Mathematics · competitions, olympiads & research
Most maths teaching stops at the answer. This starts there.
Structured preparation for the competition ladder — AMC 8/10/12, AIME, USAMO/USAJMO — and a research track where a student takes an original problem through to a written paper. Taught in small groups by mathematicians who work in the field, not by tutors reading ahead of the class.
The full competition ladder
Argument, not just answers
Taught by working mathematicians
An original paper, properly written
A different subject, not a harder one.
School mathematics asks a student to apply a method they have been shown, accurately and quickly. Competition mathematics asks them to find a method nobody has shown them — and olympiad mathematics then asks them to prove it works.
That is why strong school students often stall on their first AMC. Nothing is wrong with them; they are being asked for a skill that school had no reason to teach. It is learnable, but it is learned by working on hard problems for a long time with someone who can see where the reasoning went wrong — not by drilling more of what they can already do.
Where a student joins.
Placed by what the mathematics needs, not by school year. Each stage assumes the one before it — the ladder is the point, and skipping a rung is how students end up discouraged.
AMC 8 · 10 · 12 — the foundation
The entry point, and where most of the durable gains are made. Students learn the standard competition toolkit — number theory, counting and probability, geometry, algebraic manipulation — and, more importantly, how to recognise which tool a problem is asking for. Speed comes from familiarity, not from rushing.
AIME — technique under pressure
The step where problems stop yielding to a single idea. Work here focuses on multi-step problems, on knowing when to abandon an approach that is not converging, and on the arithmetic discipline that turns a correct method into a correct answer within the time.
USAMO / USAJMO — writing proofs
Olympiad papers are marked on argument, not answers. Students learn to write a proof a stranger can follow: stating what is assumed, justifying each step, and recognising the gap between 'I can see why this is true' and 'I have shown that it is'. Most strong competition students have never been taught this explicitly.
The research track
For students who have gone through the ladder and want to work on something open rather than something set. An original problem, worked over months with a mathematician, written up properly and submitted to a peer-reviewed journal. Topics reach into real and complex analysis, abstract algebra, linear algebra, probability, differential equations and geometry as the problem demands.
Who this is not for.
A student who needs school maths to improve. This will not help, and may knock their confidence. Competition mathematics sits beside the curriculum, not on top of it — if the foundation is shaky, fix that first.
A family looking for a credential in one term. Progress here is measured in terms and years. A student starting in Grade 11 can still gain a great deal, but the ladder rewards the student who starts in middle school and keeps going.
A student who is not interested. This is voluntary, hard, and unforgiving of half-attention. It works for students who like the problems. It does not work as something a parent decides on a child’s behalf.
Questions parents ask.
Where should my child start?
At the level the mathematics is actually at, not the grade they are in. A student new to competition maths usually starts with AMC 8 or AMC 10 foundations; one already scoring on the AMC moves to AIME technique; a student through the AIME works on olympiad-style proof writing. We assess first and place accordingly — starting too high teaches nothing but discouragement.
Is this the same as school maths, just harder?
No, and that is the point. School mathematics rewards executing a known procedure accurately. Olympiad mathematics rewards finding a method nobody has handed you, then proving it works. The second skill is what competitions test, what research requires, and what most strong school students have never been taught.
What does the research track actually produce?
Original work on a real problem, written up as a paper and submitted to a peer-reviewed journal. That is a genuinely long undertaking — the writing and revision are as much of it as the mathematics — and not every student is ready for it. It is the natural next step for students who have worked through the competition ladder and want to make something rather than solve set problems.
Does a competition result actually help with admissions?
A serious one does, because it is externally verified and hard to manufacture. An AIME qualification or a published paper says something a transcript cannot. But it works as evidence of genuine depth in a subject, not as a box to tick — which is why we would rather a student go far in one direction than collect shallow entries in several.
How much time does it take?
More than a school club and less than a full second curriculum. The competition ladder rewards consistent weekly work over months rather than a sprint before a test date, and the research track is measured in terms rather than weeks. We will be honest with you about the commitment before you start, and about whether the timing makes sense for your child's year group.
A competition record is evidence of depth — but which competitions to enter, when to register, and how a result actually ladders into an application is a strategy question. That is what our counseling plans decide.
Start with a conversation about where your child actually is.
A short call to look at what they have done so far and say honestly whether this is the right next step — and if it is, where they would start.