I walked into the conference with a green sticker on my badge, marking me as a first-timer, and a small, familiar feeling of not quite belonging. Then George Hart said, right there in the room, that mathematics is fundamentally a human experience, and it sent me straight back to a book from an earlier course, Francis Su's Mathematics for Human Flourishing, which spends its pages making the case for all the ways doing and studying math can be virtuous, and how it makes us grow as humans. Something in me settled, just slightly, hearing Hart say it out loud in a room full of people who study and create math/art for a living.
His talk, Math/Art at the Dawn of AI, is where the day's real question first showed up, though I didn't recognize it as a thread that would weave my day together yet. Hart described asking AI to generate three-dimensional mathematical sculptures, and the results were a strange kind of impressive: the images looked fantastic, the accompanying explanations sounded fantastic, and none of it quite matched. The math understanding wasn't there. Not yet, anyway. He kept circling a bigger question underneath the technical one: is AI democratizing art, handing new tools to anyone who wants to make something? Or is it terrible, stealing from human creativity without ever really understanding it? He brought up the camera as a comparison, another technology that was supposed to end an art form and instead just forced painting to change. Someone in the room raised the question of credit, of whose work this actually is when a machine generates the object and a human generates the prompt. I don't think it was answered. I don't think it can be, yet.
I sat with that question longer than I expected to, mostly because of my brother Erik. He writes code for a living, and lately most of his work hours go into reviewing what an AI has already written rather than writing it himself. He used to think of his coding as its own kind of artistry. Now he tells me the part he loved is disappearing, replaced by checking someone else's, or something else's, work. I kept thinking about him through the rest of Hart's talk, and I'm still not sure what to do with that.
Then I sat down for Ayliean MacDonald's talk, titled, of all things, It's About Time. I'd already spent two full days writing about time on my own, unprompted, before I knew this talk existed, and hearing her open by saying she's always been someone fascinated by time felt like unexpected company. She talked about an old man in her neighbourhood, a friendship built on math, who measured his own life out in seconds, among other delights, and she showed us the paper he'd worked it out on. She described a project of 32-by-32 grids, all begun differently, made by hand, the making itself stretched out and time-lapsed or shot in stills, so that endurance became part of the material. At one point I found myself silently wondering which came first for her, the mathematical understanding or the art, whether one pulls the other along or if they arrive together. I never asked. The room moved on, and so did I, and now I'm left holding the question myself, the same way Hart's room was left holding the credit question. Maybe that's fine. Maybe conferences are supposed to send you home with a few of these still open.
The talk that followed, on construals, came from Meurig Beynon, who explicitly addressed some of his ideas as a response to Hart's talk that same morning, which I appreciated, since it meant I wasn't the only one still turning Hart's questions over. He introduced the idea of a construal as an artifact that captures a partial, personal understanding of something, never the whole of it. A map isn't the campus. It's one person's negotiated relationship with the campus at one moment. He said something that I wrote down word for word: teaching is communicating your construal to someone else. I'll admit the deeper mathematics of his talk mostly went over my head. But that one idea landed, and it's already changing how I think about my own classroom. If every student is building their own partial construal of a concept, and I'm building mine, then teaching isn't handing over a finished, correct thing. It's finding a way to let two partial understandings meet.
By the afternoon, Anton Bakker was talking about lattice sculptures and puzzles that took his team a literal decade to solve on an old TRS-80 computer, back before the program that eventually solved them in minutes existed. He said something that pulled the whole day together for me: the industrial revolution took our muscle, and now something is coming for the brain too, doing the calculating and answering the questions for us. What's left, he wondered, after both of those are gone? He thinks it's the questions themselves. The wondering. The choosing of what's worth asking in the first place.
I came into today with a green sticker and a flicker of insecurity about whether I belonged in this room of mathematicians and artists. I'm leaving it with an unasked question about art and understanding, an unresolved question about credit and authorship, and a genuine, thrilling sense that the not-knowing is mine to keep. Not-knowing has always felt like room. Room for growth, for openness, for wonder. If a machine can eventually calculate anything and generate any image, what does that leave the rest of us to do, and is it enough?
References
Bakker, A., & Verhoeff, T. (2026). From Koos puzzle to lattice sculptures: Navigating vast spaces of form, meaning, and wonder. Proceedings of Bridges 2026: Mathematics and the Arts, 29–36. https://archive.bridgesmathart.org/2026/bridges2026-29.html
Beynon, M. (2026). Building bridges: Making sense of mathematics and art. Proceedings of Bridges 2026: Mathematics and the Arts, 21–28. https://archive.bridgesmathart.org/2026/bridges2026-21.html
Hart, G. (2026). Vibe coding math/art projects [Conference presentation delivered as Math/Art at the Dawn of AI]. Proceedings of Bridges 2026: Mathematics and the Arts, 515–518. https://archive.bridgesmathart.org/2026/bridges2026-515.html
MacDonald, A. (2026, August 5). It's about time [Conference presentation]. Bridges 2026: Mathematics and the Arts, Galway, Ireland.
Su, F., & Jackson, C. (2020). Mathematics for human flourishing. Yale University Press. https://doi.org/10.2307/j.ctvt1sgss.8
This first day also made me question the use of AI. I personally rarely used it, even if I was shown how it can support me teach. And no one really showed me how it can support me in my academic work.
ReplyDeleteWe are lucky in our school that students are also not likely to use AI to do work. As a math teacher, I could show them how to make critical use of it, just like I show them how a graph calculator or an excel sheet can help them visualize the math and justify decisions based on the information given by the tool. Ayliean MacDonald (2026) mentioned that “there is so much you can gain from doing things by hand”. I feel that the same applies to learning mathematics. The simplest example would be learning to do basic arithmetic (add, subtract, multiply, division) by hand before using the calculator. I know that the students who master doing those operations by hand are much more likely to notice they made a mistake while typing on their calculator. It also reminds me of Cuoco’s et al. (2010) habits of mind. Doing mathematics relies on learning strategies to solve problems or to gain understanding of a concept. If a student struggles with a concept or a problem and asks AI to help, I feel like it is a lost opportunity to learn or develop those habits of mind. Because after all, doing mathematics is not learning concepts by heart, it is learning how to make sense of mathematical ideas.
I have not yet investigated how AI can support my students’ learning because I have been focusing on many other teaching practices. Thus, I still have many questions and wonders about it. How could I use this tool without taking away a learning opportunity for my students? What is a ‘useful’ way to bring the tool in the classroom?
References
Cuoco, A., Goldenberg, E. P., Mark, J., & Hirsch, C. (2010). Contemporary curriculum issues: Organizing a curriculum around mathematical habits of mind. The Mathematics Teacher, 103(9), 682-688.
MacDonald, A. (2026, August 5th). It’s about time [Conference presentation]. Bridges 2026, Galway, Ireland.
@Kristie,
ReplyDeleteThank you for your intriguing perspective of the first day of the conference. It sounded like it really set up your expectations for the rest of the days!
“Teaching is communicating your construal to someone else.” (Beynon, 2026): This got me thinking, what is the best way to communicate a concept or construal to someone else? Does it need a beginning, middle, end? Does it need a hook to capture attention? Does it require characters? Instructions for building? Words or will only images suffice? This idea of teaching connects to my research question about relationships and one of the best ways to demonstrate relationships is through narration and storytelling. The story itself may not be the point either… but the stimulation of thought and ideas that are invoked through the story (or transmission of your construal) just like the invitation presented through art to think deeper.
In relation to this idea that a map is not the campus, we are looking at a single layer – a spatial representation of a much larger concept, but not all parts of this layer/representation are equal in value to the audience. We haven’t communicated the sounds, height, emotions, colours, smells, community, inhabitants, history, safety, importance, etc. as each are separate layers of the campus concept. I am seeing how your new realization depicts teaching as two partial understandings meeting, then – I imagine – collaboratively a new construal is created together. Again, an idea from EDCP 562 comes back of making-meaning with others (or ‘learning’) as a relational activity (Chrona, 2022)!
Your final pondering is a lot to think about: “If a machine can eventually calculate anything and generate any image, what does that leave the rest of us to do, and is it enough?”
Taking your quote from Beynon and ponderings from Hart… how will a machine be able to communicate its construal to someone else so that they understand? Is this a possibility? I wonder if there will be a time that a machine’s understanding of the living reality of humanity will diverge so far that humanity’s reference point to GenAI’s narration won’t make sense any longer. Also, if GenAI’s partial construal meets mine, does our understanding grow together relationally as well? If relationships can be formed between all things (for example, human to environment, human to human, human to self) could a computer and its database be considered within the realm of more-than-human like the other animals of this planet who also consume fresh water and generate heat as part of their metabolic processes?
Now I wonder mathematically if the presence of GenAI has been the equivalent to a massive population increase in every region with a datacentre and if we have been underestimating our resource allocation with new digital residents in town.
Thank you for the interesting thought journey your post has inspired in me.
References:
Chrona, J. (2022). Wayi wah! indigenous pedagogies: An act for reconciliation and anti-racist education. Portage & Main Press.