In this paper we analyse teaching at Bauhaus (1919-1933), through the courses of Itten and Klee. We show that these courses not only aimed at teaching the styles. They aimed at increasing students creative design capacities and at providing them techniques to create their own style, in the sense of being able to be generically creative - ie be creative on as many languages as possible. The analyses of the two courses leads to identify two critical features to get a generic creative design capacity: 1-A knowledge structure that is characterized by non-determinism and non-independence; 2-A genesis process that helps to progressively "superimpose" languages on the object in a robust way. These features are strongly different from the knowledge structure and design process of Engineering Systematic Design. We finally show that these features actually correspond to two sufficient conditions for a mathematical model of sets to be "forced" (Cohen 1964) ie to lead to the creation of a new, extended model of sets that is generically different from the original one and still based on the law of this original one. This underlines the deep similarity between the logic of artistic creation and the logic of mathematical creation.