A learning engine for mathematics

A line of short lessons from school algebra to real analysis, vector calculus and beyond — built to teach reading proofs and writing them. Each skill is one sitting.

Every claim carries its status. Definition, theorem, conjecture, observation. The hypotheses sit inside the statement rather than in the prose around it, and a cited theorem cannot be written without its citation.

Practice is generated, not banked. Problems come from a template and a seed, so a skill can be worked again rather than recalled. Answers are marked by mathematical equivalence: $\tfrac{1}{2}$ and $0.5$ are the same answer.

Python computes; the browser renders. Every expression, mark and figure comes from the engine — including the one below.

$\sqrt{x^{2}} = \lvert x \rvert$

Not $x$ . The two agree only where $x \geq 0$ , and the lesson is built around that rather than around drill — it is the first place a dropped hypothesis produces a false statement.

\sqrt{x^{2}}

against

x

. They part company at

x = 0

. The picture shows where to look; the proof is in radicals-and-surds.Sampled numerically. A plot generates hypotheses; it does not settle them.sample · sympy-1.14.0+engine-1 · computed 2026-08-03

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A learning engine for mathematics

x2=∣x∣\sqrt{x^{2}} = \lvert x \rvertx2​=∣x∣

$\sqrt{x^{2}} = \lvert x \rvert$