Contemporary Art and the Mathematical Instinct is a beautiful collection of art, published as a catalog to accompany an exhibition of the same name. The exhibition is organized and circulated by the Tweed Museum in Minnesota; it is now at its third stop of its tour — the University of Richmond — until December 12. The catalog features the work of 44 artists, from Arakawa to Zwieg, with commentary; in addition, there are three historical and philosophical essays on mathematics: learning it, doing it, and looking at it. The first of these, by Steven Luecking, gives a brief but very nice overview of the history of mathematical visualization, from string models to sculpture to computer models.
Is this exhibit really mathematics? It is, and it isn't, as the curator Peter Spooner is careful to point out. The ideas that inspire these works are sometimes mathematically shallow (there is a good bit of numerology and gee-whiz fractals), and the descriptions that accompany the works might make some mathematicians itch: "The numerical ratio [22/7]... is of course that of Pi," and " ...the Klein bottle, which like the Moebius strip, is a 3-D form made of one continuous surface."
And yet, the recurring theme in these works feels very mathematical: take an idea (an algorithm, a pattern, a shape), and play with it. What happens in special cases? What happens more generally? Many of the paintings and sculptures in this collection are not only beautiful art, but also beautiful theorems. Among the 44 artists are mathematicians John Simms (a student of the dynamicist Ethan Coven) and Dennis White, along with computer scientists and engineers whose work has taken an artistic turn.
As one of the commentaries notes,
Works like Cartwright's [and that of many other artists in this collection] challenge the assumption that art derived from mathematical information must automatically be sterile, cold, and divorced from the personal.
If you struggle to explain to non-mathematicians why mathematicians use words like "beautiful" and "elegant" to describe our work, this catalog will delight you. We claim that mathematics has an aesthetic sensibility; this book is a perfect form of "proof by example."
Annalisa Crannell's primary research is in topological dynamical systems, but she is also active in developing curricular materials for courses on "Mathematics and Art" as well as materials for writing across the curriculum.