This essay presents an intellectual historical analysis on the role played by mathematics, natural phenomena, machines and machineries in the Middle Age, early & late Renaissance, and its correlated necessary culture and skill to build them. I will present how relations between theoretical science and the construction of machines cannot be taken for granted, a priori. For, I will exploit examples and six open key points on sciences, mathematics, machines and their builders. Particularly, a discussion concerning the relationship between science–theory and the development of science––art crafts produced by non-recognized scientists in a certain historical time is also presented. The main questions are: when and why did the tension between science (physics, mathematics and geometry) give rise to a new scientific approach to applied discipline such as studies on machines and machineries? What kind of science was used (if at all) for projecting machines and their machineries? Was science at the time a necessary precondition to build a machine? I also review functioning machines constructed by people who may ignored physical theory, whereas, in other cases, the ignorance of some principles—as well as the impossibility of a perpetuum mobile—induced the attempt to construct impossible machines.