Mathematical Imagery

Mathematical artists create strong, stunning works in all media and explore the visualization of mathematics

The 2023 Mathematical Art Exhibition

The 2023 Mathematical Art Exhibition was held at the Joint Mathematics Meetings in Boston, MA. These are the recipients of the 2023 Mathematical Art Exhibition Awards: “Topological Envelopes” by Richard Hammack, awarded Best Photograph, Painting, or Print; “Barth Sextic” by Edmund Harriss and Silviana Amethyst, awarded Best Textile, Sculpture, or other Medium; and “Dawn” by Jiangmei Wu, Honorable Mention.

The awards "for aesthetically pleasing works that combine mathematics and art" were established in 2008 through an endowment provided to the American Mathematical Society by an anonymous donor who wishes to acknowledge those whose works demonstrate the beauty and elegance of mathematics expressed in a visual art form.

View these and other works in various mediums submitted to the JMM 2023 Mathematical Art Exhibition.

Best Photograph, Painting, or Print

Topological Envelopes" by Richard Hammack. 10x45x45 cm laser printed paper, glue, cardstock, 2022.

I see my recent work as being closely aligned with printmaking. A piece begins as a LaTeX source code, which is typeset, laser-printed, cut, folded and glued. The objects in this submission are envelopes with non-standard topologies. They are intended to be disseminated through the mail (with the postmarked stamp a stand-in for an edition number). Consequently they are—by necessity—flat. This work consists of a card-stock box containing a dozen paper envelopes, each a topologically accurate (but flat) realization of a closed surface, such as a torus, Klein bottle or projective plane, etc. The envelopes are designed to be sent through the mail. However, for the purpose of this exhibition, I envision them arrayed on a table so that viewers can pick them up and examine them.

Best Textile, Sculpture, or Other Medium

Barth Sextic” by Edmund Harriss and Silviana Amethyst. 20x20x20 cm Wood (Ash) and Brass, 2020.

We started working together at the "Illustrating Math" semester at ICERM, with the goal of exploring toolpaths to make algebraic surfaces on a CNC mill. On a 5-axis mill, the tool can control both the position of cut and the direction, thus producing a very high finish quality with a relatively small number of paths. Our goal was to create the toolpaths to machine the surface directly from the mathematical surface, rather than through some sort of proxy, for example in first creating a mesh, and then applying a more standard strategy. The modularity of the Barth Sextic – 20 identical units – makes it an obvious choice to mill in pieces. As the sextic surface with the maximum possible number of double-point singularities (here the positions of the brass rods and the spikes on the outside mark the real singularities), this structure is mathematically interesting as well as beautiful. The engagement from the materials of the structure has already lead to many conversations with many people about the nature of singularities and algebraic surfaces.

Honorable Mention

“Dawn” by Jiangmei Wu. 48x86 cm Muslin, Watercolor, 2022.

I work in the overlapping space of art, design, mathematics, technology, and engineering by exploring the conceptual grounds, the geometric and tectonic forms, the mathematical understandings, and the material applicability of origami and origami-inspired design. In particular, I am interested in how to explore folding through spatial art installations, how to invent new folding designs based on mathematical understandings, how to digitally fabricate these new designs and structures in various materials (not necessarily paper), and most importantly, I am interested in exploring how these aspects work together within the conceptual and physical spaces in which they occur. The fabric origami work is based on a technique the artist calls "tessellation grafting." To graft a tessellation, one starts by cutting along all the edges figuratively, creating a new tessellation by inserting rectangles, again, figuratively, along all the edges and polygons connecting the vertices. To make the fabric origami, the corners of new polygons are sewn together, collapsing the polygons back to points and rectangles back to lines. Interestingly, the tessellation grafting is rooted in the dual graph of a plane graph G in graph theory. While this work is based on the duality of the Voronoi diagram and the Delaunay triangulation, other dualities can be further explored.