It is always snowing over Riemann-Lebesgue Hill. This snow is likely a bit different from what you see falling in your neighborhood. The snowflakes in the Mathemalchemy exhibit are formed using mathematics and lasers.
The Chimpunks Sorting Primes Vignette in a way expresses my path in mathematics which went from a blind acceptance of facts – here’s a formula, plug and chug, and it will work – to understanding that mathematics is a human endeavor, one where we can create the rules and see how it evolves.
I think about knots a lot these days, and I think about how complicated those knots are. My work involves knots, and knots within knots. The fanciful sea creatures I’m crocheting are a variant of knots called theta curves.
Let me begin, somewhat circularly, by quoting myself:
“I like symmetry. Or, to be more precise, I like symmetries.
You see, I’m a mathematician, and mathematicians find patterns everywhere. We can’t help ourselves. We don’t just admire things that are symmetric, we ask questions about how they are symmetric. By a mirror reflection, like a face? By a rotation, like a pinwheel? By a translation (repetition in a straight line), like a row of toy soldiers? By a glide reflection, like footprints in the sand?”
When you first saw Mathemalchemy, what struck you the most? Let’s guess it’s the two arches showing balls (spheres) of different sizes. Although the spheres in both arches become arbitrarily small, the spheres in one arch extend indefinitely, crashing into the ocean and plummeting into its depths. The spheres in the other arch approach a single point in space—that arch does not grow without bound.
These arches serve the artistic purpose of adding color to the vertical elements of the piece. In early versions of the project, they were important as drawing the eye to the highest point of the east side of the work. The arches continue to serve as a physical connection between the large sheet that honors five women mathematicians and the surrounding ocean, but also communicate a fundamental principle in mathematics.
Mathemalchemy’s beacon reflects a 2020 mathematical breakthrough.
Mathematicians Jayadev Athreya, David Aulicino and Patrick Hooper recently proved that there are an infinite number of straight paths on the dodecahedron that start at one vertex, proceed in a straight path around the Platonic solid, and return to the starting vertex without passing through any other vertices.
Bronna Butler, professional artist, math lover and Mathemalchemy team member, demonstrates how her stained glass creation illustrates one of the infinitely many dodecahedral trajectories.
About a year ago, I was lucky to have attended Ingrid’s and Dominique’s presentation at the JMM where they introduced their proposal for Mathemalchemy. I immediately offered my support, but admitted that I did not feel qualified to join the group. After all, I am a mathematician, not an artist. Dominique assured me that I’d be welcome, but I remained uncertain. I even drafted an email later that night thanking her for the opportunity, but assuring her that she was mistaken to allow me to join this team. Thankfully, I hit delete instead of send!
When people ask me what number theory (my research area) is, we invariably end up talking about primes. I tell them about how I love to see patterns and make connections, how number theory in particular has problems that are simple to understand, but lead to deep and complex theories. These themes are visible in the three representations of primes in the garden.
Discover the mathematical inspiration underpinning the creation of the Mandelbrot Bakery.
One of Marjorie Rice’s tilings, symmetry, Vladimir Arnold’s cat, dynamical systems and many more mathematical concepts are represented in this charming bakery.
Dominique Ehrmann introduced the Mathemalchemy team members to her Maquette Creation Process. See how the three maquettes helped to create, discuss, question, structure, validate and inspire them.
When Dominique asked for proposals for Mathemalchemy scenes, I sent her a proposal like this: “Something involving infinity . . . Something involving infinity . . . Zeno’s path (related to Zeno’s dichotomy paradox), a hill whose volume is approximated with cuboids, Koch snowflakes.”
Dominique’s response was polite: “I see that I have not communicated clearly what is needed. I am looking for stories.” Oh, a story! I thought, I can write a story! And so, having chosen a tortoise as a protagonist (a nod to Zeno’s Achilles paradox), I sent Dominique the following tale.