Education & Enthusiasm

Our ancestors have been investigating caves for a long time, so perhaps William Waterhouse is right in proposing that they discovered crystals and were inspired to invent polyhedra. Of course, the polyhedra that we find in antiquity (in ancient Scotland, in ancient Greece, and no doubt elsewhere, tend to be Platonic solids, which are not the polyhedra one normally thinks of when looking at gypsum crystals. But perhaps when one is just starting to think about polyhedra, the Platonic solids are the ones easiest to define and understand.

Historians don’t seem to be very interested in the history of crystals, especially before Kepler, so all we can do is look at antiquarian bits about gems and uses in medicine. But looking around today, it seems likely that we have had a community of enthusiasts for some time. Polyhedra also have fans, and polyhedra are one of the few mathematical objects that laymen can grasp and recognize as mathematical objects.

While scientists and engineers recognize the importance of crystals in science and engineering, and while mathematicians recognize the importance of polyhedra (after a century of relative indifference), their grip on the popular imagination suggests that crystals and polyhedra can play a role in education, and in communicating to the public what mathematicians, scientists, and engineers do.