From 1850 he taught analytical mechanics at the University of Pavia.

In 1863 he founded the Polytechnic University of Milan, where he worked until his death, lecturing in hydraulics, analytical mechanics and construction engineering.

He directed the Il Politecnico (The Polytechnic) review and, between 1867 and 1877, the Annali di Matematica Pura ed Applicata (Annals of pure and applied mathematics).

As a mathematician, Brioschi published in Italy various algebraic theories and studied the problem of solving fifth and sixth-degree equations using elliptic functions.

Brioschi is also remembered as a distinguished teacher: among his students at the University of Pavia, there were Eugenio Beltrami, Luigi Cremona and Felice Casorati.