Born in Brescia, Castelli studied at the University of Padua and later became an abbot at the Benedictine monastery in Monte Cassino.

[1] Days later, Galileo wrote in a letter to Johannes Kepler saying that he'd observed Venus going through phases, but took complete credit for himself.

His students included Giovanni Alfonso Borelli, Raffaello Magiotti, Antonio Nardi, and Evangelista Torricelli, the inventor of the barometer and an early proponent of the air pump.

He published Mensuration of Running Water, an important work on fluids in motion, and then his Geometrical Demonstrations of the Measure of Running Waters in which the publishing notes described him as Abbot of San Benedetto Aloysio and Mathematician to Pope Urban VIII, once a supporter of his mentor, Galileo.

He dedicated both publications to "the most Illustrious, and most Excellent Prince" Taddeo Barberini, a nephew of Pope Urban VIII.