He was the son of Simon Marie (1775–1855) an infantry captain in Napoleon's Grande Armée from a modest background, and Henriette Josephine de Ficquelmont (1780–1843), poor, but from the nobility of Lorraine.

Comte fell passionately in love with her, a feeling that she did not reciprocate,[5] and the one-sided affair ended when Clotilde suddenly died of tuberculosis a year later.

In 1862, backed by the famous mathematicians Joseph Liouville and General Jean-Victor Poncelet, Maximilien Marie was appointed professor of Mechanics at the École Polytechnique.

He published a 12-volume encyclopedia, History of the Mathematics,[8] which was divided into two parts: Théorie des fonctions de variables imaginaires (tomes I à III, Gauthier-Villars, 1874–1876, 3 vol.)

He had one elder sister, the famous positivist muse Clotilde de Vaux, and one younger brother, Léonard Marie (1820–1860), chevalier of the Légion d'honneur, who was also a military officer trained at the École Polytechnique and who died without issue at the Battle of Palikao.