Essays
Each figure raises a question it cannot answer on its own. These are the answers, written the way I would say them if we had ten quiet minutes after the bell. No prerequisites beyond curiosity, and a promise never to say “it’s intuitive” about anything that took me a decade to understand.
Against gamification
May 24, 2026 · 4 min · teaching
The case against points, badges, streaks, and leaderboards in the maths classroom — made plainly, without slogans. On the overjustification effect, Goodhart's law, and rewarding the thing itself.
Prime spirals and pattern-hunger
May 3, 2026 · 4 min · probability, teaching
Ulam's spiral lights up the primes and, unnervingly, they fall along diagonal lines. Some of those lines are real mathematics and some are the mind inventing order. A companion to the prime-spiral toy, on the honest uses of a suggestive picture.
Bézier curves are just weighted averages
April 12, 2026 · 3 min · geometry, teaching
The smooth curve behind every font and vector drawing is nothing more grand than averaging, done over and over. A companion to the Bézier toy, on de Casteljau's construction and why the curve stays inside its own cage.
The pendulum that draws itself
March 22, 2026 · 4 min · calculus, teaching
A swinging pendulum has two numbers at every instant — where it is and how fast it's moving. Plot one against the other and the motion draws a spiral. A companion to the pendulum toy, on phase space and where the energy goes.
What π actually measures
March 1, 2026 · 3 min · probability, geometry
π turns up in a dart game that has no circles drawn on it, only counted. A companion to the Monte-Carlo toy, on area as probability, and why getting one more decimal costs a hundred times the effort.
Why the Fourier drawer starts with a square wave
February 9, 2026 · 4 min · calculus, teaching
A square wave is the rudest thing you can ask a sum of smooth curves to build — which is exactly why it belongs first. On odd harmonics, rotating vectors, and the little overshoot that never goes away.