In this paper I attempt to unravel the complex discursive threads intertwined in Alain Badiou’s philosophy. I proceed by displaying the main concepts that this author formulates (event, intervention, subject, truth) and their multiple articulations. I also bring forward accounts and debates with the readings that other authors, close to Badiou´s thinking, do of these concepts: Žižek, Laclau, Milner. In doing so I place special emphasis on the radical difference established by Badiou´s mathematic device/mechanism –whether it is taken into consideration or not and how- in the conceptual formulations of the other authors, their homologies, convergences and divergences. It is obvious that, however diffused, certain misunderstandings with regard to the status of mathematics in Badiou’s approach cannot be underscored all too simply. The difficult challenge of understanding the technical mathematical concepts articulated by Badiou and widely commented upon must be confronted. More specifically, the hypothesis I advance is that the different discursive orders that Badiou applies can be redefined by looking at the modality of their intersections. These intersections, I claim, could be understood by using the idea of knots as a useful analogy: the implicit nodal logic in Badiou’s work is key to clarifying (and eradicating) these misunderstandings.