Stefan Collini offers a few brief reflections on the history and current state of the institution we call the university, and then goes on to propose a vocabulary and a perspective which enable us to discuss the role of such institutions in more fruitful terms than the clichés about ‘contributing to economic growth’ which currently dominate public debate on the topic. This lecture was given in memory of John Wyon Burrow (1935-2009), who was the first holder of a chair in Intellectual History at the University of Sussex and was one of the founder members of the subject at this university.