The International Mathematical Olympiad
The International Mathematical Olympiad (IMO) is the most important and prestigous mathematical competition for high-school students. It has played a significant role in generating wide interest in mathematics among high school students, as well as identifying future talent.
In the beginning, the IMO was a much smaller competition than today. In 1959 the following seven countries gathered to compete in the first IMO: Bulgaria, Czechoslovakia, German Democratic Republic, Hungary, Poland, Romania and the Soviet Union. Since then, the competition has been held annually. Gradually, other Eastern-block countries, countries from Western Europe and ultimately numerous countries from around the world and every continent joined in. (The only year the IMO was not held on was 1980, when no one stepped up to host it due to financial reasons. Nowadays, this is hardly a problem, and hosts are lined up several years in advance.) In the 48th IMO, held in Vietnam, no less then 93 countries took part.
Serbia, then a part of SFR Yugoslavia, got involved in 1963. Here are presented the results of our recent national teams.
The format of the competition quickly became stable and unchanging. Each country may send up to six contestants and each contestant competes individually (without any help or collaboration). The country also sends a team leader, who partakes in problem selection and is thus isolated from the rest of the team until the end of the competition, and a deputy leader, who looks after the contestants.
The IMO competition lasts two days. On each day students are given 4.5 hours to solve 3 problems, 6 in total. The first problem is usually the easiest on each day and the last problem the hardest. Each problem is worth 7 points, making 42 points the maximum possible score. The points obtained on each problem are the result of intense negotiations and, ultimately, agreement between the problem coordinators, assigned by the host country, and the team leader and deputy, who defend the interest of their contestants. This system ensures a relatively objective grade that is seldom off by more than 2-3 points.
Though countries naturally compare each other’s scores, only individual prizes, namely medals and honorable mentions, are awarded on the IMO. Less than 1/12 of participants are awarded the gold medal, less than 1/4 are awarded the gold or silver medal and less than 1/2 are awarded the gold, silver or bronze medal. Among the students not awarded a medal, those which score 7 points on at least one problem are awarded the honorable mention. This system of determining awards works rather well. It ensures, on one hand, strict criteria and due reward for each level of performance, giving every contestant something to strive for. On the other hand, it also ensures a good degree of generosity that does not greatly depend on the variable difficulty of the problems proposed.
<i>This text was excerpted from ``The IMO Compendium.’’
Past and Future IMOs