**Mordell** is best known for his investigations of equations of the form of $y^2=x^3+k$ which had been studied by Fermat.

- Louis became fascinated by mathematics while at grammar school.
- These books presented many examples taken from the Cambridge Tripos examinations and Louis soon came to look on Cambridge University in England as the place of highest mathematical learning.
- When we wrote that Louis was "essentially self-taught" in mathematics we certainly did not wish to imply that he did not receive a good schooling, just that this schooling did little to introduce him to anything beyond elementary mathematics.
- The mathematics course at the Central High School should have taken four years to complete but Mordell took only two since his teachers quickly recognised his remarkable talent.
- Certainly Mordell would have not learnt enough mathematics at the Central High School to allow him to compete with the best students at Cambridge, but he was ambitious enough to want to do exactly this.
- Rather remarkably, Mordell's future research interests were determined by these books, and his love of indeterminate equations came from this period.
- In December 1906 Mordell travelled to England in order to take the Cambridge University Scholarship examinations.
- Mordell had to earn the money for his passage to England, and this he did, with some help from his parents, mainly by tutoring his fellow pupils for seven hours a day to earn enough to pay for his passage.
- Mordell's gamble paid off handsomely, however, for he was placed first in the Cambridge Scholarship Examination and entered St John's College.
- Mordell later wrote that he had found Baker unsympathetic and he felt that he would have done better with G H Hardy at Trinity.
- Mordell graduated as Third Wrangler in the Mathematical Tripos (ranked third in the list of First Class students) and this may at least partly be explained by the fact that his coach Bromwich did not have the success of R A Herman who coached both the First and Second Wranglers.
- There was no doctoral degree at Cambridge at this time, unlike the German universities, but Mordell remained at Cambridge to undertake research in number theory.
- Thue had already proved a result which, combined with Mordell's work showed that this equation had only finitely many solutions but Mordell only learned about Thue's work at a later date.
- At the time he wrote the essay Mordell believed that for some kkk there may be infinitely many solutions.
- Mordell was awarded the second Smith's Prize with his essay, and he went on to publish a long paper on this equation, now sometimes called Mordell's equation, in the Proceedings of the London Mathematical Society.
- Mordell submitted his subsequent work on indeterminate equations of the third and fourth degree when he became a candidate for a Fellowship at St John's College, but he was not successful.
- Mordell was bitterly disappointed at the way his paper had been received.
- In 1913 Mordell was offered a post at Birkbeck College, London, and one in Nova Scotia.
- He continued working for the Ministry of Munitions after the war ended in 1918 and it was only in the following year that Mordell was able to return to his academic post at Birkbeck College.
- In Mordell's paper in which his finite basis theorem appeared he conjectured that there are only finitely many rational points on any curve of genus greater than one.
- In 1983 Faltings proved the Mordell conjecture to be true.
- In 1922 Mordell went to Manchester University as a Reader.
- Together with Davenport and Mahler, Mordell initiated great advances in the geometry of numbers while he held the Chair of Pure Mathematics at Manchester.
- Mordell was elected a Fellow of the Royal Society in 1924, although at this stage he was still an American citizen; he became a British subject in 1929.
- After he returned to Cambridge in 1945, Mordell held the Sadleirian Chair and a fellowship at his old College of St John's where he had failed to be elected to a fellowship over thirty years before.
- In 1953 Mordell retired from the Sadleirian Chair but he most certainly did not retire from mathematics; almost half of Mordell's 270 publications appeared after his retirement.
- By 1971, although by now well into his eighties, Mordell was still travelling enthusiastically.
- As well as the honours from the Royal Society and the London Mathematical Society which we mentioned above, Mordell also received honorary degrees from several universities (Glasgow, Mount Allison and Waterloo) and was elected a member of the Academies of Oslo, Uppsala and Bologna.

Born 28 January 1888, Philadelphia, Pennsylvania, USA. Died 12 March 1972, Cambridge, England.

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Origin Usa

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive