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

superior, and emerged daily to conduct their activities in the broader community. Little is known about the four years Clavius spent in Coimbra in his late teens and early twenties, but they were undoubtedly formative ones. The city was famous in those days as the seat of an ancient university, whose most celebrated resident was Pedro Nuñez, one of the great mathematicians and astronomers of the age. There is no direct evidence that Clavius studied under Nuñez, but the mathematician Bernardino Baldi (1553–1617), who wrote a short biography of Clavius, does mention that the two knew each other. To be sure, given the young German’s interests and the small size of the University of Coimbra, it is hard to imagine that Clavius and Nuñez did not meet. But, for the most part, according to Baldi, Clavius was self-taught, gaining his knowledge of mathematics through his own careful study of classical mathematical texts.
    When Clavius was recalled to Rome in 1560, it was to continue his study of philosophy and theology, and to teach mathematics. In 1563 he was lecturing on mathematics at the Collegio Romano, and around 1565, when thirty years old, he became a professor of mathematics, a position that he would hold more or less continuously until his death forty-seven years later. Up to this point, Clavius’s career was respectable but hardly remarkable. Although recognized by his superiors for his mathematical abilities, he was nevertheless just a young faculty member toiling in obscurity among colleagues who did not much respect his field of expertise. Even years later he was still fighting for the right of the mathematics professor to take part in public ceremonies and disputations along with his colleagues, a complaint that suggests that this was not usually done. And despite holding a chair at the Society’s flagship college, he was excluded for years from the ranks of the “professed,” which tells us all we need to know about his status in the rigid hierarchy of the order.
    But sometime between 1572 and 1575, more than a decade after his return from the provinces, Clavius’s career took a dramatic turn. The newly elected Pope Gregory XIII assembled a distinguished commission to deal with an issue that had troubled the Church for centuries: calendar reform. As technical adviser to the commission the Pope selected the young Jesuit professor of the Collegio Romano who was making a name for himself as an expert on mathematical and astronomical matters. The appointment was unquestionably a great honor for Clavius, putting him at the center of one of the most ambitious projects the Church had undertaken. It also made him the official representative of the Jesuits in a high-ranking panel of the Church, whose recommendations would be known to all and would be scrutinized by scholars across Europe. Placed in such a visible position, Clavius was expected to bring honor and distinction to the Society, and enhance its prestige in the papal court. It was a difficult and even risky proposition for a young and rather obscure professor of mathematics. But Clavius and his cause had been waiting for just such an opportunity.
    ORDERING THE UNIVERSE
    The problem the commission was called to address had been in the making for more than twelve hundred years. Back in the year 325 CE the Council of Nicea had determined that Easter should be celebrated on the first full moon after the vernal equinox, which, according to the council, fell on March 21. Unfortunately the Julian calendar that was used at the time did not quite match the true length of the solar year—the time that it takes the sun to return to the exact same spot in the sky. Whereas the Julian year is 365 days and 6 hours, the true solar year is almost exactly 11 minutes shorter. Such a minuscule discrepancy does not matter from one year to the next, or even over a person’s lifetime, but an error of 11 minutes repeated more than 1,200 times does add up. By the 1570s the date of