About IMO

Introduction

The International Mathematical Olympiad (IMO) is the world’s most prestigious mathematics competition for secondary school students, often regarded as the World Championship Mathematics Competition. Each year, more than 100 countries send teams of up to six contestants to take part in a two-day contest featuring exceptionally challenging mathematical problems. The IMO gives some of the brightest young mathematical talents the opportunity to test their abilities, compete with peers from around the world, and engage with ideas far beyond the usual school curriculum.

Yet the IMO is much more than a competition. It is usually a week-long international event that brings together students, teachers, leaders, coordinators, and organisers from across the globe. In addition to the contest itself, the host country offers a rich programme of cultural, mathematical, social, and recreational activities, creating opportunities for friendship, exchange of ideas, and unforgettable shared experiences.

The IMO is held annually in a different country, typically in mid-July. In 2027, the 68th International Mathematical Olympiad will be hosted in Budapest, Hungary, marking the second time that Budapest welcomes the competition.

How it works

The IMO contest consists of six problems, each worth 7 points, giving a maximum possible score of 42 points. The problems are chosen from areas of secondary school mathematics, most commonly algebra, combinatorics, geometry, and number theory. The competition takes place over two consecutive days: on each day, contestants have four and a half hours to solve three problems, without calculators or electronic aids.

The problems require not only technical knowledge, but also exceptional creativity, insight, and precision. Solutions must include complete mathematical proofs and clear justifications. Each year, among more than 600 contestants, only a very small number manage to solve all six problems and achieve the perfect score of 42 points.

Medals are awarded to approximately half of the contestants. The thresholds for gold, silver, and bronze medals are chosen so that the numbers of medallists are approximately in the ratio 1:2:3. Contestants who do not receive a medal but solve at least one problem completely are awarded an honourable mention. The Maryam Mirzakhani Award also recognises outstanding female contestants from different regions of the world.

The selection of the problems is an international process. Participating countries may submit proposed problems in advance, which are reviewed by the Problem Selection Committee appointed by the host organisation. From these submissions, a shortlist is prepared. The final six contest problems are then selected by the IMO Jury, consisting of the leaders of the participating teams.

After the exams, the marking of the solutions is carried out through a coordination process. Each solution is assessed on a scale from 0 to 7, based on correctness, completeness, and clarity. Partial progress may receive partial credit, while full marks require a complete and correct argument. The host organisation provides coordinators, and each country is represented in the process, usually by its Leader and Deputy Leader.

The final scores are agreed between the coordinators and the representatives of each country. If agreement cannot be reached, the issue may be referred to senior coordinators and, ultimately, to the Jury. This international coordination system is one of the IMO’s most important safeguards, ensuring that solutions are judged fairly and consistently across all participating countries.

History

To avoid the wrong assumption that mathematics has nothing to do with history, let’s take a brief look at the history of the IMO itself!

1959

The year of the Dyatlov Pass mystery. Fidel Castro established a revolutionary government in Cuba. An armed uprising broke out in Tibet against Chinese influence. Algeria officially gained autonomy. Hawaii became the 50th U.S. state, and the first Barbie doll was unveiled in New York. And in that same year, the first Mathematical Olympiad was held in Brasov, with the participation of seven countries.

Born during the Cold War, the first initiative involved exclusively students from the Soviet bloc, who competed in teams of eight. To reduce the growing organisational burden, this number was later decreased to four participants. Finally, as a compromise, the size of the delegations was set at six to bring the friendly competition to as many students as possible, encouraging and connecting the nerds of numbers and the paladins of proofs.

1964 

The first Chinese atomic test, the Good Friday earthquake in Alaska, and the first recorded use of the word “hippie.” The 6th IMO was held in Moscow, now with nine participating teams, for the first time including a country outside Europe, Mongolia. Was this the turning point, one of the keys to the IMO’s success and reputation today?

Throughout the following years, the IMO opened its doors to more European nations: Finland (1965), the United Kingdom, Italy, and Sweden (1967), then Belgium and the Netherlands (1969), and Austria (1970) joined the competition. Considering modern Europe, this list may seem ordinary, but in a world defined by the Cold War, this was a remarkable opportunity. The IMO created a unique bridge between East and West, transcending politics, where the Soviet bloc and the Western world could meet at the altar of mathematics.

1971 

Bangladesh became an independent state, and the United Arab Emirates gained independence from Great Britain. Meanwhile in the UK, “Decimal Day” took place, a less scientific but very practical mathematical milestone: the British and Irish pound adopted the decimal system. Before that, one pound equalled 20 shillings or 240 pence.

For the IMO, the 1970s marked the debut of several countries beyond Europe. Cuba joined in 1971, the first Latin American country. Vietnam followed in 1974, the first from Southeast Asia. The United States joined in 1975, not only the first North American participant but also the greatest rival of the Eastern Bloc. Eventually, the series continued with Algeria in 1977, the first African nation to compete at the Mathematical Olympiad.

1980 

In retaliation for the Soviet Union’s invasion of Afghanistan, U.S. President Jimmy Carter boycotted the Moscow Summer Olympics. In response, the Soviet Union withdrew its participation from the 1980 Mathematical Olympiad in Mongolia. Following this, Mongolia announced that it would be unable to organise the competition due to a lack of resources. Without a replacement host, the IMO unfortunately did not take place that year.

There is no evidence that Mongolia cancelled hosting the event under pressure from the Soviet Union. Nevertheless, it’s a shame that politics could override the interests of the international mathematical community, and that no substitute host country could be found. This is especially regrettable given that by then the Olympiad had already crossed the Iron Curtain: it was held in Austria in 1976 and in the United Kingdom in 1979.

Luckily, reconciliation didn’t take long. In 1981, the world competition was held again, that year in Washington, D.C. Then, in 1989, Braunschweig, Germany also joined the list of host cities. In the year of the fall of the Berlin Wall, this symbolically brought an end to the era of the Cold War, not only in politics but in the world of mathematics as well.

By that time, the IMO had grown to 50 participating countries, and that number has doubled since then. The Olympiad has become a truly global competition, not only in name and prestige but also in essence: travelling the world from Cape Town to Oslo, from Tokyo to Toronto. Competitors have reached Argentina, Mexico, Brazil, explored China, Japan, and Vietnam, and discovered Australia, Canada, and South Africa.

2027

In 2027, the 68th Olympiad will return to its birthplace, Europe. History repeats itself, and so does tradition: for the fourth time, Hungary will warmly welcome students, teachers, and enthusiasts. After this journey through the IMO’s past, let’s continue to enrich this long and meaningful tradition together!

Further information, statistics, and problems are available on the official IMO website: www.imo-official.org.