Born in Milan, Cavalieri studied theology in the monastery of San Gerolamo in Milan and geometry at the University of Pisa. He published eleven books, his first being published in 1632. He worked on the problems of optics and motion. His astronomical and astrological work remained marginal to these main interests, though his last book, Trattato della ruota planetaria perpetua (1646), was dedicated to the former. He was introduced to Galileo through academic and ecclesiastical contacts. Cavalieri would write at least 112 letters to Galileo. Galileo said of Cavalieri, "few, if any, since Archimedes, have delved as far and as deep into the science of geometry."
Galileo exerted a strong influence on Cavalieri encouraging him to work on his new method and suggesting fruitful ideas. Building on the classic method of exhaustion, Cavalieri developed a geometrical approach to calculus and published a treatise on the topic, Geometria indivisibilibus continuorum nova quadam ratione promota (Geometry, developed by a new method through the indivisibles of the continua, 1635). In this work, an area is considered as constituted by an indefinite number of parallel segments and a volume as constituted by an indefinite number of parallel planar areas. Such elements are called indivisibles respectively of area and volume and provide the building blocks of Cavalieri's method.