September 22, 2025
14 min. read
If you are 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. More than 100 countries compete each year.
But the IMO is just the summit. Below it sits a rich landscape of elite math competitions suited to different ages, skill levels, and goals.
This guide ranks the top 7 international math competitions. If you are new to competitive math, you may also want to understand what is the purpose of the math olympiad.
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
Here is a quick comparison of the world’s best math competitions, ranked by prestige, difficulty, and global reach.
| 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 to 12 | High | US high school students |
| AMC 8 | 1985 | USA + international | Grade 8 and below | Moderate | Middle schoolers |
| Math Kangaroo (IKMC) | 1991 | 80+ countries, 6M+ entrants | Grades 1 to 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 international math contest comes close in terms of prestige, difficulty, or global reach.
Key Facts About the IMO
- Founded: 1959 in Romania (Brasov)
- Participants: Around 600 students from 100+ countries each year
- Format: 6 proof-based problems over 2 days (4.5 hours per day)
- Topics: Algebra, geometry, number theory, combinatorics
- Who qualifies: National team selection, typically 4 to 6 students per country after multi-stage competitions
- Team size: Each country sends up to 6 students
- Eligibility: Learn about IMO exam eligibility criteria for students of all classes
Why the IMO Is the Most Prestigious Math Olympiad
The IMO’s problems are legendary. They require deep creativity, not just knowledge.
There is no formula to memorize. Solutions demand original mathematical insight.
Past participants include Terence Tao (who won a gold medal at age 13), 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, Stanford, and Cambridge actively recruit IMO medalists.
An IMO gold medal is one of the most recognized achievements on any college application.
Learn more: How to qualify for the IMO in the USA | IMO preparation guide
2. William Lowell Putnam Mathematical Competition: Hardest University-Level Math 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 math exam at the university level.
Key Facts About the Putnam
- Founded: 1938
- Participants: Around 4,000 undergraduates annually
- Format: 12 problems over 6 hours (two 3-hour sessions)
- Scoring: 0 to 120 points. The median score is often 0 to 2.
Is the Putnam Harder Than the IMO?
This is a common question among competitive mathematicians. Both competitions are extremely difficult.
The IMO focuses on proof-based problems for high school students. The Putnam tests a broader range of university-level mathematics.
The key difference is format. IMO gives 6 problems over two days, with extended time for deep thinking.
The Putnam gives 12 problems in 6 hours, requiring faster problem-solving. Many top competitors describe both as equally challenging in different ways.
Top scorers on the Putnam (known as Putnam Fellows) gain enormous recognition in the mathematical community.
Many go on to distinguished careers in research and academia.
3. Asian Pacific Mathematics Olympiad (APMO): Regional Powerhouse
The APMO is one of the most prestigious regional math olympiads.
It serves as a key step in the pathway toward the IMO for students across the Asia-Pacific region, including the United States.
Key Facts About the APMO
- Founded: 1989
- Format: 5 problems over 4 hours
- Eligibility: Students under 20 in participating Asia-Pacific countries
- Notable: The USA participates and uses APMO scores in IMO team selection
The APMO is especially important for countries with strong math olympiad traditions, including China, South Korea, Japan, and Australia.
Performance at the APMO often directly influences which students are selected for the national IMO team.
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.
It is specifically designed to encourage and celebrate mathematical talent in young women.
Key Facts About EGMO
- 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 on its own.
It is also a proven pathway to the IMO for many female mathematicians who go on to represent their countries at the international level.
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.
It is also the primary route to the IMO for American students and one of the most widely recognized competitions globally.
The AMC Pathway to the IMO
- AMC 8 – Open to grade 8 and below
- AMC 10/12 – Open to grades 10 and 12 respectively
- AIME (American Invitational Mathematics Examination) – Top AMC scorers qualify
- USAJMO / USAMO – Top AIME scorers advance
- USA IMO Team – Top USAMO participants are selected
What Makes the AMC Different
The AMC competitions use multiple-choice and short-answer formats. This makes them more accessible than proof-based olympiads.
However, high AMC scores still require great problem-solving skills well beyond the standard school curriculum.
If you are preparing for the AMC, understanding the AMC syllabus and knowing how to prepare for the AMC are essential first steps.
The AMC is also popular internationally. Schools outside the USA can register for the AMC 8, 10, and 12 exams.
Many students worldwide use the AMC pathway to prepare for their national olympiad and IMO qualification.
Learn about AMC age limits and eligibility, and the benefits of AMC math for academic growth.
Learn more: 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 biggest math competition in the world by participation.
It is designed to make mathematics fun and accessible for students at all levels.
Key Facts About Math Kangaroo
- Founded: 1991 in France (originally called Kangourou des Mathematiques)
- Participants: 6 million+ students across 80+ countries annually
- Format: Multiple-choice, 75 to 90 minutes, level-appropriate problems
- Best for: Students of all ages looking for an engaging, low-pressure first competition
Is Math Kangaroo Prestigious?
Math Kangaroo is not designed to be an elite olympiad. Its value lies in accessibility and engagement.
It is the ideal starting point for students who want to experience competition math without the extreme intensity of olympiad-level contests.
That said, Math Kangaroo should not be underestimated. Many IMO participants first competed in Kangaroo as younger students.
It builds confidence, sharpens logical thinking, and introduces key concepts in algebra, geometry, number theory, and combinatorics.
Learn more about what Kangaroo Math is, Math Kangaroo participation details, and Math Kangaroo prizes.
Learn more: 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.
Its format closely mirrors the IMO. Originally focused on China, it has expanded to include top international teams.
Key Facts About the CGMO
- 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
The CGMO, along with EGMO, plays an important role in encouraging gender diversity in competitive mathematics at the highest level.
Why the IMO Is Still the Best Math Competition in the World
Several competitions are elite. But the IMO stands alone. Here is 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, original solutions required. |
| Prestige | Fields Medalists and Abel Prize winners began here. |
| Recognition | Top universities worldwide actively recruit IMO medalists. |
| Legacy | Has defined careers and inspired generations of mathematicians. |
How the IMO Compares to Other Top Competitions
Many students and parents ask how the IMO stacks up against other well-known math contests. Here are the most common comparisons.
IMO vs AMC
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.
The two competitions are not directly comparable in difficulty. However, the AMC is the starting gateway for American students who eventually aim for the IMO.
IMO vs Putnam
Both are considered the hardest math competitions in their categories. The IMO is the hardest for high school students. The Putnam is the hardest for undergraduates.
Both have extremely low median scores, even among top students.
Math Kangaroo vs AMC
Math Kangaroo is designed for accessibility and engagement across all grade levels. The AMC is more competitive and directly feeds into the olympiad pipeline.
For younger students (grades 1 to 6), Math Kangaroo is a better starting point. For students in grades 8 and above who want to pursue competitive math seriously, the AMC is the stronger choice.
Math Kangaroo vs Math Olympiad
Math Kangaroo focuses on fun, logical thinking, and broad participation. National and international math olympiads focus on deep, proof-based problem solving for elite students.
They serve different purposes but complement each other well. For a detailed breakdown, see our guide on the difference between Math Olympiad and Kangaroo Math.
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 to 6 | Math Kangaroo | Build love of math, low-pressure experience |
| Grade 6 to 8 | AMC 8 or Math Kangaroo | Develop problem-solving, build competition experience |
| Grade 9 to 12 (USA) | AMC 10/12, then AIME, then USAMO | Pathway toward IMO; college admissions advantage |
| Grade 9 to 12 (Global) | National olympiad, then IMO | Represent your country at the world’s top contest (example: how to qualify for the IMO from Bangladesh) |
| Female students | EGMO or CGMO | IMO-level challenge in an encouraging environment |
| Undergraduates | Putnam Competition | Hardest university-level math contest in North America |
| College students (international) | International Mathematics Competition (IMC) | Top math competition for university students worldwide |
Best Math Competitions for Kids and Middle School Students
If you are a parent or teacher looking for the best math competitions for kids, here are the top options by age group.
Grades 1 to 5: Math Kangaroo is the best starting point. It is available in 80+ countries, uses age-appropriate problems, and makes math feel like a game.
Grades 6 to 8: The AMC 8 is the most recognized competition for middle school students in the USA. Math Kangaroo remains a great option internationally.
Many countries also have junior divisions of their national math olympiad. See our guide on how to prepare for the Junior Math Olympiad for more tips.
Other popular competitions for kids include: Noetic Learning Math Contest, Math League, MathCounts (USA), and the Continental Mathematics League (CML).
The key is to start early and build confidence. Most IMO participants began serious competition math by age 12 to 14.
For students who want to aim high from the start, our guide on how to get full marks in a maths olympiad covers proven strategies.
How to Prepare for the World’s Best Math Competitions
Whether you are 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 to 14.
- Master the fundamentals. Strong skills in algebra, number theory, geometry, and combinatorics are essential at any level. Find out what types of questions are asked in math olympiads to focus your study.
- Practice past papers. Every major competition publishes archives of past problems. Solving these is the single most effective training method. Learn how to get better at solving math olympiad questions with proven strategies.
- Learn proof-writing. For olympiad-level competitions, being able to write rigorous mathematical proofs is non-negotiable. Our guide on how to improve problem-solving skills for the IMO covers this in depth.
- Use structured training. Online platforms, math circles, and olympiad books (such as Art of Problem Solving) accelerate growth significantly.
- Join a community. Forums like Art of Problem Solving (AoPS) connect students with peers and mentors who share strategies and motivation.
Learn more: 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.
What is the most prestigious math olympiad in the world?
The International Mathematical Olympiad (IMO) is the most prestigious math olympiad in the world. It has been running since 1959, draws participants from over 100 countries, and is the gold standard for pre-university mathematical excellence.
Is Math Kangaroo a prestigious competition?
Math Kangaroo is the world’s largest math competition by participation, with over 6 million students in 80+ countries. While it is not as difficult as the IMO or national olympiads, it is highly respected as an introductory competition that builds mathematical thinking skills.
What is the biggest math competition in the world?
By number of participants, the International Kangaroo Mathematics Contest (Math Kangaroo) is the biggest math competition in the world, with over 6 million students competing annually. By prestige and difficulty, the International Mathematical Olympiad (IMO) is the top competition.
What are the best math competitions for high school students?
The best math competitions for high school students include the AMC 10/12 (USA), national math olympiads, EGMO (for female students), APMO (Asia-Pacific), and the IMO. The right choice depends on your country, skill level, and long-term goals.
Is there a math olympiad for college students?
Yes. The William Lowell Putnam Mathematical Competition is the premier math olympiad for university students in North America. Internationally, the International Mathematics Competition for University Students (IMC) is the top math competition for college and university students.
Make Preparing for Math Olympiad Simple!
Final Verdict
The International Mathematical Olympiad (IMO) is the best math competition in the world. It has held that position 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 a 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.
