Among problems at the border between philosophy and mathematics, analysis and synthesis have occupied a central place for two millennia. Indeed, few are the problems of philosophy of mathematics which have existed for so long and which have stimulated so many writings. Present in filigree in Aristotle's writings,¹ they are there in person in the writings of his commentators² and in the writings of philosophers and logicians up to the beginning of the last century. One easily imagines the diversity of meanings and the multiplicity of formulations of this problem of analysis and synthesis, which designated a domain vast enough to include at the same time an ars demonstrandi and an ars inveniendi.