Francesco Brioschi, a leading figure in 19th-century Italian science: His contribution to mechanics and hydraulics, the weakness of his epistemological views, and the strength of his political contributions.

Francesco Brioschi (1824–1897), renowned for his contributions to the Theory of Algebraic Equations and the Theory of Invariants, was also an applied mathematician, theoretical mechanician, and hydraulic engineer. His scientific and technical expertise, coupled with his proven managerial skills, led him to hold significant political responsibilities. He was the founder and director of the Istituto Tecnico Superiore, later the Polytechnic University of Milan, which, thanks to him, became a driving force for the Italy’s technological development after its unification. This paper will discuss the development of his epistemological views starting from his contributions to Mathematical Physics and Analytical Mechanics, strongly inspired by his mentor Gabrio Piola, but not as thoroughly informed by the orthodox Lagrangian vision characteristic of Piola. Furthermore, we will examine his contributions to Hydraulics, which have a much more applied flavor and analyze his epistemological approach to the use of Mathematics in physical modeling. We will highlight the methodological differences that emerge in his approach to Mechanics and Hydraulics, which render his epistemology somewhat inconsistent and wavering. This weakness in his views on science, however, does not diminish the value of his contributions to Italian industrial, technological, and scientific growth: his political vision, evidenced by his institutional commitment, was remarkably precise and effective.