**Eugène Rouché** was a French geometer best known for his theorem on complex functions.

- His parents were Jean Jacques Rouché (1818-1861) and Marie Nicot (1807-1861).
- Rouché completed his schooling at the Sainte-Barbe College in Rue Valette in Paris.
- In 1852, after success in the entrance examinations to the Grandes Écoles, Rouché entered the École Polytechnique.
- Rouché graduated from the École Polytechnique in 1854 after two years of study.
- After training as a mathematician, Rouché taught for one year at Nantes where he was appointed professor of physics at the Lycée de Nantes.
- At this stage Rouché had spent only two undergraduate years for his university of mathematics and physics and he had no research degree.
- Rouché dedicated his two doctoral theses to Auguste Nouseilles (1798-1881), Principal of the Lycée Charlemagne.
- Rouché was awarded his doctorate but we have to feel a little sorry for him since Lefébure de Fourcy had a reputation as a difficult examiner.
- In 1858 Rouché was appointed as admissions examiner for the École Centrale in Paris, a position he held until 1877.
- In 1867 Rouché was nominated professor of descriptive geometry and stereotomy at the École Centrale in Paris.
- Rouché published many mathematics articles, among them were some which appeared in Comptes Rendus and some in the Journal of the École Polytechnique.
- Rouché later published a fuller version of this theorem in 1880 in the Journal de l'École Polytechnique.
- He was not the first to prove such a result and, after Rouché's paper appeared, Georges Fontené published a note in the Nouvelles Annales de Mathématiques claiming priority.
- However it is now often called the Rouché-Frobenius theorem, especially in the Spanish speaking world.
- Rouché also wrote several textbooks including Eléments d'algèbre à l'usage des candidats au baccalauréat és sciences et aux écoles spéciales Ⓣ(Elements of algebra for candidates for the baccalaureate of science and special schools) (1857), Leçons nouvelles de trigonométrie rectiligne et sphérique Ⓣ(New lessons in rectilinear and spherical trigonometry) (written jointly with L Lacour) (1857), Traité de géométrie élémentaire Ⓣ(Treatise on elementary geometry) (written jointly with Charles de Comberousse) (1864-1866), Éléments de Statique Graphique Ⓣ(Elements of graphic statics) (1889), Coupe des pierres: précédée des principes du trait de stéréotomie Ⓣ(Cutting stones: preceded by the principles of the theory of stereotomy) (written jointly with Charles Brisse) (1893), and Analyse infinitésimale à l'usage des ingénieurs Ⓣ(Infinitesimal analysis for engineers) (2 volumes) (1900-1902).
- Editions continued to be published after Rouché's death, with a new edition published in Paris by Gauthier-Villars in 1922 and another in 1954.
- Edmond Laguerre died in 1886 and Rouché became one of the editors to work on the production of his Collected Works.
- Rouché was a member of the Société Mathématique de France, serving as its president in 1883-84.
- The town of Lunel where Rouché died is close to his birthplace of Sommières.

Born 18 August 1832, Sommières, Occitanie, Languedoc, France. Died 19 August 1910, Lunel, Hérault, Languedoc, France.

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