International Mathematical Olympiads

The International Mathematical Olympiad (IMO) is an annual six-problem mathematical olympiad for pre-college students, and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980. About 100 countries send teams of up to six students, plus one team leader, one deputy leader, and observers.

The content ranges from extremely difficult algebra and pre-calculus problems to problems on branches of mathematics not conventionally covered at school and often not at university level either, such as projective and complex geometry, functional equations and well-grounded number theory, of which extensive knowledge of theorems is required. Calculus, though allowed in solutions, is never required, as there is a principle that anyone with a basic understanding of mathematics should understand the problems, even if the solutions require a great deal more knowledge. Supporters of this principle claim that this allows more universality and creates an incentive to find elegant, deceptively simple-looking problems which nevertheless require a certain level of ingenuity.

The selection process differs by country, but it often consists of a series of tests which admit fewer students at each progressing test. Awards are given to approximately the top-scoring 50% of the individual contestants. Teams are not officially recognized—all scores are given only to individual contestants, but team scoring is unofficially compared more than individual scores. Contestants must be under the age of 20 and must not be registered at any tertiary institution. Subject to these conditions, an individual may participate any number of times in the IMO.

The first IMO was held in Romania in 1959. Since then it has been held every year except in 1980. That year, it was cancelled due to internal strife in Mongolia. It was initially founded for eastern European member countries of the Warsaw Pact, under the Soviet bloc of influence, but later other countries participated as well. Because of this eastern origin, the IMOs were first hosted only in eastern European countries, and gradually spread to other nations.

...
Wikipedia