A guide to the IMO, with tips from an interview with an IMO winner.
The International Mathematical Olympiad (IMO) is the most prestigious math competition for high school students worldwide. Doing well takes dedication, strong problem-solving, and a lot of practice. This guide covers the tips, resources, and strategies to help you prepare.
What the IMO is
The IMO is an annual competition held in a different country each year. It runs over two days, with six problems total (three per day), each worth seven points. The problems span algebra, geometry, number theory, and combinatorics.
How to prepare
1. Master the basics. Before the advanced material, get a solid grip on the fundamentals: algebra, geometry, number theory, and combinatorics. These are the backbone of every IMO problem. Use textbooks, online courses, and lots of practice.
2. Solve past IMO problems. Like the SAT or AP exams, working past papers is one of the best ways to prepare. It gets you used to the format, difficulty, and problem types. Art of Problem Solving (AoPS) has extensive past problems and solutions.
3. Join math circles and camps. These give you experienced mentors, strong peers, and a focus on problem-solving techniques. Working through hard problems with others is one of the fastest ways to improve.
4. Compete in national olympiads. National math olympiads are the stepping stone to the IMO, and performing well in them is usually how you get selected. They also build experience and show you where to improve.
5. Practice under exam conditions. Work problems under a timer to build time management and reduce test-day nerves. The IMO is as much about endurance as it is about problem-solving.
6. Use online courses or a tutor. Platforms like Brilliant have courses aimed at advanced problem-solving, and a tutor can give targeted help on your weak spots.
7. Learn from people who’ve done it. Watch interviews and tutorials from past competitors. For example, here’s Rishab Jain’s interview with an IMO winner, full of strategies straight from someone who’s competed at that level.
Resources
Books
- The Art and Craft of Problem Solving by Paul Zeitz (Amazon)
- Problem-Solving Strategies by Arthur Engel (Amazon)
- 102 Combinatorial Problems by Titu Andreescu and Zuming Feng (Amazon)
- Mathematical Olympiad Challenges by Titu Andreescu and Razvan Gelca (Amazon)
Online platforms (mostly free, a good alternative to the books):
- Art of Problem Solving (AoPS): resources, forums, and online classes (link).
- Khan Academy: free tutorials on the fundamentals (link).
- Brilliant: interactive problem-solving courses (link).
- Coursera: advanced math courses from top universities (link).
Stay healthy and consistent
Look after yourself. Regular exercise, a balanced diet, and enough sleep all affect how well your brain works.
Manage stress. Find techniques that keep you calm under pressure, whether that’s meditation, breathing exercises, or mindfulness. Staying composed matters on exam day.
Be consistent. Set a study schedule and stick to it. Steady, gradual practice beats last-minute cramming.
Taking it further
Want another challenge? Consider the International Research Olympiad (IRO), an olympiad-style contest that tests science research ability. In 2024 it drew over 1,000 participants from 45+ countries, so it’s a strong way to show your talents and gain experience.
The bottom line
The IMO is a tough competition, but you can give yourself a real shot by mastering the fundamentals, working past problems, joining math circles and national competitions, and looking after your health. Consistent effort is what makes the difference. Good luck.
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