#### EXCERPT

In this, the third part of the work, we will reflect (philosophically, methodologically and culturally) on the case studies that we have presented in the second part. Accordingly, *when we refer to ‘mathematics’ (and its derivative adjectives) in what follows, we mean ‘contemporary mathematics’*, unless we explicitly state otherwise. Now, we should note right away that this essay cannot cover all the forms of doing mathematics, and, in particular, will not dwell on the practices peculiar to elementary mathematics. We therefore do not aim to produce anything like an all-encompassing philosophy of mathematics, only to call attention to a very broad mathematical spectrum that has rarely been accounted for in philosophical discussions, and which should no longer be neglected…