Louis Joel Mordell (28 January 1888 – 12 March 1972) was an American-born British mathematician, known for pioneering research in

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...

. He was born in

Philadelphia Philadelphia, often called Philly, is the largest city in the Commonwealth of Pennsylvania, the sixth-largest city in the U.S., the second-largest city in both the Northeast megalopolis and Mid-Atlantic regions after New York City. Sinc ...

United States The United States of America (U.S.A. or USA), commonly known as the United States (U.S. or US) or America, is a country primarily located in North America. It consists of 50 U.S. state, states, a Washington, D.C., federal district, five ma ...

, in a

Jew Jews ( he, יְהוּדִים, , ) or Jewish people are an ethnoreligious group and nation originating from the Israelites Israelite origins and kingdom: "The first act in the long drama of Jewish history is the age of the Israelites""T ...

ish family of Lithuanian extraction.

Education

Mordell was educated at the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

where he completed the

Cambridge Mathematical Tripos The Mathematical Tripos is the mathematics course that is taught in the Faculty of Mathematics at the University of Cambridge. It is the oldest Tripos examined at the University. Origin In its classical nineteenth-century form, the tripos was a ...

as a student of

St John's College, Cambridge St John's College is a constituent college of the University of Cambridge founded by the Tudor matriarch Lady Margaret Beaufort. In constitutional terms, the college is a charitable corporation established by a charter dated 9 April 1511. Th ...

, starting in 1906 after successfully passing the scholarship examination. He graduated as third wrangler in 1909.

Research

After graduating Mordell began independent research into particular

diophantine equation In mathematics, a Diophantine equation is an equation, typically a polynomial equation in two or more unknowns with integer coefficients, such that the only solutions of interest are the integer ones. A linear Diophantine equation equates to ...

s: the question of

integer point In mathematics, the -dimensional integer lattice (or cubic lattice), denoted , is the lattice in the Euclidean space whose lattice points are -tuples of integers. The two-dimensional integer lattice is also called the square lattice, or grid ...

s on the

cubic curve In mathematics, a cubic plane curve is a plane algebraic curve defined by a cubic equation : applied to homogeneous coordinates for the projective plane; or the inhomogeneous version for the affine space determined by setting in such an ...

, and special case of what is now called a

Thue equation In mathematics, a Thue equation is a Diophantine equation of the form :''ƒ''(''x'',''y'') = ''r'', where ''ƒ'' is an irreducible bivariate form of degree at least 3 over the rational numbers, and ''r'' is a nonzero rational number. It i ...

, the

Mordell equation In algebra, a Mordell curve is an elliptic curve of the form ''y''2 = ''x''3 + ''n'', where ''n'' is a fixed non-zero integer. These curves were closely studied by Louis Mordell, from the point of view of determining their integer points. He sho ...

:''y''² = ''x''³ + ''k''. He took an appointment at

Birkbeck College, London , mottoeng = Advice comes over nightTranslation used by Birkbeck. , established = , type = Public research university , endowment = £4.3 m (2014) , budget = £109 ...

in 1913. During

World War I World War I (28 July 1914 11 November 1918), often abbreviated as WWI, was List of wars and anthropogenic disasters by death toll, one of the deadliest global conflicts in history. Belligerents included much of Europe, the Russian Empire, ...

he was involved in war work, but also produced one of his major results, proving in 1917 the multiplicative property of

Srinivasa Ramanujan Srinivasa Ramanujan (; born Srinivasa Ramanujan Aiyangar, ; 22 December 188726 April 1920) was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, ...

's tau-function. The proof was by means, in effect, of the

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 rep ...

s, which had not yet been named after

Erich Hecke Erich Hecke (20 September 1887 – 13 February 1947) was a German mathematician known for his work in number theory and the theory of modular forms. Biography Hecke was born in Buk, Province of Posen, German Empire (now Poznań, Poland). He o ...

; it was, in retrospect, one of the major advances in

modular form In mathematics, a modular form is a (complex) analytic function on the upper half-plane satisfying a certain kind of functional equation with respect to the group action of the modular group, and also satisfying a growth condition. The theory ...

theory, beyond its status as an odd corner of the theory of

special function Special functions are particular mathematical functions that have more or less established names and notations due to their importance in mathematical analysis, functional analysis, geometry, physics, or other applications. The term is defin ...

s. In 1920, he took a teaching position in

UMIST , mottoeng = By Knowledge and Work , established = 1824 , closed = 2004 (merged into newly formed University of Manchester in 2004) , affiliation = , endowment = , officer_in_charge = , chairman ...

, becoming the

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. History In 1870 Samuel Fielden, a wealthy mill owner from Todmorden, donated £150 to Owens College (as the V ...

at the

University of Manchester The University of Manchester is a public university, public research university in Manchester, England. The main campus is south of Manchester city centre, Manchester City Centre on Wilmslow Road, Oxford Road. The university owns and operates majo ...

in 1922 and Professor in 1923. There he developed a third area of interest within number theory, the

geometry of numbers Geometry of numbers is the part of number theory which uses geometry for the study of algebraic numbers. Typically, a ring of algebraic integers is viewed as a lattice in \mathbb R^n, and the study of these lattices provides fundamental informatio ...

. His basic work on Mordell's theorem is from 1921 to 1922, as is the formulation of the

Mordell conjecture Louis Joel Mordell (28 January 1888 – 12 March 1972) was an American-born British mathematician, known for pioneering research in number theory. He was born in Philadelphia, United States, in a Jewish family of Lithuanian extraction. Educati ...

. He was an Invited Speaker of the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rename ...

(ICM) in 1928 in

Bologna Bologna (, , ; egl, label=Emilian language, Emilian, Bulåggna ; lat, Bononia) is the capital and largest city of the Emilia-Romagna region in Northern Italy. It is the seventh most populous city in Italy with about 400,000 inhabitants and 1 ...

and in 1932 in

Zürich , neighboring_municipalities = Adliswil, Dübendorf, Fällanden, Kilchberg, Maur, Oberengstringen, Opfikon, Regensdorf, Rümlang, Schlieren, Stallikon, Uitikon, Urdorf, Wallisellen, Zollikon , twintowns = Kunming, San Francisco Zürich () i ...

and a Plenary Speaker of the ICM in 1936 in

Oslo Oslo ( , , or ; sma, Oslove) is the capital and most populous city of Norway. It constitutes both a county and a municipality. The municipality of Oslo had a population of in 2022, while the city's greater urban area had a population of ...

. 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 (22 July 1902 – 22 October 1979) was a German mathematician, known for his work in algebra. He introduced injective modules in 1940. He is the eponym of Baer rings and Baer groups. Biography Baer studied mechanical engineering f ...

, G. Billing, Paul Erdős,

Chao Ko Ke Zhao or Chao Ko (, April 12, 1910 – November 8, 2002) was a Chinese mathematician born in Wenling, Taizhou, Zhejiang. Biography Ke graduated from Tsinghua University in 1933 and obtained his doctorate from the University of Manchester unde ...

Kurt Mahler Kurt Mahler FRS (26 July 1903, Krefeld, Germany – 25 February 1988, Canberra, Australia) was a German mathematician who worked in the fields of transcendental number theory, diophantine approximation, ''p''-adic analysis, and the geometry o ...

, and

Beniamino Segre Beniamino Segre (16 February 1903 – 2 October 1977) was an Italian mathematician who is remembered today as a major contributor to algebraic geometry and one of the founders of finite geometry. Life and career He was born and studied in Turi ...

. He also recruited

J. A. Todd John Arthur Todd (23 August 1908 – 22 December 1994) was an English mathematician who specialised in geometry. Biography He was born in Liverpool, and went up to Trinity College, Cambridge in 1925. He did research under H.F. Baker, and in ...

Patrick du Val Patrick du Val (March 26, 1903 – January 22, 1987) was a British mathematician, known for his work on algebraic geometry, differential geometry, and general relativity. The concept of Du Val singularity of an algebraic surface is named a ...

Harold Davenport Harold Davenport FRS (30 October 1907 – 9 June 1969) was an English mathematician, known for his extensive work in number theory. Early life Born on 30 October 1907 in Huncoat, Lancashire, Davenport was educated at Accrington Grammar Scho ...

and

Laurence Chisholm Young Laurence Chisholm Young (14 July 1905 – 24 December 2000) was a British mathematician known for his contributions to measure theory, the calculus of variations, optimal control theory, and potential theory. He was the son of William Henry Yo ...

, 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 John William Scott "Ian" Cassels, FRS (11 July 1922 – 27 July 2015) was a British mathematician. Biography Cassels was educated at Neville's Cross Council School in Durham and George Heriot's School in Edinburgh. He went on to study a ...

was one. His idea of supervising research was said to involve the suggestion that a proof of the

transcendence Transcendence, transcendent, or transcendental may refer to: Mathematics * Transcendental number, a number that is not the root of any polynomial with rational coefficients * Algebraic element or transcendental element, an element of a field exten ...

of the

Euler–Mascheroni constant Euler's constant (sometimes also called the Euler–Mascheroni constant) is a mathematical constant usually denoted by the lowercase Greek letter gamma (). It is defined as the limiting difference between the harmonic series and the natural ...

was probably worth a doctorate. His book ''Diophantine Equations'' (1969) is based on lectures, and gives an idea of his discursive style. Mordell is said to have hated administrative duties.

Anecdote

While visiting the

University of Calgary The University of Calgary (U of C or UCalgary) is a public research university located in Calgary, Alberta, Canada. The University of Calgary started in 1944 as the Calgary branch of the University of Alberta, founded in 1908, prior to being inst ...

, the elderly Mordell attended the Number Theory seminars and would frequently fall asleep during them. According to a story by number theorist

Richard K. Guy Richard Kenneth Guy (30 September 1916 – 9 March 2020) was a British mathematician. He was a professor in the Department of Mathematics at the University of Calgary. He is known for his work in number theory, geometry, recreational mathemat ...

, the department head at the time, after Mordell had fallen asleep, someone in the audience asked "Isn't that

Stickelberger's theorem In mathematics, Stickelberger's theorem is a result of algebraic number theory, which gives some information about the Galois module structure of class groups of cyclotomic fields. A special case was first proven by Ernst Kummer (1847) while the ...

?" The speaker said "No it isn't." A few minutes later the person interrupted again and said "I'm positive that's Stickelberger's theorem!" The speaker again said no it wasn't. The lecture ended, and the applause woke up Mordell, and he looked up and pointed at the board, saying "There's old Stickelberger's result!"

References

{{DEFAULTSORT:Mordell, Louis 1888 births 1972 deaths 20th-century British mathematicians Academics of Birkbeck, University of London Academics of the University of Manchester Institute of Science and Technology Academics of the Victoria University of Manchester Alumni of St John's College, Cambridge American people of Lithuanian-Jewish descent British Jews De Morgan Medallists Fellows of St John's College, Cambridge Fellows of the Royal Society Number theorists Mathematicians from Philadelphia Sadleirian Professors of Pure Mathematics Central High School (Philadelphia) alumni American emigrants to the United Kingdom

Education

Research

Anecdote

See also

References