This talk is an attempt to answer the question “How can intelligent machines efficiently communicate?” which is one of the main goals of the so-called “Semantic Communication”. I will present a joint work with Daniel Bennequin which shows our progresses towards a mathematical theory of semantic communication, inspired by the foundational works of Claude Shannon and Alexander Grothendieck. To communicate efficiently we need a language. This language is intimately related to the goal or task that the semantic source has to follow. The second part of the presentation will be devoted to the Carnap and Bar-Hillel language. It will be shown on this example why a notion of semantic information measure cannot be a scalar quantity but a space. We will give some intuition on the construction of such spaces. Finally we will propose both semantic source coding and semantic channel coding theorems.