International Mathematical Olympiad

| Main Article
| Discussion
| Related Articles  [?]
| Bibliography  [?]
| External Links  [?]
| Citable Version  [?]

|
|
|
|
|
|
|
|

This editable Main Article is under development and subject to a disclaimer.

[edit intro]

The International Mathematical Olympiad (IMO for short) is an annual mathematics contest for high school students from across the world. The format has varied over the years, but recently has been as follows. Each country can send a maximum of six participants. About 100 countries participate and the number of contestants is approximately 600.[1] The contest stretches over two days. On each day, the students are given 4.5 hours to solve three challenging problems individually. Based on relative performance, students are awarded gold medals, silver medals, bronze medals and certificates of honorable mention.

Selection procedures for the Olympiads differ from country to country. The countries that participate regularly send six students every year, selected through tests and trained specifically for the Olympiad.

The first International Mathematical Olympiad was held in Romania in 1959. Since then, the Olympiad has been held every year except 1980. The 2025 International Mathematical Olympiad was held in Australia, and the 2026 International Mathematical Olympiad will be held in China. The IMO is usually held in the month of July.

## Contents

* 1 History
* 2 Scoring and format
* 2.1 Contest format
* 2.2 Scoring
* 2.3 Medals
* 3 Problem selection
* 3.1 Proposal stage
* 3.2 Selection stage
* 3.3 Shortlisted problems
* 4 Syllabus
* 5 Selection process
* 6 Performance of countries
* 7 Cultural and technological impacts
* 8 Later achievements of Olympiad contestants

## History[edit]

The first International Mathematical Olympiad was held in Romania in 1959. Only seven countries participated: Romania, Hungary, German Democratic Republic, the erstwhile Soviet Union, Bulgaria, Poland and Czechoslovakia. For the first 5-6 years, participation was limited to countries in East Europe (and the Soviet Union). By 1970, many West European countries, including France, Italy and the United Kingdom, had started participating. The United States of America first participated in 1974 and China first participated in 1985. In 1989, the number of participating countries reached 50.

## Scoring and format[edit]

### Contest format[edit]

The current format of the International Mathematical Olympiad has been used since 1981. The contest spans over two days. On each day, the contestants are given a set of three problems to solve in a span of 4.5 hours. The problems are in the following mathematical disciplines: algebra, number theory, combinatorics and geometry. On each day, the problems are in increasing order of difficulty, and the problems on a particular day are all in different parts of mathematics.

### Scoring[edit]

After the contestants submit the problems, two people from the contestants' country (called the Leader and Deputy Leader) evaluate the contestants' problems in consultation with the contestants. Independently, each problem is evaluated by members of a Problem Committee, according to criteria evolved by the Committee. The Leader and Deputy leader of the country then discuss with the Problem Committee and come to a consensus on how many points each contestant gets on the problem. The maximum score per problem is 7.

### Medals[edit]

The top 1/12 of contestants (based on total score on the problems) receive a gold medal. Cutoffs for the gold medal vary from year to year, depending on the difficulty of the problems. The next 1/6 of contestants receive a silver medal, and the next 1/3 of contestants receive a bronze medal. A total of at most half the contestants receive medals. Of the remaining contestants, those who score full points on at least one problem, receive a certificate of honourable mention.

## Problem selection[edit]

### Proposal stage[edit]

Any of the participating countries can propose problems for the IMO. The problems are sent to the country that is hosting the IMO. From the longlist of all proposed problems, the host country selects a shortlist with 6-10 problems each from algebra, number theory, geometry and combinatorics.

Countries proposing problems are supposed to keep these problems confidential from the contestants.

### Selection stage[edit]

Three to four days before the actual contest, the Leaders from the countries arrive at the host country. The Leaders go through the shortlisted problems, and based on assessment of the level of difficulty of these problems, decide what problems should appear on the two contest days, and in what order. The leaders do not have contact with the contestants or Deputy Leader during this process.

### Shortlisted problems[edit]

Shortlisted problems are usually not disclosed to the world immediately after the Olympiad. These problems are used by a number of countries in their selection tests for students for the Olympiad next year. The shortlist is published officially just before the next year's Olympiad.

## Syllabus[edit]

There is no definite syllabus for the International Mathematical Olympiad. The four disciplines from which problems are asked are: algebra, geometry, number theory and combinatorics. Calculus is specifically avoided in the International Mathematical Olympiad. Every Olympiad problem should have an elementary solution that does not require any knowledge of calculus or any knowledge of higher mathematics. However, students are allowed to use methods from higher mathematics.

## Selection process[edit]

Selection process for the International Mathematical Olympiad differs from country to country. Countries that participate regularly in the Olympiad often have a two-tier (or even three-tier) selection process. The first round is open to the general public, and those selected in this round get to attend a training-cum-selection camp where the top six students are selected through a series of tests. The selected students may then be trained further.

The criterion for participating in the International Mathematical Olympiad is that the student should be under the age of 21, and should not have formally begun college education. Participating countries may impose further rules on eligibilty of contestants to appear in the camps.

## Performance of countries[edit]

The performance of countries varies year by year. Over the last decade, countries that have regularly performed well include China, the United States of America, Russia and Vietnam. Bulgaria topped in 2003.

The best-ever performance has been that of the United States in 1994 at Hong Kong, where all contestants got perfect scores.

## Cultural and technological impacts[edit]

The International Mathematical Olympiad is frequently described as a World Championship mathematics contest for high school students.[2] As such, along with many current Fields medalists having participated and been awarded in the olympiad beforehand, it has garnered a considerable amount of attention in the mathematical community. Some media features have been produced centered around the olympiad, such as the 2014 movie X+Y, which adapted IMO silver medalist Daniel Lightwing's life story into a positively reviewed plot.[3]

In more recent editions, the exams have been used by corporations such as Google and OpenAI to train problem-solving machine models, and have been showing increasingly better results when put in similar conditions to the actual test, increasing the relevance of a debate on whether artificial intelligence is helpful for mathematical research or not.[1]

## Later achievements of Olympiad contestants[edit]

Many Olympiad contestants have gone on to become mathematicians.

* 2006 Fields medalist Terence Tao had participated in the International Mathematical Olympiad as an Australian at the ages of 11, 12, 13. He then migrated to the United States of America, and stopped contesting in the Olympiads. Tao has won the Fields Medal for his work on proving a conjecture on arithmetic progressions of primes.

* Grigory Margulis, known for his work on Lie groups and also a Fields medalist like Tao, also participated in the Olympiads in his early years.

* Grigori "Grisha" Perelman, the reclusive Russian mathematician who gained prominence for his proof of the Thurston's Geometrization Conjecture (that includes the notoriously elusive Poincaré Conjecture as a special case) for which he was awarded the Millennium prize on 18 March, 2010 [1], also 2006 Fields Medal (but ultimately declined to accept this prize), and was a gold medalist at the 1982 IMO (as a member of the USSR team) where he scored a perfect paper.

1. ↑ 1.0 1.1 Google clinches milestone gold global math competition, while OpenAI also claims win, Reuters, 22 July 2025. Accessed on 6 March 2026.
2. ↑ Indian team ranks fourth in best ever performance at International Mathematics Olympiad, Indiatimes, 21 July 2024, accessed on 6 March 2026.
3. ↑ X Plus Y | Rotten Tomatoes, accessed on 6 March 2026.