Cumulative transmission and innovation are the hallmark properties of the cultural achievements of human beings. Cognitive scientists have traditionally explained these properties in terms of social learning and creativity. The non-social cognitive dimension of cumulative culture, the so-called technical reasoning, has also been accounted for recently. These explanatory perspectives are methodologically individualistic since they frame cumulative and innovative culture in terms of the processing of inner cognitive representations. Here we show that going beyond methodological individualism could facilitate an understanding of why some inventions are disseminated in a stable form and constitute the basis for further modifications. Drawing on three cases of cognitive history of prominent achievements of Antiquity, i.e., Homerian epics, Euclidean geometry, and Roman law, we investigate which properties of cognitive artifacts shaped cognitive niches for modifying original cognitive tasks or developing new ones. These niches both constrained and enabled the cognitive skills of humans to promote cumulative culture and further innovations. At the same time, we claim that “wide cognition,” incorporating both intracranial resources and external cognitive representations, constitutes a platform for building explanations of cognitive phenomena developing over a historical time scale.