Explorations into the deep structure of things. Essays on why mathematics is not arithmetic, interactive proofs, and the beauty hiding in abstraction.
Most curricula conflate calculation with mathematics. The distinction matters enormously. Real math is the study of structure, pattern, and logical necessity — not arithmetic.
Topology studies properties that survive continuous deformation. A coffee mug and a donut are the same object to a topologist. Genus, Euler characteristics, and why shape is stranger than you thought.
Primes appear random but hide deep patterns. The Riemann Hypothesis, Euler's product formula, and the Ulam spiral all point to an order we've only glimpsed.
Cantor showed there are different sizes of infinity. The continuum hypothesis is both true and false depending on your axioms. This is not a bug — it's a window into the foundations of reality.
Symmetry, group theory, and Noether's theorem connect aesthetic experience to physical law. Conservation of energy is a consequence of time-translation symmetry.
A coastline has a dimension between 1 and 2. Fractal geometry formalises the roughness of nature — clouds, mountains, trees — with non-integer dimensional scaling.
Explore mathematical structures directly. All demos are live — rendered in your browser.