Mathelo

The problem it solves is mine. The most expensive part of preparing to teach an olympiad student was never explaining the mathematics — it was finding a problem at the right level. Too easy and nothing is learned; too hard and the session becomes me doing the problem. The right question is a narrow target and it moves as the student improves.

So every question carries a rating and so does every student, per area — algebra, combinatorics, geometry, number theory, games and algorithms, inequalities, functional equations. A student attempts a problem, reports how it went, and both ratings move. Ask for three geometry questions the student has an even chance at in two hours, and it knows what that means for this student rather than in general.

The ratings are not guessed by a language model. The starting ladder is fitted from UKMT's own published round-one score distributions, which fixes both the spacing between question positions and the drift in difficulty over three decades; a per-question correction is then learned from actual attempts. Anything that has to stay consistent across a thousand questions is done in code, not in one long prompt.

The assistant on top of it turns a request in ordinary English into a search over tags, area and difficulty, and gives staged hints when asked — recording that a hint was used, because a solved-with-a-hint attempt is not the same evidence as a solved one.