Musings on Embodied Mathematics

What is mathematical poetry? I cannot extract a clear definition from Gizem Karaali’s paper. At most, one might infer that it is a poetic practice engaging cognition, consciousness, and creativity. Yet the author also suggests that these capacities define the human species. This raises an interesting question: why should an argument even be required for “a more humanistic understanding of mathematics”? What other understanding might one hope for? Mathematics is a creative human activity. Again, what else could it be? Even if one were to hold that mathematics ultimately derives from Platonic forms, from formal symbolic systems, or from computational processes, such positions concern the ontology of mathematics, what mathematics is. They do not eliminate the fact that mathematics is practiced by humans as a social activity. Proofs are written, arguments are debated, conjectures are proposed and refined, and standards of elegance or rigour are negotiated within communities of mathematicia...

STEAM artist Nick Sayers works squarely in the lineage of Leonardo da Vinci. Like Leonardo, he makes art by human hand — but his hand moves through gears, chains, and recycled bicycle parts. His machine-artworks do not merely depict geometry; they enact it. Ratio becomes rhythm. Constraint becomes curve. Watching one of his bicycle-driven spirograph constructions in motion feels less like observing a calculation and more like witnessing choreography. He calls it busker ballet. The phrase is exact. Geometry unfolds in time. Nick’s work satisfies, almost defiantly, the demand that art be physically made directly by a human hand. His environmental and social commitments are not decoration; they are structural, preferring reuse to waste, r epair to consumerism. His  math-informed practice appears grounded in social responsibility. But this raises a question for mathematics itself.  Must mathematics also be physically made by a human hand to be true to be genuine? If we demanded th...

My project is titled “Phylicia’s Paradox” . It is a curricular + pedagogical design for a community learning experience on the mathematics of recommender systems , designed for a general, intergenerational audience and intended to run at the Black-led Black Creek Community Farm in Toronto . Recommender systems quietly shape what people watch, hear, buy, and believe.  The core problem the project addresses  is that  many people experience them as “magic” or manipulation because the underlying math is invisible. The workshop is designed to make the math legible through the body and senses, using an explicit learning arc: Reading  (representation → similarity → ranking → feedback loops) and Writing  (changing signals, weights, constraints, and success metrics). In the detailed outline that you can download, I describe deliverables and how I will design and try out the workshop. The deliverables include a facilitator guide, participant handouts (including low-tex...

In their article, “Dancing teachers into being with a garden, or how to swing or parkour the strict grid of schooling,” Susan Gerofsky and Julia Ostertag show how grids are everywhere in education. It is so ubiquitous it can become invisible: tiled floors, rows of desks, schedules, worksheets, tables, rubrics, gradebooks. “Grid thinking” supports a certain kind of productivity, but it also limits administrative imagination—restricting learning to parceled boxes, slicing time into units, and flattening the complexities of identity, interest, and curiosity into prefab categories. The article’s best move is that it doesn’t demand we “escape” the grid. Instead, the authors suggest learning to be beside it; like jazz swing beside a strict beat. Swing doesn’t abolish discipline; it leans on it: chord progression, harmony, tempo. The point isn’t to erase constraints, but to cultivate ways of moving through them that leave room for breath, surprise, and embodied presence. Think, for example, ...

Toronto is under an Orange Warning from Environment Canada. Torontonians don’t always see beauty in the storm; the Montréalais in me still celebrates it. Through the eyes of my youth, a storm is not an inconvenience but a choreography—snow improvising in wind, the city briefly returning to texture and silence. So, I took this picture from my balcony as a break from writing.  It feels like the right moment to think again about Kepler’s  Strena seu de nive sexangula . Mordern textbooks teach that a snowflake is a hexagonal crystal lattice: H2O molecules bond in ways that privilege six directions, spaced 60 degrees apart, and the visible sixfold symmetry follows (six times 60 gives the full 360 degree circle). But on a day like today, what I want to notice is not only the number six. Kepler’s gift to teachers is the way he conducts  his inquiry, how he moves from lived experience to explanation without treating the senses as a childish prelude to “real” knowledge-m...

In this realm, mathematics has always happened in bodies. We count on fingers, trace curves, “hold” an angle open with our hands, and talk our way through an idea using rhythm, emphasis, and pauses. What Susan Gerofsky's paper " Mathematical learning and gesture:  Character viewpoint and observer viewpoint  in students’ gestured graphs of functions",  adds to the conversation is that gestures can be diagnostic of how a learner is relating to a piece of mathematics. In her work on graphing, students’ bodies sometimes stay “ou tside” the representation (as if observing the graph), and sometimes move “from within” it (as if riding the graph). Those are not just performance styles; they can mark different forms of engagements and imaginations. Wittgenstein helps us name what’s at stake: mathematics education is a set of language games, rule-governed ways of using words, symbols, diagrams, and bodies in particular settings. Meaning is not a ghost behind the sign; it is ...