Dixon's identity provides a set of mathematical relations involving hypergeometric functions and binomial coefficients that remain fundamental to the field. Alfred Cardew Dixon, a mathematician from the United Kingdom, specialized in logic, foundations, and differential equations throughout a career that spanned academic appointments at Trinity College, the University of Galway, and Queen's University Belfast.
Academic Foundation
Born in Northallerton in 1865, Dixon received his early education at Kingswood School. He later attended the University of London and Trinity College, Cambridge, where he studied from 1883 to 1886. His academic performance during this period earned him the Smith's Prize in 1888. He served as a fellow at Trinity College from 1888 until 1893.
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Dixon held a series of academic positions across Ireland and the United Kingdom. He moved to the University of Galway in 1893, remaining there until 1901. Subsequently, he accepted a professorship at Queen's University Belfast, where he served until his retirement in 1930. Following his departure from the faculty, he acted as chairperson for the London Mathematical Society between 1931 and 1933.
Mathematical Contributions
His research focused heavily on differential equations, including investigations into Abelian integrals, automorphic functions, and functional equations. He independently explored Fredholm integrals and authored The Elementary Properties of the Elliptic Functions in 1894. His work on doubly periodic functions led to the nomenclature of Dixon's elliptic functions, which satisfy the specific identity cm(z)3 + sm(z)3 = 1.
Recognition and Legacy
The Royal Society elected Dixon as a fellow in 1904, acknowledging his contributions to the discipline. In 1932, Queen's University Belfast awarded him an honorary D.Sc. degree. He passed away in 1936 in Northwood, having spent his professional life contributing to the advancement of mathematical theory and the structure of functional equations.
Fast facts
- Born: 1865, Northallerton
- Died: 1936, Northwood
- Education: Trinity College, Kingswood School, University of London
- Awards: Smith's Prize (1888), Fellow of the Royal Society (1904)
- Positions: Chairperson of the London Mathematical Society (1931-1933)
- Notable Works: Dixon's identity, Dixon's elliptic functions
Questions readers ask
What institutions employed Alfred Cardew Dixon?
He worked at Trinity College, the University of Galway, and Queen's University Belfast.
What is the identity associated with Dixon's elliptic functions?
The identity is cm(z)3 + sm(z)3 = 1.
Achievements
- Fellow of the Royal Society — 1904
- Smith's Prize — 1888
- Notable work: Dixon's identity
- Notable work: Dixon's elliptic functions
- Held posts at University of Galway, Queen's University Belfast and Trinity College
- Fields: mathematics