International Mathematical Olympiad
The oldest and most prestigious international math competition, bringing together top pre-university mathematicians from 100+ countries. Founded in 1959 in Romania.
Grade Levels
Grades 10-12 (Ages 16-19)
Format
Proof-Based · 6 questions · 2 days, 4.5 hours per session (3 problems each day)
Scoring
0-7 per problem, maximum 42 points. Gold medal: top ~1/12 of scores. Silver: next ~2/12. Bronze: next ~3/12.
Participants
~600 contestants from 100+ countries
Established
1959
July
Competition held in July (host country rotates annually)
Registration
National mathematical societies select and send teams of up to 6 students
Prizes & Recognition
Gold, Silver, Bronze medals, and Honorable Mentions. Approximately half of all participants receive medals.
About This Competition
The International Mathematical Olympiad (IMO) is the pinnacle of pre-university mathematical competition. Founded in 1959 in Romania with just 7 participating countries, it has grown to include over 100 countries, making it one of the world's most prestigious academic competitions.
Each country selects a team of up to 6 students through its national competition pipeline. The competition consists of 6 problems spread over 2 days (3 problems per day, 4.5 hours per session). Problems cover number theory, combinatorics, algebra, and geometry, all requiring complete written proofs.
The IMO has produced numerous Fields Medal winners and has been instrumental in identifying and nurturing mathematical talent worldwide. The 2025 IMO was held in Australia (Sunshine Coast), and the 2026 IMO is planned for China.
How to Prepare
Solve IMO Shortlist Problems Systematically
The IMO Shortlist (ISL) is the single best resource. Work through problems by topic: algebra, combinatorics, geometry, and number theory. Aim for problems rated C1-C3 difficulty.
Master the Art of Writing Proofs Under Pressure
You have 4.5 hours for 3 problems each day. Practice writing clean, complete proofs within time limits. A well-structured partial solution can earn significant marks.
Use Art of Problem Solving and AOPS Wiki
AoPS hosts every IMO problem with community solutions. Also study 'The Art and Craft of Problem Solving' by Zeitz and 'Problem-Solving Through Recreational Mathematics'.
Problem 1 and 4 Are Your Foundation
Problems 1 and 4 are the most accessible on each day. Securing full marks on these gives you a strong medal chance. Don't rush to the harder problems.
Build a Training Schedule Months Ahead
Top IMO contestants train for years. Set a daily practice routine of 2-3 hours minimum, alternating between focused topic study and timed mock exams.
Frequently Asked Questions
What is the IMO?
The International Mathematical Olympiad (IMO) is the oldest and most prestigious international mathematical competition for pre-university students. Founded in 1959 in Romania, it brings together the top young mathematicians from over 100 countries each July.
How do students qualify for the IMO?
Each country has its own selection process, typically involving a series of national competitions. For example, in Greece: Thales -> Euclid -> Archimedes -> National Olympiad -> IMO team. In the USA: AMC -> AIME -> USAMO -> MOP -> IMO team.
How hard are IMO problems?
IMO problems are extremely challenging, requiring creative proofs in areas like number theory, combinatorics, algebra, and geometry. Even professional mathematicians find some IMO problems difficult. The problems are designed so that the hardest ones (problems 3 and 6) are solved by only a handful of contestants.
Related Competitions
Math Kangaroo
The world's largest mathematics competition with 6 million+ participants in 90+ countries. Multiple-choice format across 6 difficulty levels, emphasizing fun and accessible problem-solving.
Balkan Mathematical Olympiad
Regional olympiad for Balkan countries including Greece, Romania, Bulgaria, and Cyprus. Important stepping stone toward IMO for participating nations.
European Girls' Mathematical Olympiad
International olympiad for female students from 55+ countries. IMO-format competition promoting gender diversity in mathematics.
Asian Pacific Mathematics Olympiad
Regional olympiad for Asia-Pacific nations. 5 proof-based problems in 4 hours, serving as an important IMO preparation event.
SASMO
A major Asia-Pacific math competition with 120,000+ students from 20+ countries. Features both multiple-choice and non-routine problem-solving sections.
Caribou Mathematics
A worldwide online math competition held six times per year. Endorsed by the Canadian Mathematical Society, with results available the same evening.