Bridges 2026 - Aug 7th (Day 3)

Today started with a plenary talk from Amy Alznauer on Why We Tell Stories. Her main argument was that we tell stories because our lives are stories, and we have questions of which we long for answers. The stories themselves are simply vehicles for council: my first stop. Alznauer introduced a quote from Walter Benjamin: "Council is less an answer to a question than a proposal concerning the continuation of a story which is just unfolding." This makes sense and connects with my experiences and discussion with Coast Salish educators on the topic of parenting; stories are often told as a means of council rather than prescriptive commands that lead to power-struggles. The stories then become a vehicle for self-reflection and introspection; the same story may be told many times with the child pulling a new message from it due to their developing experiences in life. A story becomes a way for a teller to process occurrences of cause and effect, making clearer for themselves relations in time.  

My second stop was when Alznauer brought up the idea (through quotes of Edward Shils, Wendell Berry and Doris Schattscheider) of being at the centre and alternatively (or simultaneously) at the periphery. Each location comes with benefits. As math artists, mathematics is at the periphery of fine art, and art is at the periphery of mathematics. The peripheral relation promotes beneficial qualities of engaging in generative (genius) power as an originator, with freedom and passion of a lover/amateur, with the wonder of a child. Perhaps this is why cross-curricular interdisciplinary projects offer such exciting opportunities; just by engaging simultaneously in two different disciplines, you get to access all the benefits of peripheral qualities.

My third stop was when Alznauer mentioned the tombstone of Lucy Joan Slater which read Computer Pioneer. Alznauer stated that Lucy was homeschooled and that it was a huge benefit to her as she was able to have the time to pursue whatever interested her. This connects with thoughts that I've been having about the rapid pace of 21st century life, time-pressures of government curriculum and the school system, and focused downtime for hobbies (aka boredom that leads to discovery). As Hannah Fry stated in a youtube short, "Time [pressure] - the killer of all things good." to which I absolutely agree. I'm not sure if "fear" is the right word that accompanies time-pressures, but I certainly have made many choices in my classroom out of "fear" (linguistically, perhaps literally) that I will run out of time - condensing instructions for important activities, cutting activities short ruining experiences, reducing exploration, or skipping concepts to name a few. The uninterrupted free mind that can take the time to obsess and wander and pursue imaginative ideas really makes all the difference to a creative (not just creative but generative) individual. I now wonder how I can structure my classroom to have more of this uninterrupted free time where they can pursue what interests them in mathematics, then choose how they wish to represent it... perhaps in more of a Montessori style such that students may have agency to explore several concepts all at once and spend the most time on what is most challenging to them. 

My fourth stop came from Clare Moriarty on Semiotics, Ease and Elegance: Oliver Byrne's Elements of Euclid. Moriarty drove home the fact that Byrne was obsessed with accessibility of mathematics trying to build in many ways/systems for understanding and accessing knowledge. Byrne therefore used red, yellow, blue and black in his print on Elements of Euclid freeing up mental space for geometrical reasoning by rendering each shape/angle/object/ etc in colour, then referencing it in colour during the proofs. This connects deeply with me as a math educator and - before that - a tutor trying to explain or draw things in ways that allowed my students to grasp the concepts. This monumental effort of printing a coloured book in the 1800s that tanked the printing company shows the kind of dedication (obsession) Byrne had in trying to make math accessible.

On the topic of making math more accessible, my fifth stop came during Gary Lester's talk on Art as Math Representation: A practice-based Investigation of Cognition and Pedagogy. Lester wanted to investigate why the notion of "I'm not a math's person" was socially acceptable leading him to develop an art-based sculptural approach with embedded mathematical concepts as a way to invite discussion. Lester found that the same scupture presented a very different message to very different audiences with their interpretation largely reflected by the background knowledge they brought in to the experience. Lester reminded us that when teachers teach what they already know, they fail to communicate complex mathematical ideas from the viewpoint of a novice using their vocabulary and their experiences from which to scaffold. So, how can we extract a math concept's core idea and introduce them from the viewpoint of the novice? Lester finished with two more leading questions that are thought provoking: What are the differing cognitive processes taking place between experts and novices? And, can artistic forms be used as avenue for greater engagement? This becomes another point of entry towards accessibility of complex math ideas.

Quick aside: On Aug 8th (the following day) I had the pleasure of meeting up with Georgina Ryan in the art gallery as I wanted to have a discussion with her about the differences between her findings and that of Gary Lester's. Ryan has created a website called Threaded Theorems in which she shares unique self-made embroidery patterns of advanced mathematical ideas as an accessible entry point for women to become introduced and curious. 

An example of Ryan's free patterns found on her website. What a curious shape this is! Why does every branch break into two? It looks like every part is a smaller and smaller part of the original! Interested?  Go google "Binary Tree" and "Fractals" then combine the two in a search :) 

Where Lester's findings showed that people only cognitively engage with art at the level of their background prior knowledge, separately Ryan's idea feels like a hopeful attempt to introduce and advance mathematical knowledge. These two ideas work together and become driven by curiosity. In the beginning, embroidery enthusiasts would only engage with the artistic qualities of the math ideas, but then find out more about their embroidered concepts through inquiry. I believe as long as we don't let the curious walk away and miss out on an opportunity to engage, then this could be a strong point of entry in education. 

OK, back to Aug. 7th. I attended Saad Mneimneh's talk on The Poetry of Math. This talk was a beautiful perspective shift looking at the provocation of thought stimulated by engagement with math (and poetry). Mneimneh's main argument was that both math and poetry were very similar in that they are both imaginative, use metaphor, deal with abstraction, convey deep consequences, make statements, and even provide plot twists that can excite a reader. Mneimneh likened the Collatz conjecture (google it, it's worth it!) to the poem called "The Red Wheel Barrow" by William Carlos Williams because they were both simple, elegant, basic, unusual, and had an emerging structure without needing to be complex.

Mneimneh left off with my sixth stop: every poem + math concept has a certain level of engagement (similarly to the message by Lester and Ryan the following day) that must occur for a while to be able to receive the aha! moment of realization - this is on the part of the student/receiver/witness/listener/audience. This brings me to a conversation with another poet at the conference, Britt Kaufmann, author of Midlife Calculus, about allowing the engagement on the position of the educator/presenter/performer/speaker:: "If you don't wait [as an educator] the students never receive their own dopamine hit from the joy of discovery, and the learning is truncated... waiting is so hard when you have an agenda."

A seventh stop came when Mneimneh mentioned teaching math without being creative with it is like learning the alphabet but never being allowed to write any words. Ryan furthered this analogy by saying (paraphrased) that you finish your alphabet in grade 1, then for the rest of your life you practice generating more and more complex ideas with this alphabet for the rest of your life... whereas, in mathematics, you don't stop learning the alphabet until you become an undergraduate in university... so the earlier you can shift between being a consumer of mathematics towards being a creator, the faster we will be able to see its place in our life. 

The last talk I attend that day was Susan Gerofsky's Artists Re-storying their Relationship with Math and Art. The participants of Susan's project have all experienced shame, fear, embarrassment and trauma from negative experiences in math class. Through this process of re-storying their relationship with math through embodied means, they have given themselves an opportunity to recognizing and maybe even acknowledging and utilizing mathematics in their lives and artwork. I found Gerofsky's inquiry question to be quite related to Lester's: "How do we break this intergenerational transmission of trauma?" The individuals affected by these negative experiences develop an aversion to math and claim to not be math people. My eighth stop came during her retelling of participant Carole's journey. Carole was a ceramics artist who said that the creation of a mug 24 times isn't creative but creating. It's not generative. This shift in vocabulary for me was interesting because in my classroom I always ask my students to be "creative" when doing their math projects... but perhaps, I need to re-specify that just the act of putting math somewhere other than paper is not enough, but they need to generate something with it. Our experiences in life are limited by our vocabulary to express them. 

Euler's Vision by Tom Petsinis
A dramatic reading by Susan Gerofsky (e), Kristie McClellan (i), Eveline Pye (pi), Oliver Podwysocki (+), Jim Wolper (1), Lisa Lajeunesse (=), Britt Kaufmann (0), and Tom Petsinis (Euler)

The two groups of symbols fighting over zero. 

 

I was invited to participate in the Math + Art Fashion Show in the evening. Here is me wearing a raindow truchet tile t-shirt created by electrical engineer/fibre artist Amy Wendt (seen over my left shoulder) sporting another arrangement of the same truchet tiles on her t-shirt! It was a wonderful experience. 

References: 

Alznauer, A. (2026) Lunar Music, Lost Notebooks, Pentagons, and Paralysis: How the Hidden Stories of Amateurs – of Those Who Love – Offer Vital Counsel to Both Mathematicians and Artists.    Proceedings of Bridges 2026: Mathematics and the Arts. 3-3.

Gerofsky, S., Nicol, C., Li, Z., Leung, A., and Omonade, C. (2026) Artists Re-Storying Their Relationship with Math and Art. Proceedings of Bridges 2026: Mathematics and the Arts. 427–434.

Lester, G. (2026) Art as Mathematical Representation: A Practice-Based Investigation of Cognition and Pedagogy. Proceedings of Bridges 2026: Mathematics and the Arts. 553–556.

Moriarty, C. M. (2026) Semiotics, Ease, and Elegance: Oliver Byrne’s Elements of Euclid. Proceedings of Bridges 2026: Mathematics and the Arts. 1–1

Mneimneh, S. (2026) The Poetry of Math. Proceedings of Bridges 2026: Mathematics and the Arts. 419–426.

Ryan, G. (2026) Threaded Theorems: Hand Embroidery as Mathematics Outreach. Proceedings of Bridges 2026: Mathematics and the Arts. 541–544.

Bridges 2026 - August 6th (Day 2)

Starting off my post with a fibble about my journey on August 4th-5th. The poetic form is based on the first 8 digits of the golden ratio: 1.6180339

Pack.
Westjet steals our prep time.
Call.
Eight hours forty minutes on phone.

Re-booked flight.
Reunite.
Thankful we arrived in Ireland.

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I arrived at the mathematical art gallery absolutely floored with the pieces displayed. Here's a small glimpse:

Today, we started with a plenary talk by Nick Sayers on Math-Art with Meaning. I particularly loved his emphasis on meaning which he gave the examples of poetry, societal relevance, ambiguity, universality and transcendence. Sayers uses math as a medium, not the message itself. This was my first stop. I believe that my most successful lessons have been when I've used math as a means of developing an idea (ie. graphing function art, angles, shapes and geometry) instead of as an abstract end in itself learning it for the sake of learning it. Before i dig into planning my future units, I will need to remember this brief and powerful idea of "math as medium, not as message". This is impactful because when it is used as a tool to work something into existence through a means of self-expression, then the creator feels the utility and importance of the tool - especially when it improves the quality of their life. 

Sayers foreshadowed aside ties in with his final inquiry question for us: What is the meaning of your math-art? Art for the sake of art was lost to me until a few days ago, when I read through Saad Mneimneh's presentation proceedings about "The Poetry of Math" and the thoughts that arise when we engage with poetry in the same way as a mathematical formula regardless of the creators original meaning. When the process itself brings about new thought pathways that become the keys to meaning-making for the individual, the making of the art (not necessarily the art itself) becomes meaningful to the creator. This would infer that the world is full of human-slop (not AI-slop) and that not all art is meaningful to everyone (or anyone), but the process of making it helped to transform the creator themself. Mneimneh reiterated that, "meaning is in the journey and the process" during the Q&A period. 

Throughout each of Sayers' math-art pieces, he demonstrates his positionality and intersectionality as mathematician, artist, eco-activist, father, programmer, and pro-cyclist. This brings me to my second stop: Find the intersection where all your passions, values, and skills meet. Sayers has found a unique niche where each of these pieces of his being unite and mutually strengthen each other while contributing to the betterment of society. I think this is one of the prime functions that teachers are capable of due to our unique positions of constantly and rigorously introducing new ideas, tools and experiences to our students. I keep thinking about helping students develop a relationship (and making-meaning) with others and their environments, but I keep forgetting that they need to be able to develop the strongest relationship with their own self through noticing, recognizing, and reflecting.

Our second plenary talk was with Dave Whyte on Bees + Bombs, his webpage is https://beesandbombs.com/ where he highlights his journey in developing short looping geometric animations (gifs). Listening to his journey of growth as an artist, mathematician and programmer was very inspiring as it required observation, experimentation, excitement, reiteration, and playfulness. My third stop came when he introduced a simple idea that the symbol for nothing is 0, and the symbol for everything is ♾️... so everything is nothing with a twist. This cheekily became one of his frequently used tools in his bag of tricks but the concept is profound. I visualize the twist being the flip of a zero from the numerator to a denominator. I imagine it like a mindset going from a thought of scarcity to one of gratitude. It is a really appealing metaphor of life for me. 

During the Q&A, someone asked about Whyte's creative process: he jokingly declares that he thinks things, writes them down, and then creates them... but there's so much more than that. Whyte has a vague idea about the kind of effect that would be visually attractive to him, then he experiments and tries many things. Sometime he comes up with something that he absolutely loves, an intricate visual pattern with hidden seams. Sometimes he comes up with nothing and throws it away. This brings me to my four stop of the day: Both Sayers and Whyte have exceptionally explorative (or playful) attitudes towards creative projects. McClellan helped me to connect this idea even with the talks from Aug. 5th of which I was absent. She said each presenter was extremely playful and wouldn't stop tinkering and reiterating and exploring and tweaking just for fun or out of curiosity! These examples have solidified my belief that playfulness is one of the most important qualities of a successful creator and mathematician. 

I attended six more presentations today. Surprisingly my fifth stop is the most important things I've learned have come from the Q&A sections regarding the artists preferences or creative processes. This makes me want to come to the next presentations with some pre-written generic questions all related to their creative process, or meaning-making because, as stated in stop one, the creation of the art is most transformative for the artist themself! So who better to report out on it than them of what they learned?

An example of this was during Kerry Mitchell's presentation on Creating Art with Space-filling Curves. He mentioned his favourite part of creating these pieces (ie. Fig 11 below) is that the Hilbert curve is subtly embedded in this abstract artwork, it doesn't jump out at you but you have to work to reveal it. I appreciate Mitchell's response as I feel the same way about my artwork. I subtly embed or hide easter eggs in my artwork so that it has layers of meaning for those who engage with it. There's a saying for this: "if you know, you know" abbreviated "IYKYK" online. When digging or revealing new layers within artwork, it re-ignites a viewer's interest and helps them further develop an expectation for success and discovery that motivates them to keep exploring/digging. The same happens in mathematics!

This reminds me of Aharoni's (2014) discussion of an unexpected twist in poetry (and mathematics) where one level of meaning is made while the details of a poem or story are read until the unexpected twist occurs that forces the reader to take all that accumulated data at once and re-interpreting it with a new meaning giving the reader a sensation of transcendent beauty (Su & Jackson, 2020) - giving the reader a glimpse into a larger truth by comprehending a great deal all at once. 

That's all for now!

References: 

Aharoni, R. (2014). Mathematics, poetry and beauty. Journal of Mathematics and the Arts, 8(1–2), 5–12. https://doi.org/10.1080/17513472.2014.943490

Mitchell, K. (2026) Creating Art with Space-Filling Curves. Proceedings of Bridges 2026: Mathematics and Arts. 45-52.

Sayers, N. (2026) The Mathematical Art of Bikes and Children's Toys: Using Bicycles and Everyday Materials for Geometric Drawing. Proceedings of Bridges 2026: Mathematics and the Arts. 5-12.

Su, F. & Jackson, C. (2020). Mathematics for human flourishing. Yale University Press.

Whyte, D. (2026) Bees & Bombs: My Gifs. Proceedings of Bridges 2026: Mathematics and 

        the Arts. 2-2.