In the 1860s it was discovered that a general cubic surface defined over the complex numbers has exactly 27 lines on it, and the configurations of these attracted a lot of attention. It was followed by similar statements relating to two families of algebraic curves. Why were these so interesting? It turns out that they can be characterized by properties derived from the three Dynkin diagrams E6,E7,E8 and that each age has its own mathematical manifestation of these, from the neolithic Scots to modern-day theoretical physicists. The talk will describe the multitude of interpretations of these basic mathematical objects.