The Best Math Competitions & Summer Camps for High Schoolers (2026)
On this page
The math-enrichment path for an ambitious student is a ladder, not a leap. You start with a broad, low-stakes contest like the AMC or MATHCOUNTS, earn your way up through qualifying rounds, and — if you love the work — spend a summer at a program like PROMYS, Ross, Mathcamp, or SUMaC that trades speed for depth. Nobody skips straight to the top, and nobody has to. Enter where you are, and climb from there.
Here is how the pieces fit together, and how to start no matter your current level.
The competition ladder (MAA)
The Mathematical Association of America runs the main sequence of American math contests, and they nest inside one another. Each round qualifies you for the next.
AMC 8, 10, and 12 are the entry points. The AMC 8 is for middle schoolers; the AMC 10 and 12 are the high-school multiple-choice exams (the 10 for younger or newer students, the 12 covering the full high-school curriculum). These are 25-question, multiple-choice tests taken at your school or a nearby testing site. Almost anyone can sit for them, and that is the point — they are designed to be a welcoming first rung.
AIME (the American Invitational Mathematics Examination) is the next step. Score well enough on the AMC 10 or 12 and you are invited to the AIME, a harder exam with integer answers and no multiple choice. This is where problems start rewarding genuine insight over test-taking speed.
USAJMO and USAMO sit at the top. Combined AMC and AIME performance can qualify you for these olympiad-style exams — the junior version (USAJMO) and the senior version (USAMO). These are proof-based: a handful of problems over two days, where you write full mathematical arguments rather than final answers. Reaching this level is a serious national distinction.
The through-line: AMC 8/10/12 → AIME → USA(J)MO. You do not sign up for the olympiad directly; you earn your way up the ladder one exam at a time.
Middle and elementary school on-ramps
If a student is younger, the ladder starts earlier.
MATHCOUNTS is the flagship middle-school competition. It runs as a series — school, chapter, state, and national rounds — mixing individual and team formats, including a fast-paced "Countdown" round. It is one of the best ways for a middle schooler to build contest instincts before the high-school AMCs.
MOEMS (Math Olympiads for Elementary and Middle Schools) reaches even younger students. Teams work through short monthly problem sets across the school year, emphasizing clever problem-solving over raw computation. It is a gentle, low-pressure introduction to the idea that math can be puzzling and fun rather than just procedural.
Both are excellent places for a beginner to develop the habit of sitting with a hard problem — the single most transferable skill in all of this.
The elite summer programs
Contests reward speed and pattern recognition. Summer programs reward the opposite: living inside a few deep ideas for weeks. These are residential, intensive, and genuinely transformative for the right student. Admission is competitive and usually hinges on a written problem set rather than a resume.
PROMYS (Program in Mathematics for Young Scientists), hosted at Boston University, immerses students in number theory and mathematical discovery. Students work through carefully designed problem sequences and build up the theory largely on their own, with mentors and counselors guiding rather than lecturing.
The Ross Mathematics Program shares that philosophy — "think deeply of simple things" is its long-standing motto — and likewise centers on number theory taught through guided exploration. Ross and PROMYS share intellectual DNA and are often mentioned in the same breath.
Canada/USA Mathcamp is broader in scope: a fast-paced program spanning many areas of higher mathematics, with a flexible, student-driven course catalog. It suits a curious generalist who wants a wide tasting menu of advanced topics rather than a single deep dive.
SUMaC (the Stanford University Mathematics Camp) offers focused courses in areas such as abstract algebra, number theory, and topology, and runs both residential and online sessions in recent years — worth confirming on the official site for the current summer.
A rough comparison — always verify current details on each program's official page:
| Program | Host | Flavor |
|---|---|---|
| PROMYS | Boston University | Number theory, guided discovery |
| Ross | rotating host universities | Number theory, "think deeply of simple things" |
| Canada/USA Mathcamp | rotating campuses | Broad higher math, flexible catalog |
| SUMaC | Stanford | Focused advanced courses (algebra, topology, more) |
International and homeschool students: several of these programs welcome applicants from outside the United States and do not require a traditional school transcript — admission rests on the entrance problem set, not your enrollment status. Mathcamp in particular has a long history of international participation, and PROMYS and Ross evaluate applicants primarily on their submitted work. Check each program's eligibility page, as details vary by year.
How to start, and why it matters
If you are a beginner, register for the AMC 8 or AMC 10 (or MATHCOUNTS if you are in middle school). Do not aim for a top score. Aim to finish the exam, review every problem you missed, and notice which types of thinking felt unfamiliar. The learning is in the review, not the ranking.
If you are already advanced — comfortably qualifying for the AIME, say — your next move is a summer program application. Start early: entrance problem sets are released months ahead, and they are meant to take weeks of honest effort. A thoughtful, complete submission matters far more than a slick one.
Why bother? Two reasons. First, colleges read these credentials fluently — an AIME qualification or a summer at PROMYS signals real mathematical maturity in a way a grade never can. Second, and more importantly, this work changes how you think. Wrestling with a problem you cannot immediately solve, and eventually cracking it, builds a kind of intellectual stamina that pays off in every quantitative field.
A rough timeline: AMC contests fall in the winter (typically November), AIME in the early spring, and the USA(J)MO in March. Summer program applications generally open in late winter and close in the spring for that same summer. So a student targeting a program often spends the fall and winter on contests and the same window preparing an application.
For our full, verified list of math programs — with current dates, eligibility, and links — see our math competitions and programs page, part of our broader academic competitions guide.
A note on foundations
The deep problem-solving these contests and camps demand does not exist in a separate universe from your regular coursework — it strengthens it. Students who build real fluency in algebra, functions, and number sense find that standardized-test math becomes far more manageable, because the SAT and ACT Math sections reward the same clear reasoning, just on easier problems. A strong math foundation makes both the contests and the tests easier. If you want help building that base, IvyStrides' SAT prep focuses on the underlying skills rather than tricks — you can book a free consultation to talk through where a student stands.
Frequently asked questions
Do I need to be a math genius to start? No. The AMC 8, AMC 10, and MATHCOUNTS are open, welcoming exams meant for a wide range of students. The whole point of the ladder is that you begin where you are and climb gradually. Most strong "math kids" started by simply showing up to a contest and doing the review afterward.
Which summer program is best? There is no single best — they differ in flavor. PROMYS and Ross go deep into number theory through guided discovery; Mathcamp offers a broad menu of advanced topics; SUMaC runs focused courses. Read each program's official description and pick the one whose style fits how you like to learn.
Can international or homeschooled students apply? Often yes. Several of these programs admit students based on a written entrance problem set rather than a transcript or enrollment status, which makes them friendly to international and homeschool applicants. Always confirm eligibility on the official site, since rules vary by program and year.
When should I apply to a summer program? Applications generally open in late winter and close in spring for that summer. Because entrance problem sets are meant to take weeks, start as early as you reasonably can rather than rushing near the deadline.
How do contests connect to the SAT or ACT? The reasoning habits are the same; the difficulty is not. Contest math is harder and rewards creative problem-solving, so students who train on it usually find test-section math straightforward. Building that foundation is exactly what good SAT prep reinforces.