Sir Alfred Cardew Dixon, 1st Baronet Warford FRS (22 May 1865 – 4 May 1936) was an English

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

Biography

Dixon was born on 22 May 1865 in

Northallerton Northallerton ( ) is a market town and civil parish in North Yorkshire, England. It is near the River Wiske in the Vale of Mowbray and had a population of 16,832 in 2011. Northallerton is an administrative centre for York and North Yorkshire ...

, Yorkshire, England. He studied at the

University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in Post-nominal letters, post-nominals) is a collegiate university, federal Public university, public research university located in London, England, United Kingdom. The ...

and graduated with an MA. He entered

Trinity College, Cambridge Trinity College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any ...

, in 1883 and graduated as

Senior Wrangler The Senior Wrangler is the top mathematics undergraduate at the University of Cambridge in England, a position which has been described as "the greatest intellectual achievement attainable in Britain". Specifically, it is the person who achiev ...

in the Mathematical Tripos in 1886. In 1888, Dixon was awarded the second

Smith's Prize Smith's Prize was the name of each of two prizes awarded annually to two research students in mathematics and theoretical physics at the University of Cambridge from 1769. Following the reorganization in 1998, they are now awarded under the names ...

, and also appointed a Fellow of Trinity College, Cambridge. He took the degree of Sc.D. at

Cambridge University The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

in 1897. He was Professor of Mathematics at

Queen's College, Galway The University of Galway () is a public research university located in the city of Galway, Ireland. The university was founded in 1845 as "Queen's College, Galway". It was known as "University College, Galway" (UCG) () from 1908 to 1997 and as ...

, from 1893 to 1901. In 1901 he was appointed to the chair at

Queen's University Belfast The Queen's University of Belfast, commonly known as Queen's University Belfast (; abbreviated Queen's or QUB), is a public research university in Belfast, Northern Ireland, United Kingdom. The university received its charter in 1845 as part of ...

, which he held till 1930, receiving the title of Emeritus Professor on retirement. Dixon was elected to the Royal Society in 1904 and after he retired from Queen's University Belfast, he served as president of the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's Learned society, learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh ...

from 1931 until 1933. Queen's University Belfast conferred on him the honorary degree of D.Sc. in 1932.

Research work

Dixon was well known for his work in differential equations. He did early work on Fredholm integrals independently of Fredholm. He worked both on

ordinary differential equation In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable (mathematics), variable. As with any other DE, its unknown(s) consists of one (or more) Function (mathematic ...

s and on

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to ho ...

s studying Abelian integrals, automorphic functions, and

functional equation In mathematics, a functional equation is, in the broadest meaning, an equation in which one or several functions appear as unknowns. So, differential equations and integral equations are functional equations. However, a more restricted meaning ...

s. In 1894 Dixon wrote ''The Elementary Properties of the Elliptic Functions''.''The Elementary Properties of the Elliptic Functions, with Examples'' by Alfred Cardew Dixon, Palala Press 2016, Certain elliptic functions ( meromorphic doubly periodic functions) denoted cm and sm satisfying the identity cm(''z'')³ + sm(''z'')³ = 1 are known as Dixon elliptic functions.

Dixon's identity In mathematics, Dixon's identity (or Dixon's theorem or Dixon's formula) is any of several different but closely related identities proved by A. C. Dixon, some involving finite sums of products of three binomial coefficients, and some evaluating ...

is any of several closely related identities involving

binomial coefficient In mathematics, the binomial coefficients are the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers and is written \tbinom. It is the coefficient of the t ...

s and

hypergeometric function In mathematics, the Gaussian or ordinary hypergeometric function 2''F''1(''a'',''b'';''c'';''z'') is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is ...

References

External links

* {{DEFAULTSORT:Dixon, Alfred Cardew 1865 births 1936 deaths 20th-century English mathematicians Academics of Queen's University Belfast Alumni of Trinity College, Cambridge Fellows of Trinity College, Cambridge Fellows of the Royal Society Senior Wranglers People from Northallerton Cambridge mathematicians