French army officer and mathematician; born at Rouen Oct. 30, 1844 died at Versailles May 21, 1889. He studied at the Ecole Polytechnique, and afterward at the Ecole de Metz, becoming lieutenant in 1866 and captain in 1870. He was decorated on the battle-field of Pont-Noyelles, and fought also at Bapaume and Saint-Quentin. In 1873 Halphen became tutor at the Ecole Polytechnique, and in 1880 the Académic des Sciences of the French Institute awarded him the chief mathematical prize for his "Mémoire sur la Reduction des Equations Différentielles Linéaires aux Formes Intégrales." In 1881 his work on the classification of curves ("Journal de l'Ecole Polytechnique," lvii. 1) was crowned by the Academy of Berlin. In 1886 Halphen was made a member of the Académic des Sciences. He returned to active service in 1887 as major. Of Halphen's many mathematical treatises may be mentioned: "Sur la Théorie des Points Singuliers des Courbes"; "Sur les Congruences"; "Sur les Equations Différentielles"; "Sur les Courbes Gauches, les Fonctions Elliptiques," etc. He devoted the last three years of his life to his "Traité des Fonctions Elliptiques et de Leurs Applications" (Paris, 1886-89; the third volume posthumous). A full list of his works is given in the "Journal des Mathématiques," 1889.
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