Introduction: The Idiosyncratic Nature of Renaissance Mathematics

Abstract

Ever since its foundation in 1540, the Society of Jesus had had one mission—to restore order where Luther, Calvin and the other instigators of the Reformation had brought chaos. To stop the hemorrhage of believers, the Jesuits needed to form a united front. No signs of internal disagreement could to be shown to the outside world, lest the congregation lose its credibility. But in 1570s two prominent Jesuits, Cristophorus Clavius and Benito Perera, had engaged in a bitter controversy. The issue at stake had apparently nothing to do with the values on which Ignazio of Loyola had built the Society of Jesus. And yet the dispute between Clavius and Perera was matter of concern for the entire Jesuit community. They were arguing over the certitude of mathematics. There are many ways of telling the stories of Renaissance mathematics. Starting with the Quaestio de certitudine mathematicarum—the dispute that involved Clavius and Perera—is just an example. One may, as Carl Boyer does in his A History of Mathematics (Merzbach and Boyer 2011), begin by outlining the conditions that allowed mathematics to reach new heights in the sixteenth and seventeenth centuries. Chief among these conditions were the rediscovery of Greek geometry—in particular the works of Euclid and Apollonius—and the Latin translations of Arabic algebraic and arithmetic treatises. Or, following the example of Klein (1968), one may trace the transformations undergone by ancient concepts such as that of arithmos (number in Greek) during Renaissance times. But, I believe, no event epitomizes the spirit of Renaissance mathematics better than the Quaestio.