Simple groups, Lie groups, and the search for symmetry

During the 19th century, group theory shifted from its origins in number theory and the theory of equations to describing symmetry in geometry. In this video we talk about the history of the search for simple groups, the role of symmetry in tesselations, both Euclidean, spherical and hyperbolic, and the introduction of continuous groups, or Lie groups, by Sophus Lie. Along the way we meet briefly many remarkable mathematical objects, such as the Golay code whose symmetries explain partially the Mathieu gr