The university has become the home of the expert and yet, in the knowledge society, knowledge is distributed throughout society. There are grave contradictions facing any attempt to legitimise the university. The world in which universities find themselves is a world not just of complexity and change; it is a world of supercomplexity. Supercomplexity is that state of affairs where our fundamental frameworks of knowing, being, and acting are challenged. In an age of supercomplexity, the task of the university is clear. It is that of the continuing expansion of supercomplexity and of developing the capacity to live at ease amidst supercomplexity. The supercomplexity facing the university is partly of its making; but, through globalization and detraditionalization, it is also generated in and across the world. If research is the public production of supercomplexity, teaching is the interpersonal production of supercomplexity. Case studies, debates, action learning and structured dialogues are characteristic of teaching for supercomplexity.