Simple groups, Lie groups, and the search for symmetry II | Math History | NJ Wildberger

This is the second video in this lecture on simple groups, Lie groups and manifestations of symmetry.

During the 19th century, the role of groups shifted from its origin in number theory and the theory of equations to its role in 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 groups, the exceptional Lie groups discovered by Killing, and some of the other sporadic simple groups, culminating with the Monster group of Fisher and Greiss.

The classification of finite simple groups is a high point of 20th century mathematics and the cumulative efforts of many mathematicians.

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