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

He was born in Nimes in France on 13 August 1842. He studied at the Nimes Lycee and the Montpellier Lycee before being accepted at the Sorbonne.^{[3]}

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.

Darboux received his Ph.D. from the École Normale Supérieure in 1866. His thesis, written under the direction of Michel Chasles, was titled *Sur les surfaces orthogonales*. In 1884, Darboux was elected to the Académie des Sciences. In 1900, he was appointed the Academy's permanent secretary of its Mathematics section.

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

Darboux's contribution to the differential geometry of surfaces appears in the four-volume collection of studies he published between 1887 and 1896; see links below for access to these texts.

In 1902, he was elected to the Royal Society; in 1916, he received the Sylvester Medal from the Society.

He was a plenary speaker in the International Congress of Mathematicians 1908, Rome.^{[4]}

There are many things named after him:

- Darboux basis
- Darboux chart
- Darboux cubic
^{[5]} - Darboux derivative
- Darboux equation
- Darboux frame
- Darboux integral
- Darboux net invariants
- Darboux
^{[6]}or Goursat problem^{[7]} - Darboux transformation
- Darboux vector
^{[8]} - Darboux's problem
- Darboux's theorem in symplectic geometry
- Darboux's theorem in real analysis, related to the intermediate value theorem
- Darboux's formula
^{[9]} - Christoffel–Darboux identity
^{[10]} - Christoffel–Darboux formula
^{[11]} - Euler–Darboux equation
^{[12]} - Euler–Poisson–Darboux equation
^{[13]}

1887–96. *Leçons sur la théorie générale des surfaces et les applications géométriques du calcul infinitésimal*. Gauthier-Villars:

1898. *Leçons sur les systèmes orthogonaux et les coordonnées curvilignes*. Tome I. Gauthier-Villars.^{[14]}

- ^
^{a}^{b}Jean Gaston Darboux at the Mathematics Genealogy Project **^**Eisenhart, L. P. (1918). "Darboux's contribution to geometry".*Bull. Amer. Math. Soc*.**24**(5): 227–237. MR 1560051. doi:10.1090/s0002-9904-1918-03052-8.**^**https://www.royalsoced.org.uk/cms/files/fellows/biographical_index/fells_indexp1.pdf**^**"ICM Plenary and Invited Speakers since 1897". International Congress of Mathematicians.**^**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**^**Lovett, E. O. (1899). "Review:*Leçons sur les Systèmes Orthogonaux et les Coordonnées Curvilignes*, Tome I, by Gaston Darboux".*Bull. Amer. Math. Soc*.**5**(4): 185–202. doi:10.1090/s0002-9904-1899-00584-6.

- "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.

- 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

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