# IMO

The International Mathematical Olympiad is a two day math competition held each summer. Participating countries send teams of up to six students. In addition there is one team leader, one deputy leader, and observers. Each day participants take a 4.5 hour, 3 question essay exam. The participating countries trade-off in hosting the event, which in its entirety usually lasts 10- 14 days. For more information on the IMO, please visit the IMO's website at www.imo-official.org or visit https://www.imo2021.org/

## History

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

## Content

The IMO is a rigorous two day competition including problems that would challenge most professional mathematicians. The content ranges from extremely difficult precalculus 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 at play 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. (Wikipedia)

In addition to comprehensive mathematical knowledge, success on the IMO requires truly exceptional mathematical creativity and inventiveness. As an example, here is a problem from the 1998 IMO:

• Let I be the incenter of triangle ABC. Let the incircle of ABC touch the sides BC, CA, and AB at K, L and M, respectively. The line through B parallel to MK meets the lines LM and LK at R and S, respectively. Prove that angle RIS is acute.

## U.S. Participation

Each year since 1974, a small team of exceptionally talented high school students has represented the United States at the International Mathematical Olympiad (IMO).

Following the 3-4 week Mathematical Olympiad Summer Program (MOSP), the U.S. Team and the adult leaders travel to the site of the International Mathematical Olympiad (IMO). There, the most talented high school students from over 90 nations compete in an extremely challenging two day examination. The examination is constructed by the leaders of the participating teams from a pool of problems submitted earlier by the invited nations. Both the construction of the examination and the subsequent grading of the papers are conducted in elaborate and highly democratic proceedings designed to preserve security and objectivity.

During the period of the IMO, the students are entertained by the host nation. In addition to visiting local points of interest in the host city, there is ample opportunity for informal interaction among the team members and leaders and their counterparts from the other participating countries.

## Mathematical Association of America Involvement

The officers of the Mathematical Association of America (MAA) and the Committee on the American Mathematics Competitions (CAMC) endorse the following objectives of participation by the United States in the IMO:

• To provide opportunities for meetings and contacts among present and future mathematicians and scientists of different countries.
• To enrich the education and training for research in the mathematical sciences of 30 of our nation's most talented students by means of an intensive four week seminar in mathematics and problem solving beyond the standard syllabus.
• To stimulate and encourage mathematical excellence among the students and teachers of America's high schools through the example set by these talented students and the favorable publicity the United States Team receives as a consequence of its participation in the IMO.
• To use this friendly competition as a forum for the exchange of mathematical and educational ideas that might prove helpful in setting priorities for secondary school mathematics in the United States.
• To foster unity of interest among all nations. Mathematics, because of its universal nature, is ideally suited for this role.

For a complete list of the American Mathematics Competitions offical contest dates, including the IMO and where it will be held, please visit our calendar at amc.maa.org/calendar.