International Mathematical Olympiad
Mathematical competitions have played important roles in the tradition of many countries for centuries, surely dating as far back as the Greeks competing to solve geometry problems. In the XVI century, the Italians competed to resolve cubic polynomials, the French held competitions in the XVIII century, and Hungary organized the Eotvos competitions since 1894, which is most likely the closest antecedent to the Mathematical Olympiad held today. The first Mathematical Olympiad took place in Leningrad (now Sankt Petersburg) in 1934, organized by B. N. Delone and G. M. Frijtengolts. The International Mathematical Olympiad (IMO) was first held in 1959, hosted by Romania, to which Hungary, Bulgaria, Poland, Czechoslovakia, East Germany, and USSR were invited. Since then, it has been held, with each participating country hosting it by turns. As time went by, the number of participating countries has been increasing, with 73 countries in the 34th IMO in Istanbul, Turkey (in 1993, this was the year when Slovenia first took part). It has now become the well-known competition for young mathematics enthusiasts all over the world.
When the IMO first began, each country was allowed up to eight participants. In 1982, this was scaled back to four members, but in 1983 the number was increased to six, which is where it still stands. The contestants must be no more than 20 years old and must not have any post secondary-school education. There is no limit to how many times a person may participate in the IMO, provided the individual meets the age and schooling requirements. The usual size of an official delegation to an IMO is (a maximum of) six students, along with the Leader and Deputy Leader. The student competitor writes two papers, on consecutive days, each paper consisting of three questions. Each question is worth seven marks. Only a whole number of marks are given, so there can be no half mark score.
Each invited country can send in up to six questions for consideration for the final competition papers. These submissions are reviewed by the host country's competitions committee, and a short list of about thirty questions is made. In recent years, there has also been a list of twelve preferred questions. The choice of the questions on the actual competition papers is made by the International Jury. The International Jury consists of the Chief Delegate (Leader) from each participating country, together with a Jury Executive of four named by the host country. Decisions are made by a simple majority vote. The International Jury meets a few days in advance of the competition in a sequestered location in order to choose the papers. The official languages of the IMO are English, French, German and Russian. Since Spanish is spoken in a large number of participating countries, it has become an unofficial “official” language. In recent years, English has been the working language of the International Jury, with the other official languages available whenever required.
The International Jury members receive the short list of questions on arrival at the sequestered site. They have little time to review these problems before meeting to discuss which problems will be included. An honor system requires delegates to identify any suggested problems that are well known, in text books, or have been used in training programs. Some problems are eliminated as too easy or too hard. After considerable debate, the six problems are chosen, and their wording in all the official languages is agreed. The leaders of countries, whose students require other languages, then translate the questions into the required language. All papers, in all languages, are then inspected by all members of the International Jury, to ensure that all translations are appropriate.
The Program for IMO is almost the same every year. The Leaders arrive at the site ahead of the Deputy Leaders and the Contestants. The Leaders from each country get together to discuss and select 6 problems from dozens of short-listed problems that had been scrutinized beforehand. Then, each Leader translates the selected ones into his/her own language. After this process is completed, the Deputy Leaders and Contestants will arrive at the venue.
The Opening Ceremony is held, and the Contest begins the following day to last for two days. Each Contestant has to answer 3 questions in each of the two days in his/her own language in for 4 and a half hours. After the Contest, the program shifts to entertaining activities such as sightseeing and games, for three days. During this period, the Contestants will have good opportunities to develop international friendship, through sharing talks and entertainment with each other. Meanwhile, the Leaders and Deputy Leaders mark the exam papers, and have Coordination sessions to discuss whether the marking has been done fairly and correctly.
The last day is for the Closing Ceremony, and the Gold, Silver, and Bronze medals will be awarded for excellent performances. The International Mathematical Olympiad is an individual competition. Only individuals compete. There is no team competition. Medals are awarded to approximately the top half of the participating students. Gold, Silver and Bronze medals are awarded in the ratio of 1:2:3, with no more that 1/12 of the students getting a Gold Medal, no more that 1/4 of the students getting either a Gold or a Silver Medal and no more that 1/2 of the students getting a medal of any kind. In order to encourage more students, and to encourage students to solve complete problems, recent practice has awarded a Certificate of Honorable Mention to any student (not receiving a medal) who obtained full marks for at least one problem. That evening, the IMO ends with Farewell Banquet.