Mathematical Work in the Digital Age. Variety of Tools and the Role of Geneses

This chapter focuses on the particularities of mathematical work in the digital age. It opens with historical considerations that relate to the development of mathematical work to do arithmetic when symbolic or mechanical tools and algorithmic methods were used. He goes on to define the new mathematical work by introducing concepts of reference in the interaction between human and machine. The notion of valence of mathematical work makes it possible to account for the operating domain of interactions as well as for the possible adaptations of an evolving subject-milieu system, whether for the accomplishment of a task or in the course of learning mathematics. A difference between the work of the designer and that of a user is established, especially in terms of the effects on reasoning, proof, modelling activity and the creation of digital artefacts. The adaptation in a process of idoneity between the teaching and the learning project, as well as between the intention of the designer and the realisation by a user, is discussed.