**Jules Hoüel** was a French mathematician who publicised non-Euclidean geometry. He also worked on mathematical astronomy.

- One finds the spelling Houel, Hoüel, Hoûel or Houël but deciding which is 'correct' shows immediately the problem.
- On his birth certificate his name appears as Houël but it appears as Hoüel on his baccalaureate certificate, and all his published papers and books give the Hoüel version.
- When he signed his name it usually looks like Hoüel but sometimes it appears as Hoûel.
- After marrying, Jean Baptiste and Elisabeth lived sometimes at Bombanville, sometimes at Périers at their parents' home, but by 1823, around the time Jules was born, they only lived at Bombanville.
- In October 1838 Jules began his schooling, entering the third grade of the Royal College of Caen.
- Hoüel entered the Collège Rollin in Paris on 29 October 1841.
- Faurie's reports show that Hoüel began his studies well and made excellent progress.
- Hoüel sat the written examinations for entry to the École Normale Supérieure in August 1843 and on 15 October of that year he was given an oral examination.
- Hoüel, ranked eighth, was admitted with a half-fees scholarship.
- Two of the twelve who entered with Hoüel had dropped out, so he was ninth from ten students.
- In his third year of study, Hoüel did teaching practice which was at the Collège Rollin in M Faurie's class.
- Faurie's report is very positive and says that Hoüel will make a good teacher.
- Hoüel had always lacked confidence as a public speaker, something which had been first noted by his teacher Faurie when he was a student at the Collège Rollin.
- After leaving the École Normale Supérieure, Hoüel was appointed as a mathematics teacher to the Collège de Bastia in Corsica in September 1846.
- A second report states that "M Hoüel is undoubtedly an educated teacher, but he does not have the qualities needed to maintain discipline in a large class." The year 1848-49 went very badly and the headmaster of the Royal College of Bordeaux asked for Hoüel to be transferred to a school where the classes were much smaller.
- The Minister chose not to send Hoüel to a post in or near Paris but instead assigned him a position at the Lycée de Pau, a much lower quality school than the one he had taught in.
- At Pau, Hoüel received somewhat better reports for 1849-50 although his teaching was said to be too theoretical and he did not enthuse his pupils.
- On 8 March 1851 Hoüel was appointed to the Lycée de Alençon.
- The Minister of Education declared on 22 September 1852 that the higher mathematics classes at Alençon were to be closed and Hoüel was to be transferred to the Lycée de Poitiers to teach elementary mathematics.
- Hoüel, with support from several others, begged to be allowed to remain in Alençon.
- Hoüel continued teaching at Alençon and, at the same time, worked on his doctoral thesis.
- On 18 August 1855, Hoüel submitted two theses to the Faculty of Science in Paris.
- Urbain Le Verrier was impressed with Hoüel's research work and tried to persuade him to accept a post at the Observatory in Paris.
- Hoüel, however, decided not to accept the offer and spent the next four years undertaking research at his home in Thaon.
- Hoüel was appointed to the chair of pure mathematics in the Faculty of Science at Bordeaux in 1859 and held this post until his death.
- Hoüel published, Essai d"une exposition rationnelle des principes fondamentaux de la Géométrie élémentaire, a work on geometry, in 1863.
- Hoüel became interested in non-euclidean geometry once he had been made aware of the work of János Bolyai and Nikolai Lobachevsky.
- Hoüel's 'Essai' of 1863 having come by chance into the hands of a young architect of Temesvár in Hungary, this youth Franz Schmidt, desirous of continuing his mathematical studies wrote for counsel to Hoüel.
- Hoüel had answered helpfully, and later implored the aid of Schmidt to procure Bolyai's work ...
- Schmidt succeeded in procuring for Hoüel two copies of Bolyai's work.
- One Hoüel proceeded to translate himself, the other he sent to Battaglini, asking him to make known in Italy this wonderful idea.
- At Hoüel's suggestion Schmidt collected material which enabled him to write the first biography of Bolyai which he did in 1868.
- Among his other researches, Hoüel compiled log tables Table de logarithmes à cinq décimales pour les nombres et pour les lignes trigonométriques, suivies des logarithmes d'addition et de soustraction et de diverses tables usuelles Ⓣ(Five-decimal logarithm table for numbers and trigonometric lines, followed by addition and subtraction logarithms and various usual tables) (1858).
- One important feature of Hoüel's work was his extensive correspondence with other mathematicians.
- Following a detailed, 80-page-long presentation of the terms of the debate in their historical context, the book consists of 191 letters between Jules Hoüel and Joseph Marie de Tilly, 66 letters between Hoüel and Darboux, and 11 letters between Hoüel and Victor-Amédée Le Besgue, written between 1867 and 1868, as well as a few letters between Hoüel and Catalan, Kowalski, and Beltrami.
- His obituary written by Gaston Darboux shows that Hoüel had a brilliant career as a professor, producing outstanding research papers and making a remarkable contribution to mathematics through his extensive correspondence.

Born 7 April 1823, Thaon, Calvados, France. Died 14 June 1886, Périers sur le Dan (near Caen), France.

View full biography at MacTutor

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive