Higher education research frequently refers to the complex external conditions that give our old-fashioned universities a good reason to change. The underlying theoretical assumption of such framing is that organizations are open systems. This paper presents an alternative view, derived from the theory of social systems autopoiesis. It proposes that organizations, being open systems, are yet operationally closed, as all their activities and interactions with the environment are aspects of just one process: the recursive production of themselves, according to a pattern of their own identity. It is their identity that captures exactly what can and what cannot be sustained in their continuous self-production. Examining the organizational identity of universities within the theoretical framework of autopoiesis may hence shed new light on their resistance to change, explaining it as a systemic and social phenomenon, rather than an individual and psychological one. Since all processes of an autopoietic system are processes of its self-production, this paper argues that in the case of traditional European universities, the identity consists in the intertwinement of only two processes: (1) introducing continuous change in the scope of scientific knowledge and (2) educating new generations of scholars, who will carry on this activity. This surprisingly leaves at the wayside seemingly the most obvious "use of the university": the adequate education of students for the job market.