Infinitesimal: How a Dangerous Mathematical Theory Shaped the Modern World by Amir Alexander

was known) relied heavily on Aristotelian philosophy, it was essential that students in the Jesuit colleges be immersed in Aristotle before they fully engaged in religious study.
    But if the curriculum of the Jesuit colleges was diverse and wide-ranging, it was also rigorous, clearly ordered, and hierarchical. The relative value of the different disciplines was never in doubt: At the top was theology, comprised of the infallible teachings of the Catholic Church. Below it was philosophy, both moral and natural, which taught truths about the natural and human world and might be required in order to understand religious teachings. And below philosophy were the ancillary fields such as languages and mathematics, which did not deal with truth themselves but could prove useful in understanding the higher disciplines. Here, as elsewhere in the Jesuit world, order prevailed. Each field had its place in the grand scheme of the disciplines. The truths of theology were the highest, and no philosophical doctrine, even if supported by the authority of Aristotle himself, could ever contradict a theological truth. Mathematical sciences ranked lower still, and their results did not even qualify as truth, but only as hypotheses. It was a seamless hierarchy of knowledge in which Thomist theology reigned supreme.
    The clear order of the disciplines at the Jesuit colleges contrasted well with the offerings at the universities of the time, where studies were often haphazard and students typically attended unrelated lectures. Many students lost their way in this unstructured maze. The Jesuits, in contrast, offered a clear sequence of learning, beginning with languages and the many branches of Aristotelian philosophy, then moving on to theology. Along with the regulated and orderly life of the colleges and the upstanding moral example of the Jesuit instructors, this rigid progression kept the students on track and away from the temptations that afflicted their peers.
    But the hierarchy of truth was, for the Jesuits, more than a pedagogical device. It reflected their unyielding faith that a clear and undisputed hierarchy was essential for reconstituting the godly order lost in the Reformation. It governed society itself, and it governed the Church, from the Pope to the lay congregation. Hierarchy, the Jesuits believed, must prevail in the world if heresy were to be defeated and if truth were to triumph over error. After all, was not the scourge of the Reformation itself the result of a breakdown in the proper order of knowledge? Did not Luther, a mere monk, dare to challenge the authority of the Pope himself? Did not Luther and, later, Zwingli, Calvin, and others posit their own novel theologies in opposition to the authoritative teachings of the Church? And what was the result? Chaos and confusion, in which the single authoritative voice of the Roman Church was drowned by a cacophony of competing voices. It seemed obvious to the Jesuits that the collapse of the ancient unity of Christendom, and the chaos that followed, were the direct result of the collapse in the proper order of knowledge. Only by preserving this strict hierarchy of knowledge would truth prevail and heresy be defeated.
    Since truth, for the Jesuits, was unchanging, and eternal, and founded on the authority of the Church, then novelty and innovation posed an unacceptable risk, and must be fervently resisted. “One should not be drawn to new opinions, that is, those that one has discovered,” warned theologian Benito Pereira of the Collegio Romano in 1564. Instead, one must “adhere to the old and generally accepted opinions … and follow the true and sound doctrine.” Two decades later, General Acquaviva exhorted his cohorts to avoid not only innovation, but also having “anyone suspect us of trying to create something new.” Innovation, so prized today, was regarded with deep suspicion by the Jesuits.
    Legem impone subactis —impose your rule upon the subjects!—was the