Arthur Cayley facts for kids

Quick facts for kids Arthur Cayley FRS
Born	(1821-08-16)16 August 1821 Richmond, Surrey, UK
Died	26 January 1895(1895-01-26) (aged 73) Cambridge, England
Education	King's College School
Alma mater	Trinity College, Cambridge (BA, 1842)
Known for	Algebraic geometry Group theory Cayley–Hamilton theorem Cayley–Dickson construction
Awards	Smith's Prize (1842) De Morgan Medal (1884) Royal Medal (1859) Copley Medal (1882)
Scientific career
Fields	Mathematics
Institutions	Trinity College, Cambridge
Academic advisors	George Peacock William Hopkins
Notable students	H. F. Baker Andrew Forsyth Charlotte Scott

Arthur Cayley (born August 16, 1821 – died January 26, 1895) was a brilliant British mathematician. He focused mainly on algebra and helped create the modern way of studying pure mathematics in Britain.

As a child, Arthur loved solving tricky math problems just for fun. He went to Trinity College, Cambridge, where he was excellent at many languages. These included Greek, French, German, and Italian, as well as mathematics. Later in life, he worked as a lawyer for 14 years.

Cayley came up with the Cayley–Hamilton theorem. This theorem states that every square matrix is a root of its own characteristic polynomial. He also was the first to define a group in the modern way. This is a set with a binary operation that follows certain rules. Many math ideas are named after him, like Cayley tables and Cayley graphs.

Early Life and Schooling

Arthur Cayley was born in Richmond, London, England, on August 16, 1821. His father, Henry Cayley, was a merchant who lived in Saint Petersburg, Russia. Arthur spent his first eight years in Russia.

In 1829, his family moved back to Blackheath, near London. Arthur went to a private school. When he was 14, he attended King's College School. His teachers quickly saw that he was a math genius. They told his father that Arthur should go to the University of Cambridge instead of joining the family business.

University Education

Arthur Cayley started studying at Trinity College, Cambridge, when he was only 17. This was quite young for university at the time. At age 20, he wrote three important papers for the Cambridge Mathematical Journal.

His teachers at Cambridge were George Peacock and William Hopkins. Cayley finished his studies at the top of his class, earning the title of Senior Wrangler. He also won the first Smith's prize. He stayed at Cambridge for four more years after graduating. During this time, he wrote 28 more papers for the Mathematical Journal.

Life as a Lawyer

Because his university fellowship had a time limit, Cayley needed to choose a job. Like many smart people of his time, he decided to become a lawyer. He started working in law in London in 1846, when he was 24 years old. He specialized in a type of law called conveyancing.

During this time, he became good friends with James Joseph Sylvester, another mathematician. They often walked together, talking about math ideas. Even while working as a lawyer for 14 years, Cayley wrote between 200 and 300 math papers.

Becoming a Professor

Around 1860, a new math professorship was created at Cambridge University. It was called the Sadleirian Professorship. The person in this role was expected to teach pure mathematics and help advance the science.

Arthur Cayley was chosen for this position when he was 42. He gave up his well-paying job as a lawyer for a smaller salary. However, he never regretted it. This new job allowed him to focus all his energy on mathematics, which he loved most. He got married and settled down in Cambridge, enjoying a very happy home life.

At first, he only taught lectures for one term each year. Later, this was extended to two terms. He often lectured on the math topics he was currently researching. He also helped review math papers for many different scientific groups.

In 1872, he became an honorary fellow of Trinity College. Three years later, he became a full fellow, which meant he also received a salary. His friends even raised money for a portrait of him.

Cayley also made important contributions to algebraic geometry. He worked with George Salmon to discover the 27 lines on a cubic surface. He also helped start the study of ruled surfaces in algebraic geometry.

In 1876, he published a book called Treatise on Elliptic Functions. He also strongly supported university education for women. He helped teach at Girton College and was chairman of the council for Newnham College. He cared deeply about their progress.

In 1881, he was invited to give lectures at Johns Hopkins University in Baltimore, USA. He accepted and lectured there for five months in 1882.

Leading the British Association

In 1883, Cayley became the President of the British Association for the Advancement of Science. This was a very important role. The annual meeting was held in Southport, England.

As president, Cayley gave a speech about the progress of pure mathematics. This speech was a big public event, and he made sure it was easy for everyone to understand.

His Collected Works and Legacy

In 1889, the Cambridge University Press asked Cayley to prepare all his math papers for publication. He was very happy about this request. He edited seven large volumes of his papers himself.

While working on these books, he was very ill. He passed away on January 26, 1895, at the age of 73. Many important people attended his funeral at Trinity Chapel.

The rest of his papers were edited by Andrew Forsyth, who took over his professorship. In total, his collected math papers fill thirteen large volumes and include 967 different works. Cayley always loved reading novels and traveling. He also enjoyed paintings and architecture. He even did water-colour painting, which sometimes helped him draw math diagrams.

Cayley is buried in the Mill Road cemetery in Cambridge.

Many mathematical terms are named after him, showing his lasting impact:

See also

In Spanish: Arthur Cayley para niños

• List of things named after Arthur Cayley