Math, Art, and Communication: How Mathematicians Engage the World
BLOG: Heidelberg Laureate Forum
Misinformation has become one of the greatest societal problems of this age. It is often regarded as a pandemic because false or misleading information can spread rapidly, especially across social media and online platforms.
Whether it is about vaccines, climate change, or political events, the sheer volume of misleading narratives threatens public health, undermines science, and destabilizes societies. In the age of information, it has never been more important for scientists to communicate accurately and clearly.
Yet this is easier said than done. Particularly in mathematics, typically seen as a solitary, abstract discipline, clear communication is rarely straightforward. At the 11th Heidelberg Laureate Forum this year, a panel of mathematicians demonstrated that math can also be a profoundly creative and interactive art form. Whether through hands-on workshops, sculptures, and even playwriting, the panel members showcased their work in how mathematics can be more tangible, accessible, and engaging for broader audiences.
Topological Sculptures
Moira Chas, an Associate Professor of Mathematics at Stony Brook University, has long been passionate about both mathematics and the arts. Her work in topology – one of the more abstract branches of mathematics – is excellently complemented by her artistic endeavors. For the duration of the Forum, some of her topological wire sculptures were on display, and she brought some with her on stage as well.
Topology is a branch of mathematics that studies the properties of shapes and spaces that remain unchanged under continuous transformations, such as stretching or bending, without tearing. Unlike plain geometry, which focuses on precise measurements, topology is more concerned with the fundamental characteristics of objects, like connectedness or the number of holes they have.
A classic example of a topological object is the Klein bottle: a non-orientable surface that has no distinct “inside” or “outside.” This structure was first described in 1882 by the mathematician Felix Klein. A true Klein bottle can only exist in four dimensions but it can be represented approximately in three-dimensional space. This is difficult to comprehend and visualize, which is where Chas’ artistic endeavors come in.
During the panel, Chas shared her innovative approach to explaining mathematical concepts through sculptures. She described her fascination with the Klein bottle and shared several wire sculptures she had created to represent this topological object.
Holding up one of her wire sculptures, Chas asked the audience to imagine the bottle’s form: “This might not be the image you have in your mind when you think of a Klein bottle. But for a mathematician, it’s a space with certain properties, and these sculptures help to make those properties more real,” she explained.
For Chas, communication through art is not just about translating abstract mathematical ideas into physical forms, however. It is also about engaging the senses and imagination in the process. “In math, we often answer the question, ‘What do I mean by this term?’ That’s what these sculptures help people explore. They encourage a deeper understanding by letting you interact with the concept physically.”
Chas has taken her creative expression even further by writing a play that explores the lives of mathematicians and the beauty of mathematical ideas. Her play about Alicia Boole, a pioneering mathematician in four-dimensional geometry, won a Simon Center Playwriting Competition award.
“Alicia Boole was the daughter of George Boole, who discovered Boolean algebra, but her path was very different. She didn’t receive formal mathematical training but fell in love with four-dimensional geometry. The play is really about her passion for discovery,” said Chas.
This type of work explores the personal stories of mathematicians and their struggles, humanizing them and thus making their stories more relatable to people from all backgrounds.
“It’s very hard to describe her complex ideas in a 20-minute play. It’s only a glimpse of her ideas but I want to emphasize that we are all searching for understanding and she’s one person who put in tremendous time and effort and also enjoyed the process most of the time.”
Hands-on Learning
The panel also featured another creative communicator, Érika Roldán, who is currently leading the research group Stochastic Topology and its applications at the Max Planck Institute for Mathematics in the Sciences.
On the first day of the Heidelberg Laureate Forum, Roldán introduced “The Fence Challenge,” where the task is to enclose as much area as you can with “pentominoes” (five-block dominoes). In addition to being a fun challenge, this citizen science projects actually helps participants develop their mathematical visualization and also helps researchers inch closer towards solving a combinatorics problem.
In fact, Roldán emphasizes that her colleagues explore the more playful side of mathematics.
“Well, one of the things that I’m super grateful for now is to be able to be a research group leader, and have my students and postgrads doing research and also outreach. They’re doing mathematics visualization and video games within these projects.” The researcher says that in addition to making math more accessible, this is also useful for the mathematicians. “They’re attaining skills by doing this and also a knowledge and understanding of the impact that they can have in society. I think this will also reduce the isolation that we know is a well-being problem in academia and the sense that what we are doing has no immediate impact in society.”
Yudhistira Andersen Bunjamin, an associate lecturer at the University of New South Wales in Sydney, shared his experience in designing mathematics workshops for high school students. His approach centers on hands-on learning and narrative storytelling. Rather than focusing on specific mathematical problems, Bunjamin’s workshops aim to convey the broader principles of mathematical thinking.
“We don’t just teach them math facts. We try to show students what it means to think mathematically,” said Bunjamin. He and his team spend years designing these workshops, constantly refining the process. “It starts with a learning outcome. For example, one of our workshops teaches students what it means for something to be impossible in mathematics – what non-existence looks like.”
However, the best approach depends on the audience. Bunjamin notes that one of the workshops was carried out in a remote part of Australia, where the population of Indigenous Australians was higher than in other areas, and where the analogies and general approach used in other areas may not have been as effective. In another instance, he recalled a workshop with a lot of international students whose level of English was not the same as their peers who grew up in Australia. “We’re starting to think ‘does this translate well?'”
Even something as simple as counting can be cultural, says Coumba Sarr, who holds a PhD in Number Theory from the University of Caen, Normandy.
In Wolof, a West African language spoken by over 10 million people, counting follows a special additive and multiplicative structure. Wolof numbers are basically counted in groups of five, and for numbers beyond five, combinations of smaller numbers are used. The number ’16’ for instance is counted additively as ’10 & 5 & 1,’ and the numbers beyond twenty require both addition and multiplication. For instance 34 is depicted as “3*10+4” and the same goes for all higher numbers. This structure provides a natural way to teach mathematical operations, embedding mathematical reasoning within the language itself. “What we would like to suggest is that maths is a very universal language,” the panelist added.
The panel kept coming to this idea, that if you want to communicate math or science, if you want to get your message across clearly, it is important to appeal to things that are inherently human. Making maths accessible requires not just knowledge but also empathy, and the same goes for all science communication. It is not just about talking to people, it is about getting them to connect to it, to engage their curiosity and imagination.
Ultimately, the panelists agreed that math communication should be seen as an essential skill for every mathematician. “We all need to be ambassadors of science,” said Chas. At the end of the day, it is not just about solving problems – it is about helping others see the beauty and the joy of mathematical thinking.
Darum geht es ! mathematische Visualisierung
Viele Menschen sind Augenmenschen, sie denken in Bildern.
Es gibt auch die Menschen, die in Begriffen denken, das nennt sich Physikalisch Denken.
Und es gibt Menschen, die denken im Hören, ein Komponist, der die Noten aufschreibt, der hört auch den Ton dazu.
Und wenn dann noch die Kunst dazu kommt, die Kleinsche Flasche zähle ich zur Kunst, dann wird es geradezu verrückt, weil Begriffe wie innen und außen aus den Fingern gleiten.