Amir R. Alexander

“Where the Jesuits insisted on clear and simple postulates, the new mathematicians relied on a vague intuition of the inner structure of matter, whereas the Jesuits celebrated absolute certainty, the new mathematicians proposed a method rife with paradoxes, and seemed to revel in them; and whereas the Jesuits sought to avoid controversy at all cost, the new method was mired in intractable controversies... It was everything that the Jesuits thought mathematics must never be, and yet it flourished... It was known as the method of indivisibles.”

“...the whole point of studying and teaching mathematics was that it demonstrated how universal truth imposed itself upon the world—rationally, hierarchically, and inescapably. Ideally, the Jesuits believed, the truths of religion would be imposed on the world just like geometrical theorems, leaving no room for avoidance or denial by Protestant or other heretics and leading to the inevitable triumph of the Church.”

“It was clear to Clavius that Euclid's method was successful in doing precisely what the Jesuits were struggling so hard to accomplish: imposing a true, eternal, and unchallengeable order upon a seemingly chaotic reality.”

“Theological and philosophical disputes could rage forever, he [Christopher Clavius] believed, because there was no universally accepted way to decide who was right and who was wrong. ...But mathematics was different: with mathematics, the truth forces itself upon its audience whether they like it or not. One could dispute the Catholic doctrine of the sacraments, but one could not deny the Pythagorean theorem; and no one could deny the correctness of the new calendar, based as it was on the detailed mathematical calculations.”