[2] In 1872, Halphen settled in Paris, where he became a lecturer at the École Polytechnique and began his scientific studies.

Of the four sons, three joined the military and two of them died in World War I. Louis Halphen (1880-1950) was a French historian specialized in medivial times; Charles Halphen (1885-1915), was deputy secretary of the Société mathématique de France.

[4] Georges-Henri Halphen received in the Steiner prize of the Prussian Academy of Sciences in 1882 along with Max Noether.

In 1881 Halphen received the Grand Prix of the Académie des sciences for his work on linear differential equations: Mémoire sur la Reduction des Equations Différentielles Linéaires aux Formes Intégrales.

[8] He was elected to the Académie des sciences in 1886 in the Section de Géométrie, replacing the deceased Jean Claude Bouquet.