Algorithms take nowadays a central place in the public debate: they structure our social interactions, they modify our work, our means of transport, and also our scientific and medical instruments. But who can say what exactly an algorithm is? Since there is no real consensus among the experts, it is important to give an epistemological foundation to this debate. By giving a precise mathematical representation to the algorithms, it becomes possible to assign them a genuine scientific status. In particular, the use of geometric tools will allow us to distinguish the notion of algorithm from other related and yet different ones, like that of computation or that of program. This analysis will thus open the way to develop an ontology proper to computer science, and to look at the latter as a mathematized theory, in the same way as physics.