# John M. Sullivan

## Artists

## Statement

My art is an outgrowth of my work as a mathematician. My research studies curves and surfaces whose shape is determined by optimization principles or minimization of energy. A classical example is a soap bubble which is round because it minimizes its area while enclosing a fixed volume. Like most research mathematicians, I find beauty in the elegant structure of mathematical proofs, and I feel that this elegance is discovered, not invented, by humans. I am fortunate that my own work also leads to visually appealing shapes, which can present a kind of beauty more accessible to the public.

## Artworks

"Minimal Flower 3" shows a nonorientable minimal surface spanning (like a soap film) a certain knotted boundary curve. The surface, like the knotted boundary itself, has 322 symmetry, meaning three-fold and two-fold rotational symmetry but no mirrors. The mathematical surface is thickened into a three-dimensional sculpture by simulating the process of blowing a bit of air in between two parallel sheets of soap film. To create a more pleasing result, the surfaces are actually modeled in 3D hyperbolic space. This sculpture is an homage to Brent Collins, whose "Atomic Flower II" has the same topology.

"Minimal Flower 4" shows a nonorientable minimal surface spanning (like a soap film) a certain knotted boundary curve. The surface, like the knotted boundary itself, has 422 symmetry, meaning four-fold and two-fold rotational symmetry axes but no mirrors. The mathematical surface is thickened into a three-dimensional sculpture by simulating the process of blowing a bit of air in between two parallel sheets of soap film. To create a more pleasing result, the surfaces are actually modeled in 3D hyperbolic space.