"Catholics... believed that the grace of God was bestowed upon sinners only through the holy Church and its sacraments, enacted by an ordained priest. Protestants, conversely, believed in a "priesthood of all believers," meaning that God would bestow his grace directly upon them. Catholics believed that Christ was physically present in the bread and wine during the sacrament of the Mass. Protestants believed that Christ was either present everywhere or that the Mass was a mere commemoration of his sufferings . Catholics believed that God would take into account a man's good works in this world in determining whether be saved or lost. Protestants believed that only faith and divine grace mattered. Catholics believed that the Bible required interpretation by the hierarchy and the traditions of the Church. Protestants believed that the Bible was a clear guide for righteous behavior, accessible to anyone. What these arguments had in common were that they were entirely inconclusive."

“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.”

“...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.”

“The fact that the tragic story of Évariste Galois, the mathematical genius who burned brightly but all too briefly, is not as unusual as one might think among mathematicians of his and subsequent generations. It is, rather, the most famous and dramatic of an entire genre of mathematical stories that originated in the early decades of the nineteenth century but is still going strong today. Consider, for example... Niels Henrik Abel.. János Bolyai... Srinivasa Ramanujan... John Nash... Kurt Gödel... Alexander Grothendieck... Grigory Perelman... Among modern mathematicians, it seems, extreme eccentricity, mental illness, and even solitary death are not a matter of random misfortune. They are, rather... reserved only for the most outstanding members of the field.”

“Theological and philosophical disputes could rage forever, he 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.”

“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.”