After a 36-year teaching career, I am now a 3D math artist and interactive book creator. Students convinced me long ago that my nice-looking calculus graphs could qualify on their own as art. I now spend my time conceiving, creating, and showing math art, trying to bring the joy and visual beauty of mathematics to an unsuspecting audience.
In the popular culture, math is commonly perceived as being separate from art, and people often cry "I'm not a math type, I'm creative!" But as makers and viewers of math art, we enjoy using both halves of our brains! My work displays mathematical relationships and visual patterns in a way that I hope makes people stop, notice, and say, "That's cool! That's math?"
I wanted to show, visually, the patterns and unpredictability of the prime numbers. Picturing the number line as beads, we have four strings of beads representing integers from 2 to 1000; green are primes and yellow are composites. The strings spiral outward and upward, wrapped around four shapes: cylinder, cone, paraboloid, and flat disk. Can you see how the primes line up better along columns of the cylinder? What makes them behave like that? What is the last prime bead on each string? This image is included in my 2025 JMM talk, "Spirals and Polyhedral Lattice Paths: Where are the Prime Locations?"
Based on the beautiful Barth Sextic, known for its sixth-degree equation in x, y, and z, these images trace the evolution of the poofy star at the top, from egg to polyhedron to stellated stardom. The equation, if you must know, takes the form 4 (p^2 x^2 - y^2) (p^2 y^2 - z^2) (p^2 z^2 - x^2) - (1 + 2 p) (x^2 + y^2 + z^2 - 1)^2 w^2 = 0.
Unlike polyhedra with defined faces and planar polygons, these different shapes are generated by changing the parameters p and w in the above equation and watching them respond obediently. The bubble-like appearance is achieved by using 3D contours and transparency values. I have always loved this shape, especially the art piece seen at JMM 2023 by Silviana Amethyst and Edmund Harriss.
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