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

first Jesuit college in the Holy Roman Empire was founded in Cologne in 1556, at a time when the empire appeared on the verge of succumbing to the Lutheran surge. But with the college in place, Cologne became a Catholic stronghold, and a base for future expansion of Jesuit activities. In the following decades, with strong support from the ruling Wittelsbach and Habsburg families, the Jesuits founded dozens of colleges in Bavaria and Austria, and took over the administration of existing universities. They even went so far as to found a special school in Rome dedicated to training the promising young Germans for positions as high Church officials. Upon completing their studies, the graduates of this “Collegium Germanicum” returned home, where they became bishops and archbishops, and the backbone of the Catholic revival in Germany. In the Low Countries, too, the Jesuits were exceedingly active: when the northern provinces turned to Protestantism and took up arms against their Habsburg sovereign, the Jesuits helped make the southern provinces into a Catholic bastion. Thanks in great part to their efforts, the region was saved for the Catholic Church, acquired its own separate identity, and ultimately gained independence as the modern state of Belgium.
    Much like Germany, sixteenth-century Poland seemed well on its way to accepting one form or another of Protestantism when Catholic noblemen invited the Jesuits to open their colleges there in the 1560s. They soon gained the trust and support of the Polish royal family, which helped the Jesuits expand from five colleges in 1576 to thirty-two colleges by 1648. The Jesuits became the educators of the Polish ruling class, both the rural aristocracy and the urban elite, while in Rome they educated a devoted cadre of priests who returned to Poland to take up the leadership of the Church. So close were the Jesuits to the Polish monarchs, that King Sigismund III (1587–1632) was known as the “Jesuit King” and his son Jan II Kazimierz (1648–68) was a member of the order and a cardinal before assuming the throne. Poland was transformed: a nation that had previously prided itself on religious tolerance, and had opened its churches and parishes to the reformers, became the devout Catholic land we still recognize today. In Poland as elsewhere, the Jesuit intervention proved decisive.
    The upright disciples of Ignatius accomplished what the worldly Renaissance popes could not: they arrested the seemingly unstoppable progress of Protestantism across Europe and revived the power and prestige of the Roman Church. Wherever the Society raised its standard and opened its colleges, a new energy of spiritual devotion and purposefulness of action infused the old Church and inspired its followers to make a stand against the heretics. A grateful Pope Gregory XIII acknowledged as much when he addressed the general congregation of the Society in 1581:
    Your holy order … is spread throughout the entire world. Anywhere you look you have colleges and houses. You direct kingdoms, provinces, indeed, the whole world. In short, there is this day no single instrument raised up by God against heretics greater than your holy order. It came to the world at the very moment when new errors began to be spread abroad. It is all important therefore … that this order increase and prosper from day to day.
    ORDER OUT OF CHAOS
    The Miracles of St. Ignatius , a massive painting originally intended to grace the altar of Antwerp Cathedral, hangs today at the Kunsthistorisches Museum in Vienna. It is the work of the Flemish painter Peter Paul Rubens (1577–1640), whose modern-day reputation rests largely on his erotic depictions of ample women that challenge our ideal of female beauty. But Rubens was a devout Catholic who attended Mass every morning, and was on intimate terms with the Jesuits in his home city of Antwerp. In 1605, when the Jesuits were campaigning to have their founder canonized, Rubens contributed