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06.12.2023   kl. 11:15 - 12:15

Early modern (European) symbolic algebra: a rhetorical project ?

DIAS Lecture by Giovanna Cifolletti, Membres émérites et honoraires, Directrice d'études de l'EHESS

From Early modern (European) symbolic algebra: a rhetorical project ?

My research project aims to understand the sense of the symbolic algebra of Viète and Descartes, in the context of 16th-century Europe. To apply a sociological scheme could hardly bridge the gap between mathematical theory and practice on the one hand and the actual concerns of scientists and practitioners (including masters of crafts and merchants) on the other. Hence I opted for a social history approach in the sense defined by Lucien Febvre in connection with 16th-century people: our purpose is to see how people formulated their problems and found strategies to solve them.

This invites us to search for information in documents about the history of books and printing, of universities, of academies and civic schools. At the theoretical level, we look for the connections of algebra, geometry and arithmetic with other disciplines or liberal arts: besides mathematics, these include grammar, rhetoric and logic or dialectic; within mathematics, there are the links with the mathematical arts music and astronomy as well as with many subordinate arts such as optics or chronology, calendars and commercial arithmetic. Febvre’s approach insists on paying attention to the perspective of the actors, not only as an intellectual curiosity but as the search for an actual comparison with our research. In fact, Lucien Febvre shares categories with the people he studies: for instance putting problems and solutions at the center of intellectual life is a typical move of 16th-century rhetoric and logic.

With the study of symbolic algebra we are in a similar position: algebra in the 16th- century was transformed to become the science of formulating problems and their solutions. Today we shall see in particular how 15th- century vernacular rhetoric and logic of Lorenzo Valla created the conditions for this transformation in the works of Jacques Peletier, so that on this basis algebra itself replaced logic in Descartes and Fermat.


Giovanna Cifoletti, Professor and Directrice d'Etudes à l'EHESS, L’école des hautes études en sciences sociales, the School for Advanced Studies in the Social Sciences, Histoire des sciences et des techniques, Doctor of Philosophy.
Her research areas are the History of Mathematics, especially early modern algebra. Intellectual and social European and Mediterranean history in the early modern period. Abacus Schools: texts and commercial practices. Mathematics, rhetoric and logic in early modern Europe, especially among jurists and mathematicians.

The lecture takes place in the DIAS Auditorium, Fioniavej 34from 11:15 to 12:15. Everybody is welcome and no registration is needed.