Optimal Geometry as Art

Images by John M Sullivan

Department of Mathematics, University of Illinois


Fine-art prints of three of my mathematical images were included in the exhibit "Art and Mathematics 2000" at the Cooper Union in Manhattan, Nov-Dec 2000, and then moved to the Koussevitzky Art Gallery in Pittsfield, MA in March 2001. These same images were displayed electronically in Bologna, Oct-Dec 2000, as part of Matematica, Arte e Cultura, an exhibit consisting mostly of prints by M.C. Escher.

In June 2001, the prints were exhibited, along with my video The Optiverse, at MIT as part of Felice Frankel's conference on Image and Meaning. In July, the prints moved to the Bridges exhibit at Southwestern College, Kansas. Along with my sculpture Minimal Flower 3, one of the prints was exhibited (Nov 2001 through Jan 2002) in Dayton, OH as part of Intersculpt 2001, a coordinated international exhibit of digital sculpture and computer art. The video The Optiverse is part of a new exhibit on Mathematics and Art coordinated by the Ringling School of Art and Design, opening in February 2002.

I prepared the following statement about my work for the various exhibit catalogs.

Optimal Geometry as Art

John M. Sullivan

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.

"Minimal Flower 3" is an homage to Brent Collins, whose sculptures have been very inspirational to me. For this sculpture, I designed the boundary curve and an initial surface by hand, and then used software to model a minimal surface. This, mathematically, is the optimal shape a soap-film spanning across the boundary would achieve. The geometric equilibrium of a minimal surface, where the curvatures of the surface always balance in a saddle configuration, adds to its beauty.

My print, "Foamy Partition: Weaire-Phelan" gives an interior view of a soap froth. The particular geometric structure of this froth, discovered in Ireland by Weaire and Phelan, partitions space into equal-volume cells, in what is likely to be the optimal way. Two other prints derive from "The Optiverse", a video showing an optimal way to mathematically turn a sphere inside-out, which was a joint project with George Francis, Stuart Levy, and Camille Goudeseune. "Optiverse: Framework Interior" shows a triangulated computer simulation of part of the everting sphere; "Optiverse: Minimax Sphere Eversion" uses bubble-like transparency to show the whole eversion.

Biographical Sketch

John M. Sullivan was born in 1963 in Princeton, NJ. After earlier degrees from Harvard and Cambridge, he received his Ph.D. in Mathematics from Princeton in 1990. He was then a postdoctoral fellow at the Geometry Center, and taught at the University of Minnesota. Sullivan moved to the University of Illinois in 1997, where he is an Associate Professor of Mathematics.