Overview

1.

What is the IMO?

The International Mathematical Olympiad (IMO) is the World Championship Mathematics Competition for High Students School held annually. It started in Romania in 1959 as an eastern European regional competition. For the first years few it was restricted to the same east block countries, but its membership (which is by invitation only) has gradually expanded to over seventy countries from five continents. Canada has been a member since 1981, when the competition was held in Washington, D.C.
The usual size of an official delegation to an IMO is (a maximum of) six students and (a maximum of) two leaders. There is no official ``team''. The student competitors write 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!

2.

The question papers.

No later than four months before the competition, 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 honour system requires delegates to identify any suggested problems that are well known, in text books, or have been used in training programmes. Some problems are eliminated as ``too easy'' or as ``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.

3.

The competition.

Students arrive a couple of days before the actual competition days, to give them time to recover from jet-lag, climate changes, etc., and to settle in to the host site. The actual competition consists of two papers, each of three questions, each paper lasting four and one half hours. This is in itself, a bit of an endurance test. Try working for four and one half hours without a break! Traditionally, question 1 is relatively easy and question 6 is the hardest! However, the leader's opinions on the relative difficulty of the questions is not always the same as the students'! Remember that the students are the best in their countries, and we certainly have the best in the world present.
The papers are on successive days. After they have been written, the students are now ``free'' from worries! They now have a cultural and entertainment programme while the papers are marked. This programme varies according to the taste of the host country. None the less, all programmes enable the visiting students to get a glimpse of the best of the host country.

4.

The marking of the papers.

Because of the diversity of languages used, the leaders from each participating country mark their own students' papers in the first instance. However, they are not permitted to make any marks on the scripts. They then present their students' papers, sometimes with translations, to the team of markers (known as coordinators) appointed by the host country. Sometimes the coordinators will ask the leader to suggest a mark, sometimes it is the other way round. Eventually, the leaders and the coordinators must agree on a mark, which is entered into the official mark book, and the book is signed by both parties. In the vast majority of instances, there is quick agreement on what the mark should be (leaders are always hopeful for a better mark). If there is a protracted disagreement, the Chief Coordinator attempts to mediate. If that does not work, the case is presented to the full International Jury for resolution by majority vote.

5.

The results.

The International Mathematical Olympiad is an individual competition. Only individuals compete. There is no team competition. Unfortunately, some countries have adopted the practice of adding together their students' scores to get a team total that is used to rank the countries. For example, if anyone told you that Canada ranked 11th out of 48 countries in Beijing, that information would be strictly unofficial.
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 Honourable Mention to any student (not receiving a medal) who obtained full marks for at least one problem.

6.

The social and cultural programme.

Students will be present at an International Mathematical Olympiad for about nine days. They will typically write the competition on days four and five. While the papers are being marked (which usually takes three days), the students take part in social and cultural events organised by the host country. As examples of such events at recent IMOs, there have been visits to:
the Great Wall of China,
the Winter Palace in Beijing,
the Royal Palace of the Kings of Hanover,
the Lower Saxony Windmill Park,
the Tintidbilla Nature Reserve near Canberra,
the Australian National Botanic Garden in Canberra,
the Bay of Pigs in Cuba.
Traditionally, the IMO ends with two events: a medal presentation ceremony and a final banquet/party. The medal presentation ceremonies are formal joyous events. Here is a chance for the best to receive their medals amidst public acclaim, with considerable media coverage. It is customary to have a very high ranking person from the host country as the presenter of the Gold Medal awards. The final banquet/party is a more relaxed event, with pledges of friendships across the globe. There is an atmosphere of goodwill that transcends national, political, religious and other artificial boundaries. If only the world were left in the hands of mathematicians!

7.

Training and selecting students for an IMO.

Different countries have different methods of training and selecting students for an IMO. The Canadian way is based on the philosophy of choosing students twelve weeks before the competition, so that they can then concentrate in a relaxed way on their problem solving skills.
In Canada, the Canadian Mathematical Society is the sponsoring organisation. With the help of a large number of Canadian mathematicians at many different universities, colleges and schools, the CMS tries to identify those students who are ``possibles'' for the IMO team, not only for the current year, but also for the next two or three years. We are very grateful to the Canadian Mathematics Foundation at the University of Waterloo, for assistance in identifying the ``possibles''. The CMS runs a Correspondence Training Programme for the ``possibles'' (other interested students may also participate). The primary input into the selection process is the student's performance on the Canadian Mathematical Olympiad (CMO), which is run by the CMS. (The CMO is the Canadian Championship Mathematics Competition for High School students). Additional valuable information is obtained from the Asian Pacific Mathematical Olympiad. Performance in the Correspondence Training Programme, other competitions, and additional factors are taken into consideration. With all the evidence in place, a small selection committee meets and discusses all eligible candidates. Their task is unenviable. Although they have to choose from the very best in the country, and although the ``top'' members of the Canadian team are usually very clear, they must choose six and only six. Actual experience of being at an IMO goes a long way to performing well! Some attempt is made to have at least one member of the team with prior IMO experience.
After the team has been chosen in early May, the students chosen must prepare themselves for the trip. They are helped in at least two ways. Thanks to the good graces of Professor Dunkley, they are invited to the Waterloo seminar, where they will meet with at least one of the leaders. Then, two weeks before travelling to the actual IMO, the team meets with the leaders at the Residential Training Seminar. Here the students hone their skills by reviewing the topics normally covered on the IMO questions and by trying many, many different problems. They also write mock IMO papers of four and one half hours duration, to gain some experience and stamina. The Residential Training Seminar is also useful for building team spirit and a friendly atmosphere of cooperation. After all, these young students will be ambassadors for their country. We have discovered that Canadians are indeed welcome in all countries around the world.
With the support of N.S.E.R.C., a junior training programme was instituted in 1991. This enables six of next year's prospects to spend one week in the company of this year's team and the coaches. By getting together, we hope that they will experience some of the pleasures of the residential training programme and learn a little more about what an actual IMO is like.

8.

The IMO in Canada in 1995.

The International Jury has accepted an invitation from Canada to be the host nation in 1995. We requested this year since it coincides with the 50th anniversary of the founding of the Canadian Mathematical Society in 1945. The Executive of the CMS decided on Toronto as the host city, and York University eagerly accepted the invitation to be the main competition site. At least seventy five countries are expected to accept invitations to participate. About 900 people, students, leaders, observers and local organisers, are expected to be present in Canada for about two weeks in July 1995.
The regulations of the IMO require that the host country absorb all of the costs for the official participants from the official arrival day to the official departure day. Based on the actual costs of the IMO in Canberra, Australia in 1989, and on the very thorough estimates provided by York University, we have projected a budget of $1.5 million. There is also the need for a large number of workers, particularly in the Toronto area. We welcome help from the mathematical community, especially those with organisational skills, language skills, etc. What will make this work and be a truly great Canadian event, will be the dedication and assistance of the whole Canadian mathematical community. If you wish to be part of the team, please get in touch with us.