The understanding of the possible geometries in dimension 3 is one of the triumphs of 20th century mathematics. In this talk Martin Bridson explains why such an understanding is impossible in higher dimensions. When one wants to describe the symmetries of any object or system, in mathematics or everyday life, the right language to use is group theory. How might one go about understanding the universe of all groups and what kinds of novel geometry might emerge as we explore this universe?

Martin Bridson became Head of the Mathematical Institute on 01 October 2015. To mark the occasion he gave this Inaugural Chairman's Public Lecture.