September 22, 2025
8 min. read
If you’re searching for the best math competition in the world, the answer depends on who you are — but one contest stands above all others: the International Mathematical Olympiad (IMO).
Since 1959, the IMO has been the gold standard of pre-university mathematics — 100+ countries, the world’s hardest proof-based problems, and a legacy that has launched Fields Medalists and legendary mathematicians.
But the IMO is just the summit. Below it sits a rich landscape of elite competitions suited to different ages, skill levels, and goals. This guide ranks the top 7, explains what makes each great, and tells you exactly which one you should target.
What Is the #1 Math Competition in the World?
The International Mathematical Olympiad (IMO) is widely considered the best math competition in the world. Founded in 1959, it is the oldest, most prestigious, and most difficult high school mathematics competition globally, drawing top students from over 100 countries each year.
Top 7 Math Competitions in the World — At a Glance
| Competition | Founded | Countries | Who Can Enter | Difficulty | Best For |
|---|---|---|---|---|---|
| IMO | 1959 | 100+ | High school (national selection) | ⭐⭐⭐⭐⭐ Extreme | Elite proof-writers |
| Putnam | 1938 | USA/Canada | Undergraduates | ⭐⭐⭐⭐⭐ Extreme | University students |
| APMO | 1989 | Asia-Pacific + USA | Top students under 20 | ⭐⭐⭐⭐ Very High | Asia-Pacific region |
| EGMO | 2012 | Europe + guests | Female high school students | ⭐⭐⭐⭐ Very High | Girls in math |
| AMC 10/12 | 2000 | USA + international | Grades 10–12 | ⭐⭐⭐ High | US high school students |
| AMC 8 | 1985 | USA + international | Grade 8 and below | ⭐⭐ Moderate | Middle schoolers |
| Math Kangaroo | 1991 | 80+ countries, 6M+ entrants | Grades 1–12 | ⭐ Accessible | All students |
1. International Mathematical Olympiad (IMO) — The Gold Standard
The IMO is the undisputed best math competition in the world for pre-university students. No other contest comes close in terms of prestige, difficulty, or global reach.
Key Facts
- Founded: 1959 in Romania
- Participants: ~600 students from 100+ countries
- Format: 6 proof-based problems over 2 days (4.5 hours each)
- Topics: Algebra, geometry, number theory, combinatorics
- Who qualifies: National team selection — typically 4–6 students per country after multi-stage competitions
Why It’s the Best
The IMO’s problems are legendary for requiring deep creativity, not just knowledge. There is no formula to memorize — solutions demand original mathematical insight.
Past participants include Terence Tao, Peter Scholze, and dozens of Fields Medal winners.
A perfect score at the IMO is extraordinarily rare. Even a single medal is a career-defining achievement. Universities like MIT, Harvard, and Cambridge actively recruit IMO medalists.
→ Learn how to qualify for the IMO in the USA | IMO preparation guide
2. William Lowell Putnam Mathematical Competition — Hardest University Contest
For undergraduate students, the Putnam Competition is the equivalent of the IMO. Held annually in the USA and Canada, it is widely regarded as the hardest mathematics examination in the world at university level.
- Founded: 1938
- Participants: ~4,000 undergraduates annually
- Format: 12 problems over 6 hours (two 3-hour sessions)
- Scoring: 0–120 points — the median score is often 0–2
The Putnam is the competition for college students aspiring to graduate study, research, or academia. Top scorers (Putnam Fellows) gain enormous recognition in the mathematical community.
3. Asian Pacific Mathematics Olympiad (APMO) — Regional Powerhouse
The APMO is one of the most prestigious regional Olympiads and serves as a key step in the pathway toward the IMO for students across the Asia-Pacific region, including the United States.
- Founded: 1989
- Format: 5 problems over 4 hours
- Eligibility: Students under 20 in participating Asia-Pacific countries
- Notable: USA participates and uses APMO scores in IMO team selection
4. European Girls’ Mathematical Olympiad (EGMO) — Top Competition for Girls
Founded in 2012, EGMO has rapidly become one of the world’s most important math competitions, specifically designed to encourage and celebrate mathematical talent in young women.
- Founded: 2012
- Format: IMO-style — 6 problems over 2 days
- Eligibility: Female students under 20 in European and guest countries
- Impact: USA, China, and many non-European nations send guest teams
EGMO is not only a top-tier competition in its own right — it is a proven pathway to the IMO for many female mathematicians who go on to represent their countries.
5. American Mathematics Competitions (AMC 8, 10, 12) — Best Entry Point in the USA
The AMC series is the most important math competition pathway in the United States and the primary route to the IMO for American students. It is also one of the most widely recognized competitions globally.
The AMC Pathway to IMO
- AMC 8 → open to Grade 8 and below
- AMC 10/12 → open to Grades 10 and 12
- AIME (American Invitational Mathematics Examination) → top AMC scorers
- USAJMO / USAMO → top AIME scorers
- USA IMO Team → top USAMO participants
The AMC competitions use multiple-choice and short-answer formats, making them more accessible than proof-based olympiads. However, high AMC scores still require deep problem-solving skills well beyond standard curriculum.
→ What is a good AMC score? | AMC awards and honors | Average AMC scores
6. International Kangaroo Mathematics Contest (IKMC) — World’s Largest Math Competition
With over 6 million participants across 80+ countries, Math Kangaroo is the most widely participated math competition in the world. It is designed to make mathematics fun and accessible for students at all levels, from Grade 1 through Grade 12.
- Founded: 1991 (France)
- Participants: 6 million+ students across 80+ countries annually
- Format: Multiple-choice, 75–90 minutes, level-appropriate problems
- Best for: Students of all ages looking for an engaging, low-pressure first competition
Math Kangaroo is the ideal starting point for students who want to experience competition math without the extreme intensity of Olympiad-level contests. Many IMO participants first competed in Kangaroo as younger students.
→ How to prepare for Math Kangaroo
7. China Girls Math Olympiad (CGMO) — Elite Competition for Female Mathematicians
The CGMO is a prestigious, invitation-only competition for female high school students, with a format closely mirroring the IMO. Originally focused on China, it has expanded to include top international teams.
- Format: 8 proof-based problems over 2 days
- Eligibility: Invitation-only for national teams of female high school students
- Prestige: USA, Russia, and other elite nations regularly participate
Why the IMO Is Still the Best Math Competition in the World
Several competitions are elite, but the IMO stands alone. Here’s why:
| Factor | Why the IMO Wins |
|---|---|
| History | 65+ years running — the oldest international math competition |
| Global scale | 100+ countries — no other olympiad comes close |
| Difficulty | 6 open-ended proof problems; creative solutions required |
| Prestige | Fields Medalists, Abel Prize winners began here |
| Recognition | Top universities worldwide actively recruit IMO medalists |
| Legacy | Has defined careers, inspired generations of mathematicians |
Which Math Competition Should YOU Enter?
Choosing the right competition depends on your age, skill level, and goals:
| If you are… | Start with… | Goal |
|---|---|---|
| Grade 1–6 | Math Kangaroo | Build love of math, low-pressure experience |
| Grade 6–8 | AMC 8 or Math Kangaroo | Develop problem-solving, build competition experience |
| Grade 9–12 (USA) | AMC 10/12 → AIME → USAMO | Pathway toward IMO; college admissions advantage |
| Grade 9–12 (Global) | National olympiad → IMO | Represent your country at the world’s top contest |
| Female students | EGMO or CGMO | IMO-level challenge in an encouraging environment |
| Undergraduates | Putnam Competition | Hardest university-level contest in North America |
How to Prepare for the World’s Best Math Competitions
Whether you’re aiming for the IMO or just starting out with Math Kangaroo, the preparation principles are the same:
- Start early. Most IMO participants began serious competition math by age 12–14.
- Master the fundamentals. Strong algebra, number theory, geometry, and combinatorics are essential at any level.
- Practice past papers. Every major competition publishes archives of past problems. Solving these is the single most effective training method.
- Learn proof-writing. For olympiad-level competitions, being able to write rigorous mathematical proofs is non-negotiable.
- Use structured training. Online platforms, math circles, and olympiad books (Art of Problem Solving, etc.) accelerate growth significantly.
→ Free math olympiad training online | How to improve at olympiad problem-solving
What is the hardest math competition in the world?
The IMO and the Putnam Competition are generally considered the two hardest math competitions in the world. The IMO is the hardest at high school level; the Putnam is the hardest for undergraduates. Both have median scores that are extremely low, even among top students.
Is the IMO harder than the AMC?
Yes, significantly. The AMC series uses multiple-choice and short-answer problems that can be solved in minutes. IMO problems require original mathematical proofs and can take hours — or remain unsolved entirely. The two competitions are not directly comparable in difficulty.
What math competitions can middle school students enter?
Middle school students can enter the AMC 8 (USA), Math Kangaroo (worldwide), and many national olympiads that have junior divisions. These competitions are excellent for building the foundations needed for harder Olympiads in high school.
How many countries participate in the IMO?
Over 100 countries participate in the IMO each year, typically sending teams of up to 6 students each. The contest has been held every year since 1959 (with the exception of 1980), making it the longest-running international academic olympiad in the world.
Can students outside the USA enter the AMC?
Yes. While the AMC is organized by the Mathematical Association of America (MAA) and primarily targets US students, international schools can register to take the AMC 8, 10, and 12 exams. Many students worldwide use the AMC pathway to prepare for their national olympiad and IMO qualification.
Make Preparing for Math Olympiad Simple!
Final Verdict
The International Mathematical Olympiad (IMO) is the best math competition in the world, and it has been for over 65 years. No other contest matches its combination of global scale, legendary difficulty, and transformative prestige.
But every competition on this list has value. Math Kangaroo builds love of math in young students. The AMC creates the strongest high school mathematicians in the USA.
EGMO and CGMO create world-class opportunities for female mathematicians. And the Putnam challenges the sharpest university minds in North America.
The best competition for you is the one that challenges you, excites you, and gives you room to grow. Start where you are and aim for the top.
