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

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

. He was born in

Philadelphia Philadelphia ( ), colloquially referred to as Philly, is the List of municipalities in Pennsylvania, most populous city in the U.S. state of Pennsylvania and the List of United States cities by population, sixth-most populous city in the Unit ...

United States The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...

, in a

Jew Jews (, , ), or the Jewish people, are an ethnoreligious group and nation, originating from the Israelites of ancient Israel and Judah. They also traditionally adhere to Judaism. Jewish ethnicity, religion, and community are highly inte ...

ish family of

Lithuania Lithuania, officially the Republic of Lithuania, is a country in the Baltic region of Europe. It is one of three Baltic states and lies on the eastern shore of the Baltic Sea, bordered by Latvia to the north, Belarus to the east and south, P ...

n extraction.

Education

Mordell was educated at the

University of Cambridge 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 ...

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. Origin In its classical nineteenth-century form, the tripos was a distinctive written examination of undergraduate s ...

as a student of

St John's College, Cambridge St John's College, formally the College of St John the Evangelist in the University of Cambridge, is a Colleges of the University of Cambridge, constituent college of the University of Cambridge, founded by the House of Tudor, Tudor matriarch L ...

, 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 ''Diophantine'' means pertaining to the ancient Greek mathematician Diophantus. A number of concepts bear this name: *Diophantine approximation In number theory, the study of Diophantine approximation deals with the approximation of real n ...

s: the question of integer points 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 eq ...

, and special case of what is now called a Thue equation, the Mordell equation :''y''² = ''x''³ + ''k''. He took an appointment at Birkbeck College, London in 1913. During

World War I World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...

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 Aiyangar (22 December 188726 April 1920) was an Indian mathematician. Often regarded as one of the greatest mathematicians of all time, though he had almost no formal training in pure mathematics, he made substantial con ...

'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 ...

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

modular form In mathematics, a modular form is a holomorphic function on the complex upper half-plane, \mathcal, that roughly satisfies a functional equation with respect to the group action of the modular group and a growth condition. The theory of modul ...

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 defined by ...

s. In 1920, he took a teaching position in

UMIST The University of Manchester Institute of Science and Technology (UMIST) 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 univer ...

, 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 of Manchester is c ...

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 (group), lattice in \mathbb R^n, and the study of these lattices provides fundam ...

. His basic work on Mordell's theorem is from 1921 to 1922, as is the formulation of the Mordell conjecture. 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 IMU Abacus Medal (known before ...

(ICM) in 1928 in

Bologna Bologna ( , , ; ; ) is the capital and largest city of the Emilia-Romagna region in northern Italy. It is the List of cities in Italy, seventh most populous city in Italy, with about 400,000 inhabitants and 150 different nationalities. Its M ...

and in 1932 in

Zürich Zurich (; ) is the list of cities in Switzerland, largest city in Switzerland and the capital of the canton of Zurich. It is in north-central Switzerland, at the northwestern tip of Lake Zurich. , the municipality had 448,664 inhabitants. The ...

and a Plenary Speaker of the ICM in 1936 in

Oslo Oslo ( or ; ) 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 1,064,235 in 2022 ...

. 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, Baer groups, and Baer subplanes. Biography Baer studied mecha ...

, G. Billing,

Paul Erdős Paul Erdős ( ; 26March 191320September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in discrete mathematics, g ...

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 – 25 February 1988) was a German mathematician who worked in the fields of transcendental number theory, diophantine approximation, ''p''-adic analysis, and the geometry of numbers.

, 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 Turin. ...

. He also recruited J. A. Todd,

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 af ...

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 and education Born on 30 October 1907 in Huncoat, Lancashire, Davenport was educated at Accringto ...

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 You ...

, 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, Fellow of the Royal Society, FRS (11 July 1922 – 27 July 2015) was a British mathematician. Biography Cassels was educated at Neville's Cross Council School in Durham, England, Durham and George Heriot's ...

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

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

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 {{Infobox university , name = University of Calgary , image = University of Calgary coat of arms without motto scroll.svg , image_size = 150px , caption = Coat of arms , former ...

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