**Gaston Darboux** was a French mathematician who made important contributions to differential geometry and analysis and the Darboux integral is named after him.

- Gaston was born in a house which was a converted chapel of the cathedral.
- His birth certificate clearly gives 1 a.m. on 14 August but Gaston always maintained that he was born at midnight on 13 August.
- Alix took over the business and made strenuous efforts to made sure that both Gaston and Louis received a good education.
- Gaston and Louis both attended the Lycée Nîmes as day pupils, meaning that they attended from six o'clock in the morning until eight o'clock in the evening.
- Gaston entered the lycée in October 1853.
- Gaston Darboux graduated from the lycée in Nîmes on 22 July 1859 and later that year, in October, entered the special mathematics class at the lycée of Montpellier where there were special class to prepare pupils for the entrance examinations to the École Polytechnique and the École Normale Supérieure.
- After one year at lycée of Montpellier, Darboux sat the entrance examinations for the École Polytechnique, not because he wanted to enter in 1860, but simply because he wanted to please his teacher, Charles Berger, who was keen for his star pupil to sit the examinations.
- A good performance meant that Darboux gained admission but he preferred to spend another year at Montpellier and take the entrance examinations for both Grand École in the following year.
- Darboux chose to enter the École Normale Supérieure, because he wanted to become a professor.
- It was a significant decision, not just for the young man, but for the École Normale since other top mathematicians soon followed Darboux's example.
- He was delighted that the person topping the list had chosen the École Normale and he requested the Minister to allow Darboux to attend any of the courses which he liked outside the École.
- The Minister granted permission so Darboux was able to attend, at the Collège de France, the lectures of Joseph Bertrand, with whom he developed a deep friendship.
- Darboux was awarded the Licencié ès Sciences mathématiques on 9 July 1863 and the Licencié ès Sciences physiques on the 7 August 1863.
- Now Pasteur was aware that he had a student of outstanding qualities and he was very keen that Darboux remained in Paris so he created a position of "préparateur agrégé de Mathématiques" at the École Normale.
- Darboux had studied the work of Lamé, Dupin and Bonnet on orthogonal systems of surfaces.
- These results were included in Darboux's doctoral thesis Sur les surfaces orthogonales Ⓣ(On orthogonal surfaces) for which he awarded his doctorate after defending his thesis on 14 July 1866.
- M Darboux, taking as a starting point the theorem of M Dupin, according to which in any triple system of orthogonal surfaces the intersection curves of the surfaces are their lines of curvature, to which he adds as a complement the following statement: "When two systems of orthogonal surfaces intersect along the lines of curvature of these surfaces, there is a third system orthogonal to the first two," first gives a simple demonstration of this theorem by M Ossian Bonnet, that the search for all orthogonal systems amounts to the complete integration of a third order partial difference equation with three independent variables.
- The second case treated by M Darboux is that of surfaces for which the lines of curvature are plane in the three systems.
- M Darboux had already observed, in the first Part, that the surfaces of the triple orthogonal system previously discovered by M Moutard and by himself enjoy the property in question.
- Darboux had been appointed as a substitute for Joseph Bertrand to teach the special mathematics course at the Lycée Saint-Louis in Paris in 1864-65 while still undertaking research for his doctorate.
- Two years later Chasles died and Darboux succeeded him to the chair of higher geometry, holding this chair until his death.
- Darboux made important contributions to differential geometry and analysis.
- he followed in the spirit of Gaspard Monge, and Darboux's spirit can be detected in the work of Élie Cartan.
- He may now be best known for the Darboux integral which is named after him.
- In 1873 Darboux wrote a paper on cyclides and between 1887 and 1896 he produced four volumes on infinitesimal geometry which included most of his earlier work it was titled Leçons sur la théorie général des surfaces et les applications géométriques du calcul infinitésimal .
- Darboux also studied the problem of finding the shortest path between two points on a surface.
- However Darboux was also renowned as an exceptional teacher, writer and administrator.
- Darboux's varied powers combined with his personality in making him a great teacher, so that he always had about him a group of able students.
- Darboux is known for a wider range of mathematics than that described above.
- Of course Darboux received many honours for his work.
- Darboux represented France at the funeral of Lord Kelvin in Westminster Abbey in December 1907.
- In 1908 Darboux was a plenary speaker at the International Congress of Mathematicians held in Rome in 1908.
- In all circumstances of life, M Darboux proceeds methodically; one should therefore not be surprised to find this quality when he develops his course programme and writes the equations on the board in the order in which they appear.
- M Darboux remained simple and modest, although he came to a very high position.
- Darboux is buried in Montparnasse Cemetery in the City of Paris.

Born 13 August 1842, Nimes, Gard, Languedoc, France. Died 23 February 1917, Paris, France.

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