Maths as Philosophy: On Primes, Potatoes, and Universal Sets
Last week, Gerry Docherty demoed an interactive Venn diagram for our new maths course.
I was happily dragging primes and evens into their little circles when he said, almost as an aside: “The rectangle is the universal set.”
I hadn’t even noticed the rectangle.
That line hit me like a philosophy class in a single pixel: I didn’t know I was already in a frame—I could only see the circles.
Naming, Sorting… and Losing (or Finding) the Magic
Early years maths begins with sorting: red counters here, blue squares there. We name, we group, we define. Part of me always worries: is this where the world gets less magical—when we label it?
But then primes arrive like little meteorites of wonder. Sets don’t just separate; they reveal. The moment you notice the lone even prime, or the infinite mischief of the primes themselves, you realise that classification is not the death of magic—it’s one of its doorways.
The Universal Set (and Other Invisible Walls)
That unnoticed rectangle is a metaphor for life and learning. We spend hours arguing about which circle we belong in—“even” or “prime,” “traditional” or “progressive,” “online” or “in-person”—without ever asking who drew the rectangle and why.
Design question for schools: What if we taught learners to see frames first? To ask, “What’s the universal set here, and does it need to be bigger?”
Standard Form: From Jupiter to a Cell
Gerry’s second activity matched cosmic distances to numbers in standard form (hello, Jupiter) and then flipped to microscopic scales (a cell’s diameter). In two clicks we travelled from the vast to the tiny and back again. Same notation, different worlds. Maths as a language that moves across scales without losing its grammar. Philosophy calls that coherence.
Exams Take Care of Themselves
Gerry’s teaching mantra since 1982:
“I’ll teach you the maths; the exams will take care of themselves.”
That’s not anti-assessment. It’s a stance. Teach the structure of truth first; certification follows. Curiosity is the engine, not the treat at the end.
Glitch as Teacher
During the demo a dropdown broke. For a moment we were stuck in the wrong universe. Then it worked again. We laughed—and we kept going. Our team has a saying: the glitch is the field speaking. Sometimes the lesson isn’t inside the circles; it’s in the frame rate, the lag, the resilience we build together.
Mars, Potatoes, and Design Questions
We spun into The Martian, sustainable habitats, and how a maths lesson becomes a cross-disciplinary design brief. Numbers become constraints, yes—but also prompts. “Could we live there?” is a philosophical question armed with unit conversions.
What We’re Building
A maths course that teaches frames, not just facts. Sets, number, algebra—anchored in meaning, story, and scale.
Interactive tasks that invite sorting, noticing, and reframing. (Yes, you’ll still ace the exam. That’s the least interesting thing that will happen.)
Cohort training for maths educators on designing interactive courses (UDL-aligned, curiosity-first, Canvas/Pencil-ready). Come for the templates; leave with a design spine.
First see the frame. Then choose the circle.
An Invitation
If you felt that moment—the rectangle you hadn’t noticed—you’re our people. Join the pilot, or register interest for the educator cohort. Let’s teach maths as the art of seeing: the circles, the overlaps, and the quiet rectangle that holds it all.
About The Novacene
The Novacene helps schools, educators, and learning communities build systems that operate at the speed of care—not just compliance.
We design hybrid, ethical, and neurodivergent-affirming infrastructures that connect human and machine intelligence through practical, beautiful systems thinking.
Our work spans:
Advisory partnerships for leaders reimagining their schools
Strategic design support for online and hybrid provision
White-labelled frameworks for curriculum, policy, and governance
Collaborative research with ethical AI and education labs
From The Haven to Riverside Virtual College, our team has helped communities weave together platforms like Pencil Spaces, Canvas, and Google Workspace into trusted, inclusive environments for learning anywhere.
In partnership with IBM Partner Plus and the IBM Z Startups programme, The Novacene is now extending this vision globally—developing resilient, AI-aligned education systems designed for trust, inclusion, and imagination.
What if education could evolve at the same pace as our compassion? That’s the question we live by.
#FutureFlex #Verseality
First published in Building Schools in the Cloud on LinkedIn, 7 October 2025.