I will present: 1. The results of my thesis of PhD showing all the different stages of the research of a black box done by students or experts. These results are confirmed with an historic approach of the process of discovery. 2. The stages before and after conjecture will be described accurately. They will be linked to the usual baconian empirist approach and the usual newtonian rationalist approach 3. The solving of a problem around numbers that can be analysed with my model.