As will become clear in the body of the present work, a certain trend within 19th-century German mathematics, the so-called conceptual approach, seems to have been strongly associated with the rise of set theory. Therefore, it seems convenient to start by analyzing two different "mathematical styles," those that reigned in Göttingen and Berlin immediately after 1855. Such will be the topic of §§4 and 5. The reason for that particular selection of institutions is simple: the main figures in the first two parts of the book are Riemann, Dedekind and Cantor. Riemann and Dedekind studied at Göttingen, where they began their teaching career, while Cantor took his mathematical training from Berlin. It will turn out that the conceptual approach was present at both universities, but in different varieties, that we will identify as an abstract and a formal variety. The abstract conceptual approach that could be found at Göttingen promoted the set-theoretical orientation strongly.