If we were to select a shape to represent both of the disciplines involved in math art, it could very well be Bathsheba Grossman’s Borromean Rings Seifert Surface, a 4-inch steel sculpture with a mesh surface that seemingly bridges its three rings just as much as it maintains distance among them. As the math sculptor’s website explains: “Named after its use in an Italian coat of arms, these three rings are locked together inextricably, although no two of them are linked.” It is one of many, small scale steel sculptures that have made Grossman one of the most notable names in math art as well as a pioneer of 3D printing.
Grossman acknowledges that for some, the subjects of math and art — and people’s relationship with either or both — are three separate “rings” that don’t quite connect. “What I’ve learned as someone who has put a lot of math in front of a lot of laypeople is that people feel frightened and alienated by their educational experiences with symbolic math,” she explains to ARTpublika Magazine. “But when you put an object that’s plainly algorithmically driven, like so many biological objects [are] — such as a piece of coral or a seashell — most people are strongly drawn to it.” Her work often serves as the catalyst that changes people’s perceptions.
“I try to consciously strip my work of mathematical and fine art elitisms," explains Grossman. She strove to make her work approachable. To gauge her success, she looked outside of academia. When she was out at a cafe or a bar, she'd pull one of her works from her purse and casually place it somewhere on the table without any explanation. If someone nearby got excited about it, picked it up to play with it — and they very often did, particularly with one called Ora, a twisted double-tetrahedron that looks like a beautifully ornate knot — she knew she was on the right track. “If the garbage truck driver is not excited about my stuff, then I don’t think I’ve made a very good piece,” states the artist.
Grossman jokes that she entered university as a math major and left as a sculptor. While completing her BS in Mathematics at Yale University, she took sculpture classes with Erwin Hauer (1926 — 2017), whom she describes as “one of the pre-eminent math sculptors of the 20th century.” It was upon seeing Hauer’s work, which is echoed in Grossman’s undulating and repetitive patterns, that made her think: “I could do that. I will do that.” And so, she pursued an MFA in Sculpture at the University of Pennsylvania with Hauer’s former cohort Robert Engman, during which time she began to amass a portfolio of bronze, handheld-sized sculptures.
Creating these pieces by hand was a long and arduous process. “My basic problem is that I’m shit in the studio,” she explains. “Every time I put my hands on things [they went] to pieces.” What she could do, exceptionally well, was code. In the late 1990s, Grossman began to use computer-assisted design (CAD) to create virtual sculpture: “Suddenly it was, ‘A-ha!’ Now I can use the fact that I have a math degree and the fact that I’m an accomplished programmer!” She sent the virtual files with her designs to a manufacturing facility, where they were made into solid, 3-dimensional forms via 3D printing. “Now, I had a pipeline to make art!” she states.
Engman and Hauer were artists who “were so good at mathematical sculpture that they actually discovered and duplicated things that were, at the time, also mathematical research.” But, Grossman’s talent for coding enabled her to make the kind of sculpture she envisioned, and to become a pioneer of an emerging practice. “I was the person who persuaded everybody that one of the things you were going to do with 3D printing was make mathematical art,” she recalls. “That wasn’t obvious until I came out with my designs and showed them there was a correct way to do it. For several years, I had a virtual exclusive on the steel printing process.”
Through 3D printing, Grossman also popularized the gyroid. Discovered by NASA physicist Alan Schoen in 1968, the gyroid is “an infinitely connected periodic minimal surface containing no straight lines,” which — when given shape — resembles a reef of undulating ribbons. “Underlying many of her sculptures is the idea of the minimal surface, which is the smallest possible surface area that can exist within a given boundary,” explains math and science writer Stephen Ornes. “Some of Grossman’s pieces, like the twisted, pointy ‘Gyroid,’ have triply periodic surfaces, which means they’re composed of minimal surfaces that repeat, almost like tiles, in all three spatial dimensions.”
He credits the start of his career as an award-winning writer to a review of Grossman’s work. “I’d never seen anything like it” says Ornes. In his book, Math Art: Truth, Beauty, and Equations (2019), Ornes explains that Grossman actually had the pleasure of meeting Schoen at a 2004 math conference. Fascinated by the model he presented, the artist made her own model of a gyroid using a computer program called Surface Evolver after she got home. Preferring to see her work in steel, “she outsource[d] the printing to ExOne, the inventors of steel printing, and focuses on perfecting her own use of design software to get the results she seeks.”
Photos of Grossman’s gyroids accompany numerous articles on mathematics and her artworks appear in many different places, such as in the background of the CBS television show Numbers (2005 — 2010), featured David Krumholtz. Her sculpture The Rygo, which resembles a cluster of illuminated underwater caves, was installed at Vancouver’s VanDusen Botanical Garden in 2012; at two meters high, and weighing 3600 pounds, it was, at the time, the largest 3-D print in North America. Her work is so popular, the shelf in Grossman’s home that holds all of the math books that cover her math art is four feet long, and growing.
“I didn’t want to be [the kind of artist that makes] someone [feel like they have] to be really good at math, or to really have enjoyed algebra class, in order to buy my stuff,” shares Grossman. As such, many of her art is available for sale at The National Museum of Mathematics in New York, or (MoMath), which works to make math a lot more relatable by highlighting “the role of mathematics in illuminating the patterns and structures all around us.” There’s a hunger for math,” she explains. “People love symmetry, they love the biological systems that play out between order and chaos, and they’re happy to see sculpture that uses the same principles.”
These days, Grossman spends the majority of her time working as a science illustrator, or — more precisely — a “data physicalizer,” with the Crystal Proteins project that she launched in 2002. This idea, too, involves transforming data into physical form, this time using a laser to draw inside glass solids manufactured by Precision Crystal, a company Crystal Proteins partnered with in 2003. Structures that are invisible to the naked eye, but exist all around us — such as DNA, hemoglobin, rhinovirus, and the chemical chain of caffeine — are made approachable.
Grossman comes from a family of writers. Her father, Allen Grossman, was a prominent, prize-winning poet; her mother, Judith Grossman, is a novelist. Her brothers, Austin and Lev, are both successful writers. The shapes that compose Grossman’s sculptures could, too, be seen as the building blocks of narrative — the way they twist and turn, diverge and reconcile. But, unlike in writing, Grossman’s work is inspired by math, which “exists outside of time and words and progression. It’s an attribute of the universe.” She believes that when we do math, we’re exploring and wandering in a space that already exists.
Her Klein Bottle Opener (which is fully functional) is a take on the Klein Bottle, perhaps one of the most famous examples of a closed, non-orientable surface. As Ornes explains, if one were to walk along its surface, you’d return to the place you started from, but on the opposite side. Grossman’s journey with math art brought her right back to where she started, with a twist. Since the spring of 2020, she has been back in the studio, working with her hands and using actual materials. She’s creating glass, paper weight-like objects, the surfaces of which are sprayed with simple, algorithmic 2D patterns.
The mistakes and flaws that once kept her from making the sculptures she envisioned are assets in this new medium. “Glass is so forgiving,” she explains, “everything you do with it is gorgeous.” And she’s excited to play with color, something she could never do with 3D printing. “What the heck?” ponders Bathsheba Grossman, “maybe I’ll have a second act.”
Note* All images are the creative property of Bathsheba Grossman.