In this article, I focus on digital scientific archives which are made up of the leftovers of science, such as drafts, obsolete instruments, photographs, documentation, etc. The artifacts exhibited in such collections were neither meant to be representations, nor objects of gaze, but means used to achieve scientific results. As they lose functionality, they acquire aesthetic and historical value and emerge as clues, traces of past scientific practices and institutional histories. Therefore, the ways in which institutions situate these objects within the archive, the vocabularies and metadata they use, bear testimony on the manner they present and depict their past. How do the digital archives of the scientific institutions represent their histories? To address this question, I analyse the subject metadata of twenty-five institutional archives, turning them into objects of distant reading. Quantitative methods offer a way to discern the discursive frameworks that scientific institutions tend to adopt: Do they frame their collections as cultural heritage? represent them as corporate histories? emphasise technical specifications? scientific value? big names? A closer look at the metadata sets reveals that, in fact, these very different perspectives intermingle and clash with each other within the archive structures: the logic of heritage is juxtaposed with scientific classifications, institutional categories stand side by side with natural objects, and minority histories with celebrity narratives. Discussing this interplay of discourses, the article frames the digital archive of science as a specific mode of historical representation, which gives rise to a new (and still political) order of things.