Galileo was born near Pisa and died at Arcetri, near Florence. He taught mathematics at Pisa and then moved to the University of Padua in 1592. In 1610 he was appointed chief mathematic and philosopher to the Grand Duke (of Florence). In 1632 he published his Dialogue concerning the Two Chief World Systems. In 1633 he was convicted on suspicion of heresy. He abjured and was sentenced. In 1638 he published Discourses and Mathematical Demonstration concerning Two New Sciences.

Around 1590 Galileo reached a conclusion in De Motu about the inadequacy of Aristotle's conception of natural motion and the nature of matter (Galilei 1890–1909, vol. 1). In this unpublished work, he argued that all matter (at least in the sublunary world) was the same – there was no light matter that naturally moved up. All matter moved down by weight (or specific gravity). For the next twenty years he would attempt to develop these ideas into numerous insights about the nature of motion and unitary nature of matter.

In March 1610, Galileo published Sidereus Nuncius (The Starry Messenger) in which he reported his telescopic observations. He claimed that there were mountains on the moon, that there were numerous stars hitherto unseen, and that Jupiter had four moons. The observations served to support his denial of a celestial-terrestrial distinction. In April 1611, Cardinal Bellarmine wrote to the Roman College (Collegio Romano) asking it for an opinion on Galileo's observations. The members of the collegio responded quickly, affirming all of Galileo's observations, but noting that Father Christoph Clavius still had some doubts about the mountains on the moon. Galileo moved back to Florence (from Padua), accepting a position with the Medici as “Chief Mathematician of the University of Pisa and Philosopher to the Grand Duke.” In 1613 he published Letters on the Sunspots in which he first expressed his position in favor of Copernicus and discussed the phases of Venus and the rotation of spots on the sun.