Jean-Gaston Darboux FAS MIF FRS FRSE (French: [daʁbu]; 14 August 1842 – 23 February 1917) was a French mathematician.^[2]

According to his birth certificate,^[3] he was born in Nîmes in France on 14 August 1842, at 1 am. However, probably due to the midnight birth, Darboux himself usually reported his own birthday as 13 August, e.g. in his filled form for Légion d'Honneur.^[4]

His parents were François Darboux, businessman of mercery, and Alix Gourdoux. The father died when Gaston was 7. His mother undertook the mercery business with great courage, and insisted that her children receive good education. Gaston had a younger brother, Louis, who taught mathematics at the Lycée Nîmes for almost his entire life.^[5]

He studied at the Nîmes Lycée and the Montpellier Lycée before being accepted as the top qualifier at the École Normale Supérieure in 1861,^[6] and received his PhD there in 1866. His thesis, written under the direction of Michel Chasles, was titled Sur les surfaces orthogonales. During his studies at the ENS, he also took lectures in Sorbonne University and Collège de France.

In 1870, he co-founded the journal Bulletin des sciences mathématiques et astronomiques,^[7] called "Darboux's Journal" by his contemporary mathematicians. The publishing house was the Henry Gauthier-Villars et Cie Éditeurs, located in Paris.^[8]

In 1872, Darboux married the Beauvaisian milliner Amélie 'Célina' Carbonnier (1848–1911), daughter of Charles Louis Carbonnier, tailor, and Marie Victorine Anastase Hènocq. He and Célina had two children, Jean-Gaston (1870–1921), who was born at the time of the Siege of Paris and later became a marine zoologist at the Faculty of Science in Marseille, and Anaïs Berthe Lucie (1873–1970).^[9]

He participated in the foundation of the École normale supérieure de jeunes filles in 1880, an institute that aimed at training female educators and ran parallel to the École Normale Supérieure. Its first director was Julie Favre.^[10]

In 1884, Darboux was elected to the Académie des Sciences.

Darboux made several important contributions to geometry and mathematical analysis (see, for example, linear PDEs). He was a biographer of Henri Poincaré and he edited the Selected Works of Joseph Fourier.

Among his students were Émile Borel, Élie Cartan, Édouard Goursat, Émile Picard, Gheorghe Țițeica and Stanisław Zaremba.

In 1892 he was awarded honorary membership of the Manchester Literary and Philosophical Society,^[11] and in 1900, he was appointed the academy's permanent secretary of its Mathematics section.

In 1902, he was elected to the Royal Society and the American Philosophical Society;^[12] in 1916, he received the Sylvester Medal from the Society. In 1908, he was a plenary speaker at the International Congress of Mathematicians in Rome.^[13] He continued to contribute to the French Bulletin des sciences mathématiques, even after 1916.^[8]

There are many things named after him:

• Envelope theorem

• "A biography in Weisstein's World of Biography".
• O'Connor, John J.; Robertson, Edmund F., "Jean Gaston Darboux", MacTutor History of Mathematics Archive, University of St Andrews
• Jean Gaston Darboux at the Mathematics Genealogy Project