This contribution takes place in the context of a research project 1 on the epistemological and didactical issues of interactions between mathematics and computer science. We make the hypothesis that, with the introduction of digital tools and computer science content in most curricula, significantly taking into account the epistemology of mathematics, computer science and their interactions is essential in order to tackle the challenges of mathematics and computer science education in the digital era. In view of this, addressing the question of proof in mathematics and computer science is a central didactical issue, which we examine in this contribution. We will elaborate on the links between the concepts of algorithm, proof, and program, and will argue for their significance in a general reflection on didactical issues in mathematics and computer science, in their teaching at high school and undergraduate levels.