The question of the definition of what is an algorithm is recurrent. It is found in teaching, at different levels and particularly in secondary education because of the recent evolutions in high school, with immediate consequences in higher education. It is found in mediation, with the different meanings that the word ``algorithm'' is charged with in the media space. It is also found in research, with issues in different branches of computer science, from foundations in computability and complexity to applications in big data. Beyond the issue of definition, it is the raison d'{\^e}tre of the notion of algorithm that should be questioned: what do we want to do with it and what is at stake? It is by trying to specify this that we can identify didactic elements that are likely to help teach the algorithm, in interaction with mathematics or not, and to different audiences.

翻译：算法定义的问题反复出现。这一问题存在于教学中，涉及不同层次，尤其是由于高中阶段的近期变革而出现在中等教育中，并直接影响到高等教育。它也存在于科学传播领域，因为“算法”一词在媒体空间中承载着不同含义。该问题同样存在于研究领域，涉及计算机科学不同分支的议题，从可计算性与复杂性的理论基础到大数据应用皆然。超越定义问题本身，我们更应追问算法概念存在的根本理由：我们希望通过它实现什么？其中涉及哪些关键议题？正是通过尝试厘清这些问题，我们才能识别出可能有助于算法教学的教学要素——无论是否与数学相结合，也无论面向何种受众群体。