Jean Cavailles explains an essential role to mathematical problems in the history of mathematics or, as he puts it, in mathematical “becoming.” In fact, Cavailles refers to mathematical problems in order to illustrate the various characteristics that he attributes to mathematical becoming. The authors discuss the role of mathematical problems in the epistemology that Cavailles develops in his dissertations of 1938. The emphasis on mathematical problems enables Cavailles to maintain the necessity and the universality of mathematics, in a non-cumulative model of its growth. Cavailles accepts that something in the actual mathematical writings at a given time and place depends on the sociological context, the institutions, a dominant style, or the psychology of the mathematician. The authors use the term “question” to distinguish issues from the preceding “problems”.