The Origin of Mathematics 15: Symmetry Through the Ages

Abstract

From the time of the Greeks, people have been fascinated by the regular polyhedra. They provide us with one of the first complete mathematical theories: a general definition together with a complete classification of all the objects satisfying the definition. In this section the most important steps are presented in the development of a subject that goes back to the very beginnings of mathematics and is still alive today. Hippasus provided the first significant example, and Theaetetus created the mathematical theory. Pacioli revived the subject after it had lain dormant for about a thousand years. Felix Klein replaced the polyhedra by their symmetry groups and opened vast new areas of research. One path leads into function theory and algebraic geometry, while the other starts with the group of rotations of the dodecahedron and goes on to simple groups.