Brioschi was born in Milan in 1824. He graduated from the Collegio Borromeo in 1847.

From 1850 he taught analytical mechanics at the University of Pavia. After the Italian unification in 1861, he was elected to the Chamber of Deputies and then appointed twice secretary of the Italian Education Ministry. In 1863 he founded the Polytechnic University of Milan, where he worked until his death, lecturing in hydraulics, analytical mechanics and construction engineering. In 1865 he entered the Senate of the Kingdom. In 1870 he became a member of the Accademia dei lincei and in 1884 he succeeded Quintino Sella as president of the National Academy of the Lincei. 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). He died in Milan in 1897.

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.

• Intorno ad alcuni punti della statica (in Italian). Pavia: eredi Bizzoni. 1853.
• Théorie des déterminants et leurs principales applications (Mallet-Bachelier, Paris, 1856) (French translation of "La teorica dei determinanti e le sue principali applicazioni" by E. Combescure)
• Sopra un progetto di inchiesta idrometrica. [Milano]: [Tip. di Zanetti Francesco]. 1867.
• Delle traverse oblique alla direzione di un corso d'acqua. Milano: Amministrazione del Politecnico. 1866.
• Opere matematiche di Francesco Brioschi. Pubblicate per cura del comitato per le onoranze a Francesco Brioschi (G. Ascoli, E. Beltrami, G. Colombo, L. Cremona, G. Negri, G. Schiaparelli), vol. 1 (U. Hoepli, Milano, 1901–1909)
• Opere matematiche di Francesco Brioschi pubblicate per cura del Comitato per le onoranze a Francesco Brioschi... (vols. 1-5) (U. Hoepli, Milano, 1901–1909)^[1]

•  
  Intorno ad alcuni punti della statica, 1853
•  
  Delle traverse oblique alla direzione di un corso d'acqua, 1866
•  
  Sopra un progetto di inchiesta idrometrica, 1867

• Brioschi formula
• Politecnico di Milano

• Grande Dizionario Enciclopedico (UTET, 1967)
• Enciclopedia Universal (Rizzoli-Larousse, 1967)

• Mac Tutor biography
• Francesco Brioschi at the Mathematics Genealogy Project
• Tricomi: La Matematica Italiana 1800-1950 (entry on Brioschi)