Mathematical Progress or Mathematical Teaching? Bilingualism and Printing in European Renaissance Mathematics

Abstract

In mathematical books of sixteenth-century Europe the question of teaching is present throughout. The very need for mathematical books is presented as the need of explaining mathematical contents effectively and of training the readers in mathematical techniques. The book should make understanding and learning mathematics more accessible: while for most books their printing was justified by being spiritually and morally edifying, for mathematical books the explicit purpose was to make mathematics clearer to follow and easier to absorb by a larger group of people. Mathematical books were intended to make the task of teaching lighter and even superfluous, providing the basis for self-teaching. These are the statements outlining the explicit principles of the actors. These statements open some questions as to the actual use of these books. The more basic question is which kind of teaching, preceptorial, private or public, was available at that time for these subjects, the following is in what teaching situation the books were present and used: here I shall work on the interplay between bilingualism and printing. Books will be taken into consideration here in different ways: as examples of textbooks in public or in private teaching, as sources for facts concerning teaching and learning, as reading of sixteenth-century theories about mathematical teaching and learning. I hope this could be taken as a contribution to refine our future questions about the connection between scientific books and scientific teaching in early modern Europe.