The future of Cambridge University is discussed in the context of the current British and global situation of universities, the main focus being on what the core concerns of a major university should be at this time. After raising issues related to core intellectual values (truth-seeking, rationality in argument, balanced judgement, integrity, linguistic precision and critical questioning) and the sustaining of a long-term social and intellectual ecology, four main challenges are identified: uniting teaching and research fruitfully; interrelating fields of knowledge appropriately across a wide range of disciplines; contributing to society in ways that are responsible towards the long-term flourishing of our world; and sustaining and reinventing collegiality so that the university can be a place where intensive, disciplined conversations within and across generations can flourish. The latter leads into questions of polity, governance and management. Finally, the inseparability of teaching, research and knowledge from questions of meaning, value, ethics, collegiality and transgenerational responsibility leads to proposing ‘wisdom’ as an integrating concept. The relevant sources of wisdom available are both religious and secular, and in a world that is complexly both religious and secular we need universities that can be places where both are done justice. Given the seriousness and long-term nature of the conflicts associated with religious and secular forces in our world, it is especially desirable that universities in their education of future generations contribute to the healing of such divisions.