Artist Statement

Mathematical Art as a Creative System

My mathematical art is driven by two core ambitions:

1. To create geometric and topological structures of both aesthetic and mathematical interest.
   
   

2. To develop a system that optimizes creative diversity, efficiency, and productivity in the production of mathematics and art.
   
   

Mathematical Art

From Paper to 3D Printing: A Journey of Materials and Ideas

Over the past 37 years, my artistic journey has evolved alongside the materials I use. I began with handmade paper sculptures, transitioned to wooden models made with industrial woodworking tools, and now design 3D-printed mathematical sculptures and models using STEAM CAD, Great Stella, and Bambu Studio software as can be seen on this site. This progression reflects my ongoing fascination with symmetry, harmony, and order—qualities that offer me solace in a chaotic world.

Color Theory

In my graphic designs, models, and sculptures, my palette oscillates between the rich chromatic harmonies of Renaissance masters like Michelangelo and Raphael, and the soft, muted tones of Nantucket pastels. This balance of intensity and tranquility evokes both mathematical precision and artistic emotion.

Influences and Inspirations

My work is deeply influenced by mathematicians, scientists, and artists whose contributions resonate with my own creative themes. These include:

• Mathematicians: Hermann Brunn, August Möbius, Felix Klein, B.M. Stewart
  
  

• Scientists: astronomer Johannes Kepler, chemist Alan Holden
  
  

• Artists: M.C. Escher, Robert Fathauer, Henry Segerman, George Hart, Bathsheba Grossman, Rinus Roelofs, Leonardo da Vinci
  
  

Structural Geometry, STEAM CAD, and STEAManufacturing 

I use structural geometry as the inspiration and methodology for all my mathematical art and pedagogical aids. 

Structural geometry is informally defined as a mathematical discipline for the design, construction and deconstruction of geometric and topological structures such as points, lines, polygons, and polyhedra (geometry) and knots, links, braids, and weaves (topology) with geometric components including but not limited to points, lines, polygons, and polyhedra. 

STEAM CAD is the creativity engine that I invented to optimize my creative diversity, efficiency and productivity. It is a hierarchical computational production system for the production of data structures. 

Its architecture is modeled on academia and has four levels in a nested hierarchy. Thus, at the highest level there are Departments (STEAM). Then below them are disciplines. For mathematics these include subjects like calculus, geometry, topology, algebra, and linear algebra etc. At the next level down there are categories of objects. For example in geometry these are defined by the objects of study that include points, lines, polygons, and polyhedra. Finally, at the bottom are specific objects. The category of polyhedra ncludes objects like cubes, tetrahedra, and dodecahedra etc. 

Each level uses partition tensors like multiplication tables to combine components and structures as input variables and output composite structures in the output array of the table (Tables 1 and 2).

I use STEAM CAD (conceptual aided design) to not only systematically structure and organize structural geometry, but also to produce the ideas that inspire my graphic designs. 

If implemented as software and combined with Great Stella software for graphic design, Bambu Studio software for slicer design, and a 3D printer like the X1 Carbon by Bambu Labs, then STEAM CAD would complete a full cycle of STEAManufacturing system that transforms geometric ideas into graphic designs, printing G-code and finally 3D printed reality. 

Taken together; structural geometry, STEAM CAD, and STEAManufacturing provide a complete creativity system for my mathematical art as evident in 3D printed mathematical sculptures (Figures 1 and 2).