A Chain Reaction
An inspiring math professor uses crochet to illustrate the intersection of math and art
By Rachel Rodriguez
You may not think a “History of Math” class would include a lesson in art. For Moira Chas, it’s a great way to teach and inspire her students at Stony Brook. For the past several years, she has been incorporating a collection of physical objects into her teaching — objects of art, you may say — many of which she crochets or creates herself.
Chas, a professor in the College of Arts and Sciences’ Department of Mathematics since 2001, believes that we can all learn math — and for most people, it’s much easier to understand by interacting with an object.
“I use art with students to help them grasp ideas,” said Chas. “When they interact with an idea that is embodied in a different way, it contributes to their understanding. And when I see their understanding, I feel compelled to make more objects. It is very inspiring to see students, and people in general, make progress in math with the help of the objects I have made.”
A self-described late bloomer, Chas didn’t immediately turn to mathematics as a career. In fact, as a high school student, she was much more interested in writing. However, realizing that she would always be able to write, if only as a hobby, she decided to pursue mathematics as a major — a choice she describes as incredibly lucky. As soon as she started taking courses, she found that it was completely her “thing.”
Chas pursued mathematics in her native Argentina, citing the strong math tradition in her country. She attended the Universidad de Buenos Aires, and particularly enjoyed math that has a visual component. She focused on low-dimensional topology, which is closely related to geometry. She learned about fractals (a mathematical shape or pattern that repeats forever), finding them incredibly intriguing and beautiful — like art — and wanted to learn the math behind them.
“In Argentina, if you are a math major, you do only math — the only courses you take are math-related. So you may be less rounded, but delving deeper into something has its positive aspects,” she said.
Through the years, Chas explored her creative side, looking for ways to incorporate objects into her teaching. She began to crochet more than 20 years ago when she was pregnant with her daughter, finding that working with her hands helped her think and relax. Chas initially made things for her daughter, such as clothes for her and her dolls. But then she began crocheting mathematical objects — physical models such as a torus, a Möbius strip and Seifert surfaces of knots.
“I started to call the objects I create ‘art,’” she said. “I need to see them in a certain way — I don’t know if it’s beauty, but there is a certain aesthetic that I need to achieve. The objects I create are related to math, and this is what really moves me. So in that sense, my art is translation. I translate math ideas to objects, into art.”
Samples of Chas’ many creations:
Chas said she feels that when teaching, sometimes she needs to say less and show things from a different point of view, thereby incorporating art and different media into her mathematical lessons. “In academia, we have to stop and think what is the best way to teach, not just follow what was done in the past.”
This ideology has helped inspire countless students over the years. In 2017, Chas was a recipient of the College of Arts and Sciences’ Godfrey Excellence in Teaching Award, an annual award in which students confidentially nominate professors for their mentorship and teaching. One particular nomination described how Chas made abstract mathematical ideas come to life, inspiring students to ask questions and think far beyond the material covered in class. The student also noted Chas’ active participation in organizing events and programs geared to underrepresented groups in mathematics, making the mathematical community welcoming to women and minorities.
Chas has also been described as an inspiring teacher who brings out the best in her students. Connor Stewart, a former student and research mentee and current math PhD student at the CUNY Graduate Center in Manhattan, was a linguistics major during his first two years of college. Upon taking classes with Chas, he decided to make math his focus and became immersed in math research. As an undergraduate student, Stewart took part in a topology and geometry workshop that Chas organized in Summer 2019.
“Involving undergraduate students in math research is one of Professor Chas’ committed goals, and many other students in the department have been influenced by her to go on in math,” he said. “I am now in a graduate math program, and I attribute this in large part to Professor Chas’ continued encouragement, to her expectation that her students think and care deeply about the topics they study, and to the curiosity and enthusiasm for math communicated in her teaching.”
Stewart also commented on the impact Chas’ crocheted mathematical objects had on his learning. “Many times in math, when a concept has a concise statement, it can give you a false sense of understanding. Applying the concept to a simple example, with small numbers or familiar objects, can bring out subtle points that you are missing. As a student in Professor Chas’ topology class, the process of holding one of her physical models, getting stumped by it, and having to reapproach it from a new viewpoint, was an invaluable experience for clarifying my understanding of surfaces and learning to visualize mathematical objects.”
During the past year, Chas’ works have been featured in two exhibits at the Simons Center for Geometry and Physics Gallery. In the first, “Ways of Making” (Fall 2022), Chas was among three collaborators showcasing works that illustrated the connections of math, art and design. Curated and planned as a place for dialogue, the exhibit welcomed visitors to reflect on these connections while raising timeless questions such as “what is the difference between mathematical illustration and inspiration?” and, as noted from Chas’ works, “why do we love knots?”
Chas’ second exhibit, “Projections of the Klein Bottle,” curated by Lorraine Walsh, art director and curator at the Simons Center, featured some of her latest work using wire as the medium. Chas came across techniques to create objects with wire after searching for ways to create see-through shapes — something that was not easy to achieve with crochet. She said she was inspired by American artist Ruth Asawa, who is known for her wire sculptures and who counts mathematician Max Dehn as one of her influences.
Chas’ next project is a book about British mathematician Alicia Boole Stott. “She deserves to be well known,” Chas said, adding that her geometrical ideas and mathematical path are incredible. “There are so many women who inspire me, such as Ruth Asawa and Alicia Boole — they are the stars in the sky that I follow.”
Chas often gives talks about women and other underrepresented groups in mathematics, discussing why there is so little diversity and her ideas for changing that. She’s currently working on a paper with Catherine Cannizzo, a former postdoc at SCGP, in which they propose classroom activities based on the mathematics of different societies to show that the discipline is a collaborative work of humanity that is not established only on a few brilliant ideas by a handful of men.
“The idea of this paper is to show the history of math; we’re aiming to use some of the very old ideas to explain math and show how it has been done around the world throughout the centuries by all kinds of people,” Chas said. “We have to change the pattern that math is only a path for men; it’s a beautiful thing that we all have access to.”
Chas describes mathematics as a human discipline, and through her passion for art, connects it with all human things. “We think about math in different ways and understand math at different levels. Math is generous and demanding, and if you put in serious work, math will give you some form of understanding. I think it’s important to keep the curiosity alive.”