discovered 27 lines on a cubic surface. He also constructed the Chow variety of all curves in projective 3-space. He founded the algebro-geometric theory of ruled surfaces. In the field of combinatorics, he used generating functions to count trees. Specifically, he counted the $n^{n-2}$ trees on $n$ labeled vertices. These diverse contributions show how wide his mathematical reach was.

Cayley's life followed a unique path through law and academia. He was born on August 16, 1821, in Richmond, London. He spent his first eight years living in Saint Petersburg, Russia. His father, Henry Cayley, was a merchant in Russia. The family returned to Blackheath, London, in 1829. At age 14, he attended King's College School. His teachers recognized his genius and suggested he attend the University of Cambridge.

At Trinity College, Cayley excelled in many different subjects. He mastered mathematics and several languages, including Greek, French, German, and Italian. He won the title of Senior Wrangler and the first Smith's prize. Because his fellowship had a limited term, he became a lawyer in 1846. He practiced conveyancing at Lincoln's Inn for many years. During this time, he maintained close friendships with other mathematicians like J. J. Sylvester. They often discussed the theory of invariants and covariants while walking together.

In 1860, Cayley transitioned from law to a full-time academic career. He became the first holder of the Sadleirian professorship at Cambridge. He gave up a lucrative legal practice for a more modest salary. He did this to devote his energy to the advancement of pure mathematics. Initially, he lectured for only one term per year. Following university financial reforms in 1886, he could lecture for two terms. His student attendance grew from a few people to about fifteen students after this reform.

Cayley was a highly productive researcher and leader. He produced between two00 and 300 mathematical papers during his career. In 1883, he served as the President of the British Association for the Advancement of Science. He also supported the education of women at Cambridge. He was interested in the progress of Girton and Newnham colleges. He even traveled to Baltimore in 1882 to deliver lectures on Abelian and Theta Functions.

His legacy remains strong in the 21st century. His work is still cited in more than 200 mathematical papers every year. Many mathematical concepts bear his name. These include Cayley tables, Cayley graphs, and Cayley's formula. Even the Moon has a crater named Cayley. He died on January 26, 1895, at the age of 73. His funeral at Trinity Chapel was attended by leading scientists from Russia and America.

596 words

Where will your curiosity go next?

Keep exploring at your chosen reading level.

More to explore

What is Nepedia?

A free, ad-free encyclopedia for children. Every article is written at five reading levels, so the same page works for a five-year-old and a fifteen-year-old — use the level switcher above to see this one change. No account needed to read.