Arts & Mathematics

Mathematics is often presented as a sequence of Definitions, Propositions, Theorems, and Conjectures. Yet, Art has always defied definitions. This page is also hard to define, and that’s okay!

Aperiodic Monotile Puzzles

The discovery of the “hat” and “Spectre” monotiles in 2023 has inspired lots of creative renditions and even a contest. In the link above you can find resources for laser-cutting Spectre puzzles.

Spectres are strictly chiral aperiodic monotiles, even when reflections are permitted.
The hat is only weakly aperiodic, meaning that it tiles periodically if you allow reflections

Raycasting Real Algebraic Surfaces

This amazing experiment is rendered using CindyJS directly in your browser.

Seepferdchen surface is named after seahorses, presumably because of their necks!

Animating Mathematics with Manim

Once or twice, I’ve enjoyed using Manim to make animated mathematical presentations, for instance in the AMS Grad Student Blog post “Mathematics From Arts?

“And since geometry is the right foundation of all painting, I have decided to teach its
rudiments and principles to all youngsters eager for art.” – Albrecht Dürer (1471–1528)

The Geometry Center

Speaking of animating mathematics, I was delighted to learn about the Geometry Center, where spectacular videos like Outside In were created, and sad to learn that it used to be located at the University of Minnesota before being closed in 1998 – long before I arrived. An anthology of videos by the center is graciously provided by Professor Tamara Munzner, who previously worked there.

“Outside In (1994) showcases William Thurston’s approach to turning a sphere inside out.”

Thurston’s Simple Closed Curvy Mural

Another wonderfully mathematical piece of artwork which I wish had survived is this mural on a wall in Evans hall in Berkeley by William Thurston and Dennis Sullivan from 1971. I am somewhat tickled that the project was “in response to a little flurry with administration sactions of some sort when John Rhodes painted the wall outside his office, I think with a political slogan related to one of the issues of the times (Vietnam war, invasion of Cambodia, People’s Park?),” according to Sullivan. Dr. Marissa Kawehi Loving wrote about the mathematics of this mural here.

“The ‘wall curve painting,’ two meters high and four meters wide, dated and signed,
lasted on that Berkeley wall with periodic restoration for almost four decades”

Anatoly Fomenko’s Extraordinary Artwork

I first came across Fomenko’s artwork when a friend told me about “Homotopical Topology” by Fomenko and Fuchs. While he had some .. uhh, odd? .. opinions, I really like his artistic style!

"How to unclasp one's fingers in three-dimensional Euclidean space;" a tutorial in 4 acts.

Geometry Problem from Shush

Computing area of a regular heptagon and hexagon (on the reverse).

Details of mathematical tablets from 17th century B.C found in Shush.