|Died||13 December 1897 (aged 72)|
|Alma mater||Collegio Borromeo, Pavia|
|Institutions||University of Pavia|
|Doctoral advisor||Antonio Bordoni|
|Doctoral students||Felice Casorati|
|Other notable students||Eugenio Beltrami|
From 1850 he taught analytical mechanics in the University of Pavia. After the Italian unification in 1861, he was elected deputy in the Parliament of Italy 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 in 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 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 in the University of Pavia there were Eugenio Beltrami, Luigi Cremona and Felice Casorati.
- 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)
- 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.
- White, H. S. (1906). "Review: Opere matematiche di Francesco Brioschi, vols. 1, 2, & 3". Bull. Amer. Math. Soc. 12 (8): 408–409. doi:10.1090/s0002-9904-1906-01365-9.
- Grande Dizionario Enciclopedico (UTET, 1967)
- Enciclopedia Universal (Rizzoli-Larousse, 1967)