The History of Mathematics In Italy: The Role of Applications

The importance of the history of mathematics in mathematics teaching, both for the cultural education of the student and for the learning of the mathematical discipline itself, is widely shared and the subject of numerous proposals and research. Here we want to highlight and represent with examples three aspects that can increase the quality and interest of this approach: the use of primary historical sources, a connection with other disciplines and applications of mathematics, and themes inspired to recent research by historians of mathematics. We have chosen two current topics from this point of view, the first connected to the mechanics of motion and astronomy, inspired by research on Galileo and Jesuit science, the second connected to hydraulics and hydrodynamics, and inspired by studies on centuries-old Italian tradition in the science of waters.