How history of mathematics can help to face a crisis situation: the case of the polemic between Bernoulli and d'Alembert about the smallpox epidemic.

In this article, I present the eighteenth century's polemic of Bernoulli and d'Alembert concerning the smallpox epidemic and a prevention method called inoculation. Through an analysis of the polemic and the related resources, I show that this historical debate has various interests for mathematics education; and more specifically it can help teachers to confront dilemmas emerging with the COVID-19 pandemic (for example if a teacher should talk about it in class or not, how to help students to interpret the statistical data and the mathematical models connected to the pandemic and more generally, how to deal with the confusions and concerns emerging in connection to the pandemic). I describe the documents related to the historical polemic as transitional objects, having a potential to reveal the teachers' own professional or personal experiences, reflections and questions, and to stimulate dialogue with them on these issues. I illustrate this proposition by the presentation of an online reading seminar realized with a French group of teachers in April 2020.