Complexity sciences have become famous worldwide thanks to several popular books that served as echo chambers of their promises. These consisted in departing from “classical science” defined as deterministic, reductionist, analytic and mono-disciplinary. Their founders and supporters declared that complexity sciences were going to give rise (or that they have given rise) to a post-Laplacian, antireductionist, holistic and interdisciplinary approach. By taking a closer look at their content and practices, I argue in this article that, because of their physics-oriented, computationalist, (...) and mathematical assumptions, complexity sciences have paradoxically produced knowledge at odds with these four tenets. (shrink)