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.
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.
There are many things named after him:
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.
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