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

Jean-Gaston Darboux | |
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Born | |

Died | 23 February 1917 Paris, France | (aged 74)

Alma mater | Ecole Normale Supérieure (in Paris) |

Awards | Sylvester Medal (1916) ForMemRS (1902) Poncelet Prize (1875) |

Scientific career | |

Thesis | Sur les surfaces orthogonales (1866) |

Doctoral advisor | Michel Chasles^{[1]} |

Doctoral students | Émile Borel Élie Cartan Édouard Goursat Émile Picard Thomas Stieltjes Gheorghe Țițeica Stanisław Zaremba |

According to his birth certificate, 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.

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.^{[3]}

He studied at the Nîmes Lycée and the Montpellier Lycée before being accepted as the top qualifier at the École normale supérieure in 1861,^{[4]} 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*, called "Darboux's Journal" by his contemporary mathematicians. The editorial board was also formed by the mathematicians Paul Émile Appell, Émile Borel, Jacques Hadamard and Amedeo Guillet, with Darboux in the role of President. The publishing house was the Henry Gauthier-Villars et Cie Éditeurs, located in Paris.^{[5]}

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).^{[6]}

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 on rue d'Ulm. Its first director was Julie Favre.^{[7]}

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 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;^{[8]} 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.^{[9]}
He continued to contribute to the French *Bulletin des sciences mathématiques*, even after 1916.^{[5]}

There are many things named after him:

- Darboux basis
- Darboux chart
- Darboux cubic
^{[10]} - Darboux derivative
- Darboux equation
- Darboux frame
- Darboux integral
- Darboux net invariants
- Darboux
^{[11]}or Goursat problem^{[12]} - Darboux transformation
- Darboux vector
^{[13]} - Darboux's problem
- Darboux's theorem in symplectic geometry
- Darboux's theorem in real analysis, related to the intermediate value theorem
- Darboux's formula
^{[14]} - Christoffel–Darboux identity
^{[15]} - Christoffel–Darboux formula
^{[16]} - Euler–Darboux equation
^{[17]} - Darboux–Froda's theorem
- Euler–Poisson–Darboux equation
^{[18]} - Laplace–Darboux transformations

**^**Jean Gaston Darboux at the Mathematics Genealogy Project**^**Eisenhart, Luther P. (1918). "Darboux's contribution to geometry".*Bulletin of the American Mathematical Society*.**24**(5): 227–237. doi:10.1090/s0002-9904-1918-03052-8. MR 1560051.**^**"Enfance des célébrités contemporains: Gaston Darboux". March 1913.**^**"Former Fellows of the Royal Society of Edinburgh" (PDF). Archived from the original (PDF) on 2013-01-24. Retrieved 2016-01-13.- ^
^{a}^{b}*Bulletin des sciences mathématiques*(in French). Paris: Gauthiers et Villars C^{le}, Éditeurs. 1916. p. 7. **^**Roland Brasseur – Dictionnaire des professeurs de mathématiques en classe de mathématiques spéciales – 7 mai 2015 https://pdfkul.com/darboux-rb-dico-prof-spes-20150507pdf_59d309be1723dde389357150.html**^***Biographie de Gaston Darboux*by Marianne Durand at Lycée Professionnel Gaston Darboux https://www.lyc-darboux-nimes.ac-montpellier.fr/l-etablissement-en-pratique/biographie-de-gaston-darboux Archived 2020-10-28 at the Wayback Machine**^**"APS Member History".*search.amphilsoc.org*. Retrieved 2021-05-19.**^**"ICM Plenary and Invited Speakers since 1897". International Congress of Mathematicians. Archived from the original on 2017-11-08. Retrieved 2013-08-17.**^**Darboux Cubic -- from Wolfram MathWorld at mathworld.wolfram.com**^**Darboux Problem -- from Wolfram MathWorld at mathworld.wolfram.com**^**Goursat Problem -- from Wolfram MathWorld at mathworld.wolfram.com**^**Darboux Vector -- from Wolfram MathWorld at mathworld.wolfram.com**^**Darboux's Formula -- from Wolfram MathWorld at mathworld.wolfram.com**^**Christoffel-Darboux Identity -- from Wolfram MathWorld at mathworld.wolfram.com**^**Christoffel-Darboux Formula -- from Wolfram MathWorld at mathworld.wolfram.com**^**Euler-Darboux Equation -- from Wolfram MathWorld at mathworld.wolfram.com**^**Euler-Poisson-Darboux Equation -- from Wolfram MathWorld at mathworld.wolfram.com

- "Darboux, Jean-Gaston".
*Biographical Dictionary of Mathematicians*. Charles Scribner's Sons. 1991. - Lebon, Ernest (1910).
*Gaston Darboux*. Gauthier-Villars. - Fourier, Joseph (1888–1890).
*Œuvres de Fourier*. Paris: Gauthier-Villars. ISBN 2-05-100578-8.

Wikimedia Commons has media related to Gaston Darboux.

- "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