Toward disciplinary boundaries: “Mixed Mathematics” experiments at the Accademia del Cimento (1657-1667)

The Accademia del Cimento (1657–1667), established under the patronage of the Medici family and inspired by Galileo’s legacy, carried out more than a thousand experiments, focusing on pneumatics (vacuum and air pressure) and thermology (heat, cold, and freezing phenomena). Its agenda also included studies in optics, acoustics, and mechanics, which can be associated with the contemporary concept of “Mixed Mathematics” —a term that emerged around 1660 to describe the application of numerical and geometrical principles to physical phenomena. Key experiments included investigations of the propagation of sound and light through various media, pendulum oscillations, projectile trajectories, the fall and rebound of bodies. This article provides an overview of these activities, shedding light on a period when scientific disciplines were not yet specialized, and the boundaries between what we now consider distinct fields of physics were fluid and interconnected.