On the dialectical relationship between truth and proof: Bolzano, Cauchy and the intermediate value theorem

International audienceThe question of the nature of the relationship between truth in an interpretation and proof in a mathematical theory is a complex epistemological issue. From a didactic perspective, we argue that it is worthwhile to address this issue in mathematics teaching and learning. In this paper, we illustrate this in the context of the Intermediate Value Theorem, focusing on the approaches of Bolzano and Cauchy, and we discuss possible didactic implications