Louis Mordell
Encyclopedia
Louis Joel Mordell was a British
mathematician, known for pioneering research in number theory
. He was born in Philadelphia, USA, in a Jewish family of Lithuania
n extraction. He came in 1906 to Cambridge to take the scholarship examination for entrance to St John's College
, and was successful in gaining a place and support.
Having taken third place in the Mathematical Tripos, he began independent research into particular diophantine equation
s: the question of integer points on the cubic curve, and special case of what is now called a Thue equation
, the Mordell equation
He took an appointment at Birkbeck College, London
in 1913. During World War I
he was involved in war work, but also produced one of his major results, proving in 1917 the multiplicative property of Ramanujan's tau-function. The proof was by means, in effect, of the Hecke operator
s, which had not yet been named after Erich Hecke
; it was, in retrospect, one of the major advances in modular form
theory, beyond its status as an odd corner of the theory of special functions.
In 1920 he took a teaching position in Manchester College of Technology
, becoming the Fielden Reader
in Pure Mathematics at the Victoria University of Manchester
in 1922 and Professor in 1923. There he developed a third area of interest within number theory, geometry of numbers
. His basic work on Mordell's theorem is from 1921/2, as is the formulation of the Mordell conjecture.
He took British citizenship in 1929. In Manchester he also built up the department, offering posts to a number of outstanding mathematicians who had been forced from posts on the continent of Europe. He brought in Reinhold Baer
, G. Billing, Paul Erdős
, Chao Ko
, Kurt Mahler
, and Beniamino Segre
. He also recruited J. A. Todd
, P. Du Val, Harold Davenport
, L. C. Young, and invited distinguished visitors.
In 1945 he returned to Cambridge as a Fellow of St. John's
, when elected to the Sadleirian Chair, and became Head of Department. He officially retired in 1953. It was at this time that he had his only formal research students, of whom J. W. S. Cassels
was one. His idea of supervising research was said to involve the suggestion that a proof of the transcendence
of the Euler-Mascheroni constant
was probably worth a doctorate. His book Diophantine Equations (1969) is based on lectures, and gives an idea of his discursive style.
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...
mathematician, known for pioneering research in number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
. He was born in Philadelphia, USA, in a Jewish family of Lithuania
Lithuania
Lithuania , officially the Republic of Lithuania is a country in Northern Europe, the biggest of the three Baltic states. It is situated along the southeastern shore of the Baltic Sea, whereby to the west lie Sweden and Denmark...
n extraction. He came in 1906 to Cambridge to take the scholarship examination for entrance to St John's College
St John's College, Cambridge
St John's College is a constituent college of the University of Cambridge. The college's alumni include nine Nobel Prize winners, six Prime Ministers, three archbishops, at least two princes, and three Saints....
, and was successful in gaining a place and support.
Having taken third place in the Mathematical Tripos, he began independent research into particular diophantine equation
Diophantine equation
In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. Diophantine problems have fewer equations than unknown variables and involve finding integers that work correctly for all equations...
s: the question of integer points on the cubic curve, and special case of what is now called a Thue equation
Thue equation
In mathematics, a Thue equation is a Diophantine equation of the formwhere ƒ is an irreducible bivariate form of degree at least 3 over the rational numbers, and r is a nonzero rational number...
, the Mordell equation
- y2 = x3 + k.
He took an appointment at Birkbeck College, London
Birkbeck, University of London
Birkbeck, University of London is a public research university located in London, United Kingdom and a constituent college of the federal University of London. It offers many Master's and Bachelor's degree programmes that can be studied either part-time or full-time, though nearly all teaching is...
in 1913. During World War I
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
he was involved in war work, but also produced one of his major results, proving in 1917 the multiplicative property of Ramanujan's tau-function. The proof was by means, in effect, of the Hecke operator
Hecke operator
In mathematics, in particular in the theory of modular forms, a Hecke operator, studied by , is a certain kind of "averaging" operator that plays a significant role in the structure of vector spaces of modular forms and more general automorphic representations....
s, which had not yet been named after Erich Hecke
Erich Hecke
Erich Hecke was a German mathematician. He obtained his doctorate in Göttingen under the supervision of David Hilbert. Kurt Reidemeister and Heinrich Behnke were among his students....
; it was, in retrospect, one of the major advances in modular form
Modular form
In mathematics, a modular form is a analytic function on the upper half-plane satisfying a certain kind of functional equation and growth condition. The theory of modular forms therefore belongs to complex analysis but the main importance of the theory has traditionally been in its connections...
theory, beyond its status as an odd corner of the theory of special functions.
In 1920 he took a teaching position in Manchester College of Technology
UMIST
The University of Manchester Institute of Science and Technology was a university based in the centre of the city of Manchester in England. It specialised in technical and scientific subjects and was a major centre for research...
, becoming the Fielden Reader
Fielden Chair of Pure Mathematics
The Fielden Chair of Pure Mathematics is an endowed professorial position in the School of Mathematics, University of Manchester, England.In 1870 Samuel Fielden, a wealthy mill owner from Todmorden, donated £150 to Owens College for the teaching of evening classes and a further £3000 for the...
in Pure Mathematics at the Victoria University of Manchester
Victoria University of Manchester
The Victoria University of Manchester was a university in Manchester, England. On 1 October 2004 it merged with the University of Manchester Institute of Science and Technology to form a new entity, "The University of Manchester".-1851 - 1951:The University was founded in 1851 as Owens College,...
in 1922 and Professor in 1923. There he developed a third area of interest within number theory, geometry of numbers
Geometry of numbers
In number theory, the geometry of numbers studies convex bodies and integer vectors in n-dimensional space. The geometry of numbers was initiated by ....
. His basic work on Mordell's theorem is from 1921/2, as is the formulation of the Mordell conjecture.
He took British citizenship in 1929. In Manchester he also built up the department, offering posts to a number of outstanding mathematicians who had been forced from posts on the continent of Europe. He brought in Reinhold Baer
Reinhold Baer
Reinhold Baer was a German mathematician, known for his work in algebra. He introduced injective modules in 1940. He is the eponym of Baer rings....
, G. Billing, Paul Erdős
Paul Erdos
Paul Erdős was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory...
, Chao Ko
Chao Ko
Ke Zhao or Chao Ko was a Chinese mathematician born in Wenling, Taizhou, Zhejiang, People's Republic of China.Zhao graduated from Tsinghua University in 1933 and obtained his doctorate from the University of Manchester under Louis Mordell in 1937. His main fields of study were algebra, number...
, Kurt Mahler
Kurt Mahler
Kurt Mahler was a mathematician and Fellow of the Royal Society.He was a student at the universities in Frankfurt and Göttingen, graduating with a Ph.D...
, and Beniamino Segre
Beniamino Segre
Beniamino Segre was an Italian mathematician who is remembered today as a major contributor to algebraic geometry and one of the founders of combinatorial geometry....
. He also recruited J. A. Todd
J. A. Todd
John Arthur Todd FRS was a British geometer. He was born in Liverpool, and went to Trinity College of the University of Cambridge in 1925. He did research under H.F. Baker, and in 1931 took a position at the University of Manchester. He became a lecturer at Cambridge in 1937...
, P. Du Val, Harold Davenport
Harold Davenport
Harold Davenport FRS was an English mathematician, known for his extensive work in number theory.-Early life:...
, L. C. Young, and invited distinguished visitors.
In 1945 he returned to Cambridge as a Fellow of St. John's
St John's College, Cambridge
St John's College is a constituent college of the University of Cambridge. The college's alumni include nine Nobel Prize winners, six Prime Ministers, three archbishops, at least two princes, and three Saints....
, when elected to the Sadleirian Chair, and became Head of Department. He officially retired in 1953. It was at this time that he had his only formal research students, of whom J. W. S. Cassels
J. W. S. Cassels
John William Scott Cassels , FRS is a leading English mathematician.-Biography:Educated at Neville's Cross Council School in Durham and George Heriot's School in Edinburgh, Cassels graduated from the University of Edinburgh with an MA in 1943.His academic career was interrupted in World War II...
was one. His idea of supervising research was said to involve the suggestion that a proof of the transcendence
Transcendental number
In mathematics, a transcendental number is a number that is not algebraic—that is, it is not a root of a non-constant polynomial equation with rational coefficients. The most prominent examples of transcendental numbers are π and e...
of the Euler-Mascheroni constant
Euler-Mascheroni constant
The Euler–Mascheroni constant is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter ....
was probably worth a doctorate. His book Diophantine Equations (1969) is based on lectures, and gives an idea of his discursive style.