Barré de Saint-Venant developed a version of vector calculus similar to that of Grassmann (now understood as exterior differential forms) which he published in 1845.

Barré de Saint-Venant would follow in his father's footsteps in science, entering the École Polytechnique, in 1813 at sixteen years old, and studying under Gay-Lussac.

Following a disagreement on an issue of road with the Municipal Administration of Paris, he was suddenly retired as "Chief Engineer, second class", on 1 April 1848.

In 1850 Saint-Venant won a contest to be appointed the chair of Agricultural Engineering at the Agronomic Institute of Versailles, a post he occupied two years.

[5] He went on to teach mathematics at the École des Ponts et Chaussées (National school of Civil Engineering) where he succeeded Coriolis.