This was the final day of the conference. The agenda for the day was to:
- attend the two plenary talks,
- watch the four short mathematical plays,
- participate in the free math community event with my family,
- read my poem in the poetry open mic along with my partners.
- attend the Poets dinner and socialize with the other mathematician/poets.
- attend/participate in the informal music night after I put my children to bed.
(I haven't written the agenda for the other days, but this was the shortest list of them all so far!)
Matt Zucker was the first speaker talking about Reaction-diffusion Truchet Tiles. Reaction-diffusion patterns are complex spatial structure that emerge naturally when two or more chemical substances interact locally and spread through space at different rates (wiki) yielding organic-looking structures responsible for patterns like coral patterns, leopard sports, zebra stripes, and fish skin patterns (Fig. 2 from Zucker, 2026). My first stop came when Zucker reveals this project was inspired by Sabetta Matsumoto who asked a question about Matt Zucker's 2025 Bridges talk about his Squiggly Orbs - since that point he was inspired to use Reaction-diffusion patterns to tile. I think this interaction embodies the type of supportive, inspiring interactions that arise from a community of like-minded individuals. I really felt at home in this curious, excited, generative/creative, mathematical community.
My second stop came at the end of Zuckers talk when he tried to generalize his artwork for the audience: good math art is a good riddle! His argument was that it invites the audience to ask "what are the rules that produce this pattern/shape/art?" This invitation to participate was also communicated by Lester and Ryan in my blog post of Aug. 7th creating a very strong point of entry for mathematical engagement.
This statement connects deeply with me as this mentality created a dramatic shift in my success as a mathematics student in highschool; I wasn't very successful with all the traditional drill-type questions used to hone my skills, but I absolutely loved puzzles, riddles, sudoku, etc. When I came to the realization that each drill-type question was just another daily sudoku, I started enjoying "trying out" each puzzle to see if I could get it, so it really took the pressure off of trying to get the solution for every single one. This connection absolutely reflects the foundation of thinking echoed across the presentations I've seen:
- Gary Lester saying that artistic sculptures invite conversations and interpretation.
- Georgina Ryan saying that the artwork (embroidery) invited curiosity through known media (or format... connecting to Nick Sayers below).
- Kerry Mitchell saying his subtle artwork reveals hints of a pattern, but you must work for it. Only then will connections jump out at you over time reigniting motivation to keep digging.
- Saad Mneimneh saying you must be able to engage with math art to achieve the aha! moment.
- Britt Kaufmann saying students receive a hit of dopamine from discovering connections on their own and to give them time to do so.
- Nick Sayers saying math as medium - not the message. I interpret this as trying to tell a riddle with the math, not just presenting the format of the riddle and saying "see? the format? see it? that's all"
The second plenary talk of the morning was by electrical engineer/fibre artist Amy Wendt whose work I've had the pleasure of wearing during the Math/Art Fashion show the night before. Her talk was titled Modular Kirigami Knitting where kiri = cut, gami (kami) = paper. Her work extended beyond paper to materials like Ultrasuede and Kevlar. Wendt represented each line of a knitted piece (visualized as back-and-forth loops like a meandering river system) as a two dimensional pathway, then weaved them together creating surface-covering approximations that were not only 2D but also 3D allowing conforming to body parts like shoulders (Fig.10 below from Wendt, 2026).
The next stop came during the poetry reading: Jim Wolper likened teaching math to being a jazz musician who is playing the 'hits' in yet another club alongside hundreds of other jazz musicians each night. Motifs foreshadow connections to related theorems that are interspersed throughout the melodies. I absolutely feel this alternative perspective of teaching. Being anchored by the curriculum, the roots run deep with connections and all good teachers (musicians) must know them, but they improvise based on reactions from the audience, how they feel, whatever inspired them recently, their techniques and capabilities, etc. What a fantastic metaphor for teaching.
Reading my poem about my daughter, meteorology and its comparison to prophetic fortune telling.
The final stop came when Duston Wetzel read a poem that he titled Many Faces that captures his feelings of inclusion in this mathematics community that truly echoes my own.
References:
Wendt, A. (2026) Modular Kirigami Knitting. Proceedings of Bridges 2026: Mathematics and the Arts.
379–386.
Zucker, M. (2026) Reaction-Diffusion Truchet Tiles. Proceedings of Bridges 2026: Mathematics and the Arts. 157–164.
“I think this interaction embodies the type of supportive, inspiring interactions that arise from a community of like-minded individuals. I really felt at home in this curious, excited, generative/creative, mathematical community.”
ReplyDeleteIt is true that Bridges create this community where people feel safe and where people challenge and support each other in their work. I would love to have a classroom with that chemistry. I think it would make learning and doing mathematics much more fun!
Your comments reminded me of all the Building Thinking Classrooms in Mathematics (Liljedahl, 2021) elements I have been trying to implement last year. The ones I have been using the most are using vertical surfaces, encouraging students to answer their peers’ questions, and autonomous notes taking. I felt like my students were slowly discovering the benefits of team work, and that students were more willing to exchange with each other. But we still have a lot of work to do. My colleague tried a lot of randomized grouping and vertical surfaces as well. Every week, she would come up with something amazing that happened in a random group. I am excited because her students will be my students this year, and I feel like we might end up with a math community that looks like a Bridges community through fostering teamwork, healthy communication, offering as much autonomy to the students as possible, and also, by doing activities that foster relationships between students (like making math-art).
References
Liljedahl, P. (2021). Building thinking classrooms in mathematics, grades K-12: 14 teaching practices for enhancing learning. Corwin.
Olly, your description of Zuckers’ idea that “good math art is a good riddle” and, in particular, your emphasis on the invitation to participate really stayed with me. It made me think about invitation more broadly. I began thinking about artwork as an invitation into someone else’s process. An invitation can be accepted or declined. It can be something we are excited to attend, or one of those things we secretly hope we will not be able to attend.
ReplyDeleteAs I thought about my own experience at Bridges, I realized that I did not engage with or attend to every piece of art or every mathematical explanation. Sometimes it was because of the way the information was presented, and sometimes it was because I simply did not have enough knowledge to truly engage with what was being offered. There were moments when my brain rebelled, and I had to will myself back to the party, so to speak. That was an excellent reminder of what teaching asks us to do.
Teaching is one invitation after another. Every lesson is an invitation for students to enter into an idea, to wonder, to make, to question, or to see something differently. But students get to choose whether they want to attend the party.
That makes the presentation of the invitation important. As teachers, we need to consider our guest list. Who are we inviting? What do we know about them? What might make them want to come in? What might make the invitation inaccessible or difficult to understand? At the same time, we need to remain open to the possibility that the people who accept the invitation may bring something we never anticipated.
This is where I started thinking about plus-ones. We may design an invitation for a particular group of students, but the students who actually arrive bring their own experiences, ideas, cultures, questions, and ways of seeing. They were not necessarily part of the original audience we imagined, but they can change the conversation once they arrive. I think there is something important here for me about accessibility. It is not simply about making sure everyone can receive the invitation. It is also about creating an invitation that is open enough for students to enter in different ways and for their contributions to change what happens once they are there.
My experience at Bridges reminded me that even as an adult learner, I will not accept every invitation. Sometimes I am not ready for what is being offered. Sometimes I do not yet have the knowledge to enter into it. Sometimes the invitation itself does not quite reach me. Remembering what it feels like to be the person sitting at the party trying very hard to stay engaged makes me want to think more carefully about the invitations I offer my students—and whether I have left enough room for the unexpected plus-ones who might arrive.