Solving cubic equations by a formula that involves only the elementary operations of sum, product, and exponentiation of the coefficients is one of the greatest results in 16th century mathematics. This was achieved by Girolamo Cardano's Ars Magna in 1545. Still, a deep, substantial difference between the quadratic and the cubic formula exists: while the quadratic formula only involves imaginary numbers when all the solutions are imaginary too, it may happen that the cubic formula contains imaginary numbers, even when the three solutions are anyway all real (and different). This means that a scholar of the time could stumble upon numerical cubic equations of which he already knew three (real) solutions and the cubic formula of which actually contains square roots of negative numbers. This will be lately called the 'casus irreducibilis '. Cardano's De Regula Aliza (Basel, 1570) is (at least, partially) meant to try to overcome the problem entailed by it.

How much was a medieval monastery reminiscent of a modern prison? Or insane asylum? And if it was in the least - what can such a metaphor tell us about power relations structuring the life of medieval monks? The purpose of this compilation thesis (sammanläggningsavhandling) is to render explicit and analyze relations of power and modes of control comprising the social tissue of early medieval Benedictine monasteries. By bringing up the examples of tenth- and eleventh-century monasteries of St Gall, Fulda, and Bury St Edmunds, this thesis seeks to understand what power was in medieval monasteries, how and between whom it was exercised, what and how it affected in terms of collective and individual identity. The thesis consists of three introductory chapters, four previously published empirical articles, and a concluding remarks section. Article 1 investigates the problem of surveillance and patterns of social control dispersed in the monastery of St Gall. Article 2 studies the early and high medieval institutional expectations and means of enforcement of the monk’s role. Article 3 scrutinizes an example of a persecution process and a set of defense measures in the hands of the St Gall community warding off an unwanted visitor. Article 4 examines a number of internal monastic conflicts from several monasteries and strategies, both political and cognitive, guiding them. In investigating these problems, the thesis proceeds in a manner of deliberate anachronism. It asks questions about how human subjectivity was manufactured in early medieval St Gall, what were a medieval monastery’s ‘conditions of possibility’ to operate as a social regime, or oral and literary means of conflict management etc. The crucial modern social theories on which the thesis hinges are: Erving Goffman’s notion of ‘total institution’, and Michel Foucault’s analysis of power, as well as Pierre Bourdieu’s logic of action.