Jordan Ellenberg has a truly wonderful article in Slate.

The entities we study in science fall into two categories: those which can be classified in a way a human can understand, and those which are unclassifiably wild. Numbers are in the first class—you would agree that although you cannot list all the whole numbers, you have a good sense of what numbers are out there. Platonic solids are another good example. There are just five: the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron. End of story—you know them all. [...]

In the second class are things like networks (in mathematical lingo, graphs) and beetles. There doesn’t appear to be any nice, orderly structure on the set of all beetles, and we’ve got no way to predict what kinds of novel species will turn up. All we can do is observe some features that most beetles seem to share, most of the time. But there’s no periodic table of beetles, and there probably couldn’t be.

Mathematicians are much happier when a mathematical subject turns out to be of the first, more structured, type. We are much sadder when a subject turns out to be a variegated mass of beetles. [...]

[...] [Perelman's proof of the conjecture of Poincaré] means … that we can think about proving general statements about three-dimensional geometry in a way that we can’t hope to about beetles or graphs.

I am sure you all want to know what a ‘genus one helicoid’ is. Apparently, it’s the new, new thing in minimal surfaces.

The article mentions some of the applications of minimal surfaces in mixtures of polymers and architecture too; the latter might exploit, for example, the physical ruggedness of the minimal surfaces. However, the next sentence left me utterly stunned:

Calendars are another use for this work, highlighting the aesthetic qualities of minimal surfaces.

Calendars? It sounds loony; but this feeling will go away in a hurry the moment you take a look at the pictures in these two galleries. Indiana University’s Mathias Weber, the author and host of these galleries says they are meant to convey “some of the intriguing enchantment that a mathematician feels when exploring the mathematical objects.”

The enchantment is more than intriguing; it’s amazing.