Clavius was the preeminent mathematician and astronomer in the Jesuit order in the sixteenth century. Very little is known about his early life, apart from the fact that he was born in the German region of Franconia, near the town of Bamberg. Even his name is a matter of conjecture: the Latinized “Clavius” has been suggested to derive from the German “Schlüssel” (key) or “Klau” (claw), but no convincing evidence as to his name is known to survive. Clavius entered the Jesuit order at Rome in 1555, admitted by its founder, Saint Ignatius of Loyola. He matriculated at the University of Coimbra in Portugal in 1556, where his mathematical talents were obvious, but the weakness of the Coimbran curriculum and instruction required him to be essentially self-taught in the subject. In May 1561 Clavius returned to Rome, where he began his study of theology at the Collegio Romano. Ordained in 1564, he began teaching mathematics (including astronomy) at the Collegio Romano in the same year; aside from a sojourn of several months to Messina in 1574 and a two-year stay in Naples in 1595–97, Clavius remained in Rome as professor of mathematics at the Collegio for the rest of his life.

Clavius's first published work was his influential Commentarius in Sphaeram Joannis de Sacro Bosco; it appeared in 1570 and was the standard textbook on astronomy for generations. Indeed, Tycho Brahe, Johannes Kepler, and Galileo Galilei were all influenced by it. Clavius's astronomical work made him highly instrumental in the calendar reform of 1582 that resulted in the introduction of the Gregorian calendar.

Clavius's primary contributions to pure mathematics came in the context of his Latin edition and extensive commentary on the Elements of Euclid, which first appeared in 1574 and was the main text used in the Jesuit mathematical curriculum. Descartes’ education at La Flèche exposed him to the works of Clavius, certainly through his edition of Euclid and quite probably to his 1608 Algebra (another standard textbook in the Jesuit curriculum). Descartes was not in the habit of citing any prior sources for his mathematical work, so the Cartesian oeuvre contains almost no references to Clavius.