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Louis Joel Mordell (28 January 1888 - 12 March 1972) was a British mathematician, known for pioneering research in number theory. He was born in Philadelphia, USA, in a Jewish family of Lithuanian 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 equations: the question of integer points on the cubic curve, and special case of what is now called a Thue equation, the Mordell equation

Y² = X³ + k.

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 operators, which had not yet been christened for 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, and the Sadleirian Chair, as Head of Department, and 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 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.

See also: Chowla-Mordell theorem.

O'Connor, John J; Edmund F. Robertson "Louis Mordell". MacTutor History of Mathematics archive.