Jean Gaston Darboux

Jean-Gaston Darboux
File:Jean Gaston Darboux, ante 1917 - Accademia delle Scienze di Torino 0123 B.jpg Jean-Gaston Darboux
Born	(1842-08-14)14 August 1842 Nîmes, France
Died	Paris, France
Alma mater	Ecole Normale Supérieure (in Paris)
Thesis	Sur les surfaces orthogonales[1] (1866)
Doctoral advisor	Michel Chasles
Doctoral students	Émile Borel Élie Cartan Édouard Goursat Émile Picard Thomas Stieltjes Gheorghe Țițeica Stanisław Zaremba
Notable awards	Sylvester Medal (1916)

Jean-Gaston Darboux FAS MIF FRS FRSE (14 August 1842 – 23 February 1917) was a French mathematician.

Life

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.

He studied at the Nîmes Lycée and the Montpellier Lycée before being accepted as the top qualifier at the École normale supérieure in 1861, and received his Ph.D. 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.

File:Darboux as a student of the Ecole Normale.png

Darboux as a student of the Ecole Normale. ca. 1865

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 Cle Éditeurs, located in Paris.

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).

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.

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; 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. He continued to contribute to the French Bulletin des sciences mathématiques, even after 1916.

Named in his honour

There are many things named after him:

• Darboux basis
• Darboux chart
• Darboux cubic
• Darboux derivative
• Darboux equation
• Darboux frame
• Darboux integral
• Darboux net invariants
• Darboux or Goursat problem
• Darboux transformation
• Darboux vector
• Darboux's problem
• Darboux's theorem in symplectic geometry
• Darboux's theorem in real analysis, related to the intermediate value theorem
• Darboux's formula
• Christoffel–Darboux identity
• Christoffel–Darboux formula
• Euler–Darboux equation
• Darboux–Froda's theorem
• Euler–Poisson–Darboux equation

Work

Papers and essays (incomplete list)

• 1870. Sur les équations aux dérivées partielles du second ordre Annales scientifiques de l’É.N.S. 1re série, tome 7 (1870), p. 163-173
• 1871. Sur la représentation des surfaces algébriques Bulletin des sciences mathématiques et astronomiques, tome 2 (1871), p. 155-158
• 1872. Mémoire sur les surfaces cyclides Annales scientifiques de l’É.N.S. 2e série, tome 1 (1872), p. 273-292
• 1872. Sur les relations entre les groupes de points, de cercles et de sphères dans le plan et dans l’espace Annales scientifiques de l’É.N.S. 2e série, tome 1 (1872), p. 323-392
• 1872. Sur un théorème relatif à la continuité des fonctions Bulletin des sciences mathématiques et astronomiques, tome 3 (1872), p. 307-313
• 1875. Mémoire sur les fonctions discontinues Annales scientifiques de l’É.N.S. 2e série, tome 4 (1875), p. 57-112. In it were introduced the Darboux integral (based on the limit of upper and lower integrals) and Darboux's theorem in analysis.
• 1875. Sur la composition des forces en statique Bulletin des sciences mathématiques et astronomiques, tome 9 (1875), p. 281-288
• 1890. Sur le déplacement d’une figure invariable Annales scientifiques de l’É.N.S. 3e série, tome 7 (1890), p. 323-326

Books

1873. Sur une classe remarquable de courbes et de surfaces algébriques et sur la théorie des imaginaires. Gauthier-Villars.

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.

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

• Vol. 1. The Darboux frame is introduced in Section 4 of this volume.
• Vol. 2.
• Vol. 3.
• Vol. 4.

1898. Leçons sur les systèmes orthogonaux et les coordonnées curvilignes. Tome I. Gauthier-Villars.

See also

• Envelope theorem

External links

Media related to at Wikimedia Commons

• .
• Jean Gaston Darboux at the Mathematics Genealogy Project