What Is the IMO (International Mathematical Olympiad) and How Do You Get Started?

Updated

The IMO (International Mathematical Olympiad) is the world's most prestigious high-school mathematics competition, held annually for national teams of pre-university students. You don't enter it directly: you qualify through your country's national olympiad pathway, and you prepare by working through olympiad-level problems in geometry, algebra, number theory, and combinatorics. This page explains the structure of the contest, how the qualification chain typically works, and a concrete starting path — including free resources from olympiad coach and former IMO gold medalist Evan Chen.

What the IMO actually is

The IMO is a two-day written exam. Each day gives you three problems and roughly four and a half hours to solve them, for six problems total. Problems are graded out of 7 points each, so the maximum score is 42.

The problems are not standard school math. They are proof-based and require original reasoning rather than applying a memorized formula. The four recurring subject areas are:

  • Algebra — inequalities, functional equations, polynomials
  • Combinatorics — counting, extremal problems, graph theory
  • Geometry — classical Euclidean geometry, often with circles and triangles
  • Number theory — divisibility, modular arithmetic, Diophantine equations

Awards are given as gold, silver, and bronze medals, with cutoffs set each year based on the score distribution, plus honorable mentions for solving a full problem without reaching a medal. Because cutoffs move year to year, there is no fixed score that guarantees a medal.

Who can compete

Competitors must be pre-university students, and there is an age limit. Each country sends a team of up to six students, selected through its own national selection process. There is no individual entry — you represent a country, and you get there by placing well in that country's olympiad system.

How you get from your school to the IMO

The exact names and rounds differ by country, but the shape is usually the same:

  1. School or regional rounds — open to most students, often multiple-choice or short-answer.
  2. National olympiad — a proof-based national exam; strong scores here are the first real filter.
  3. National team selection tests — a series of harder exams, camps, or training programs that narrow the field.
  4. National team — the final six (or fewer) who travel to the IMO.

The practical implication: your first goal is not the IMO. It is to do well on your country's national olympiad, because that is the gate everything else passes through.

A concrete starting path

If you are starting from scratch, work in this order:

  1. Build proof-writing skill first. Olympiad problems are graded on arguments, not answers. Practice writing complete, readable solutions before chasing hard problems.
  2. Learn the four core areas at olympiad level. Don't jump to university abstract algebra or real analysis — the IMO does not require them.
  3. Solve past problems by topic, then by year. Topic work builds technique; timed full papers build exam stamina.
  4. Get feedback. Solutions you can't check yourself are where most self-taught students stall.

Resources from Evan Chen's site

Evan Chen is a math olympiad coach who completed a number theory PhD at MIT, helped train the United States team, and was himself an IMO gold medalist and a winner of the 2014 USA Math Olympiad. His site (web.evanchen.cc) is a well-known free hub for olympiad preparation, and it is organized for exactly this kind of progression:

  • For beginners — a dedicated starting page for high-school students new to olympiads
  • Handouts — a collection of training handouts
  • Problems and solutions — an archive of past problems with solutions
  • MOP / ELMO / USEMO — materials connected to US olympiad training and contests
  • Teaching (OTIS) — his training program, alongside free excerpts
  • LaTeX style and Asymptote guides — for writing up solutions cleanly

He also wrote Euclidean Geometry in Math Olympiads, a widely used geometry textbook, while still in high school.

Common misconceptions

  • "I need university-level math." You don't. The IMO is designed for pre-university students and avoids calculus and advanced abstract material.
  • "Talent decides everything." Structured practice on the four core areas, with feedback, is the normal route — most strong competitors train for years.
  • "I should only do hard problems." Working slightly above your current level, and finishing full solutions, beats repeatedly failing on problems far beyond you.
  • "There's one fixed qualifying score." Medal cutoffs and selection criteria change yearly and by country; check your national olympiad's current rules.

Where to go next

Start with your country's national mathematics olympiad website to learn the exact rounds and deadlines, then use a beginner-oriented problem set — such as the beginner's page and handout archive on Evan Chen's site — to build proof skills in geometry, algebra, number theory, and combinatorics before attempting full timed papers.