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Arthur Cayley’ Biography and Career Essay

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Updated: Nov 25th, 2019

Early Life

Arthur Cayley was born on 16 August 1821 in Richmond, England (Crilly). His parents, Henry Cayley and Maria Antonia Doughty, were business people in St. Petersburg, Russia and Arthur Cayley was born in England as his parents visited England briefly (Crilly). Arthur Cayley lived in Russia for eight years in his childhood.

He joined a private academy in London and at the age of fourteen joined King’s college in London (Crilly). Arthur Cayley joined Trinity College in Cambridge at the age of seventeen and graduated in 1842 and in October of the same year, he became the youngest fellow in that college (Weintraub). He taught in Trinity College, Cambridge for three years during which time he engaged in research. Arthur Cayley joined law school before his tenure as a fellow expired and joined the bar in 1849 (Crilly).

His Career

Arthur Cayley practiced law for fourteen years between 1849 and 1863. As an advocate, Arthur Cayley majored in conveyance. Conveyance refers to drafting of documents used for changing ownership of a property. He wrote over 300 mathematical papers during his leisure time, which led him to securing a position in the Royal society in 1854 (Weintraub). Arthur Cayley received a Royal medal from the Royal Society after serving the society for seven years.

In 1863, he quit his legal career and took up teaching mathematics at Cambridge as a professor (Weintraub). This granted him a chance to undertake full time research in mathematics. He married Susan Moline in the same year he took up teaching mathematics at Cambridge (Weintraub).

Arthur Cayley was a decisive administrator at Cambridge who encouraged women to pursue higher education. His administrative capabilities manifested in his contributions in drafting of college rules and regulations (Crilly). He contributed greatly in various fields within mathematics.

In Algebra, Arthur Cayley contributed to algebraic theory, which involves application of arithmetical workings and formal controls to conceptual images instead of particular digits. He contributed to group theory, which delves into algebraic structures or groups (Crilly).

In addition, Arthur Cayley contributed greatly to linear algebra, a discipline that involves the study of vector spaces and matrices and is usually easy to understand (Crilly). Linear algebra utility manifests in mathematical physics and coding hypothesis. Arthur Cayley was instrumental in developing graph theory that involves networking of convergence points arising from lines. Graph theory is crucial in fields like computer science and chemistry among others (Crilly).

Combinatorics owes its origins to Arthur Cayley (Famous Mathematicians). It is an area of mathematics dwelling on identification, setting, and execution within a discrete system. He also contributed in developing elliptic equations used to define any occurrence that does not change from time to time (Crilly). Arthur Cayley made the theory of matrices formal. He wrote ‘Memoirs on Quantics’, a paper that dwelt on quantics. Quantics are polynomials exhibiting similar total degrees for every concept (Crilly).

In geometry, Arthur Cayley narrowed to analytical geometry by applying invariant theory. Analytical geometry uses algebraic images and procedures to represent and solve geometrical related problems (Famous Mathematicians). Arthur Cayley proved that the arrangement resulting from intersection of vectors is always invariant.

In addition, he introduced an idea of space in projective geometry and confirmed that Euclidean geometry is part of projective geometry. Other than mathematics, Arthur Cayley had interest in mechanics and astronomy. In astronomy, he took special interest in lunar studies and came up with two popular reports on dynamics (Famous Mathematicians).

Major Achievements, His Last Days and Quotes

In the course of his legal and teaching career, Arthur Cayley received various medals and assumed various positions in several organizations.

He became an associate of the Royal Society in 1852 and received a Royal Society Medal in 1859 (Crilly). In 1865, Arthur Cayley became a Fellow of the Royal Society of Edinburgh and later on became the President of London Mathematical Society between 1868 and 1870 (Weintraub). In 1882, he received the Royal Society Copley Medal and London Mathematical Society De Morgan Medal in 1884 and later Arthur Cayley acquired a lunar feature, Crater Cayley (Weintraub).

In 1883, he assumed the Presidency of the British Association for the Advancement of Science and received honorary degrees from Oxford University, Dublin University, Edinburgh University, Gottingen University, Heidelberg University, Leiden University and Bologna University (Famous Mathematicians).

Arthur Cayley contributed in founding of the British school of pure mathematics and authored a treatise on ‘Elliptic Functions’ in 1876. He compiled his mathematical papers at Cambridge University and was able to edit seven of the papers (Crilly). Arthur Cayley suffered internal injuries in the course of compiling the papers and this would cause his death on 26 January 1895 aged 74 years.

His predecessor, Andrew Forsyth, edited the rest of Arthur Cayley’s papers and named them ‘Collected Mathematical Papers’ consisting of 967 papers (Crilly). His favorite quotes included “As for everything else, so for a mathematical theory: beauty can be perceived but not explained” and “Projective geometry is all geometry” (Weintraub).

Works Cited

Crilly, Tony. Arthur, Cayley. 2013. Web. <>.

Famous Mathematicians. Arthur Cayley. 2013. Web.12 June 2013 <>.

Weintraub, Steven H. Biography of Arthur Cayley (1821-1895). 2013. Web. <>.

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