Organisation of the International Mathematical Olympiad
Abstract
The International Mathematical Olympiad (IMO) is the largest, oldest and the most prestigious scientific Olympiad in the world. Its standard can only be maintained by a well concerted international collaborative effort. Nevertheless each year it is organized in a different country and each venue lends to the IMO a different cultural flavour. The local organization must be clearly intertwined with the core international collaboration processes that happen at each IMO and the need to maintain the traditions and standards imposes on the organizers certain academic and procedural requirements.
Introduction
Every year in around 100 countries students are offered the chance to participate in a selection process for participation in the IMO. Millions of students from around the world are included in this process – many of whom participate in their country’s National Mathematical Olympiad – out of which some 600 are selected to participate in the IMO. When the two accompanying leaders and a number of official observers are included, over 800 people make international journeys to be involved in each IMO.
There are larger competitions around the world, most of them handled via correspondence, but this is the largest scientific Olympiad, and its prestige is very carefully maintained by a group of mathematicians from all over the world who constitute the International Jury of the IMO. In effect, the two accompanying persons of each delegation are generally part of the team’s training program and their commitment to the IMO is such that they help assemble and run the IMO at all the different venues throughout the world.
A scientific Olympiad does not handle the number of people (or receive the publicity!) of the sporting Olympics, and its budget is miniscule in comparison, but it is still a complex event. The host nation needs to organise lodging and board, recreational activities and competition venues and materials for around one thousand participants and organizers and this entails an amount of money not easily attained for the hosting institution. Some of the funding for the IMO comes from local organizations and government in recognition of the positive impact the IMO and Mathematical Olympiads in general have on the country. More recently, due to rising participation in the IMO, efforts have been made to ask for worldwide donations such as the one given by Google Inc. for 5 years starting in 2011 in the Netherlands, resulting in the creation of the IMO Foundation. Local monies are also needed for the travel expenses of each delegation, meaning that about one third of the cost of an IMO is assumed by the participating countries.
The prestige of the IMO is unquestioned and widely recognized. Many universities worldwide seek out IMO participants for their maths programs. This prestige is carefully maintained by the internal process of the IMO: the confidential compilation and selection of challenging original problems, the transparent and careful implementation of the exam, the meticulous and homogeneous grading of each paper to uphold the worth of each medal granted and the consistent handling of information. These processes are outlined in more detail below.
Participation in the IMO
One of the advantages of the change of venue of the IMO throughout its history has been the increased participation of countries in the region of the host or organizing country.
General requirements of an IMO
Each IMO has a well-established programme. The International Jury arrives first to choose the exam. Then the contestants arrive and an inauguration ceremony officially marks the beginning of the Olympiad. After that the two important days of exams occur followed by days of grading before the awards ceremony. Then all delegations leave. Throughout, there are well-defined moments apart from the ceremonies when the organizers can offer the visitors a glimpse of their country.
Generally the IMO lasts 10 days and its activities are so tightly scheduled that most if not all of the logistical planning is done ahead. All the materials that aid its implementation are provided by the organizers. Everything from the registration process to the printing of name tags is handled by the IMO system (see below) and each year new applications are developed that can further help with the standard preparations for the IMO. Besides this, a lot of work is done in design of the logos and materials and communication of the event to enhance its impact and to help fund it.
At the same time as logistical preparations are being made such as choice of venues, materials, guides, transportation, tourism and entertainment, other more academic issues are being taken care of like the invitation of the coordination group and the problem selection committee and the compilation of the short list of problems for the IMO.
The funding model used to support each IMO varies from event to event. Countries have diverse social and political arrangements, but somehow the money must be found to fund the competition. This may come from government, commercial enterprises, charities, donations or mathematics enrichment organizations.
IMO website and applications
The IMO website (imo-official.org) was first put into production in Slovenia where it was developed for support of IMO 2006 by a Slovenian math olympiad delegate Matjaž Željko who still manages and expands it voluntarily. The necessity of such a site can only be underlined by the impeccable and extremely efficient organization of IMO 2006.
Technology today can help organize any event, but the IMO is a contest that has some very well-defined procedures uprooted and transplanted each year from venue to venue, so automating many of the scheduling procedures (such as registration, arrivals and departures, coordination times) and the printing of information (such as name tags, exam papers in all the languages coordinated according to seating arrangements, questions and answer sheets) makes sense.
Perhaps one of the most important historical characteristics of the IMO website is the database of results. Still being supplied for the early years, it allows all the former IMO medallists to be displayed with their actual scores and other important statistics. In this sense it is primarily an information site.
Compiling and selecting the IMO problems
The problems used at the IMO must be original, challenging, solvable with elementary mathematical arguments and in fact, use only elementary mathematics in their statement, in order to attempt to measure the young participant’s problem-solving ability.
Over the years the problems at the IMO have grown harder and harder. It is unlikely nowadays for a participant to be able to solve most of them without some training. Creating an original problem in elementary mathematics that is challenging enough for the level of training of some of the participants has become a challenge in itself. Recognizing a problem as one used before in so many different National Mathematical Olympiads and all kinds of other competitions throughout the world is a knowledge and memory feat. Only people immersed in the Olympiad scene can have the means to keep up with this. In fact, one of the important tasks of the International Jury of the IMO, which is composed of one delegate from each country called the team Leader, is to propose and choose the problems for the IMO. In proposing they or the members of their country’s Olympiad are supposed to have the expertise to create a challenging IMO-level problem. In choosing they collaborate in making sure the problem is acceptable, original and unknown.
Before the process of selection begins, an important task is to compile the short list of proposed problems for the IMO. These problems are submitted by the official members of each country that are in charge of the process of participation of their team in the IMO. Problems should be kept confidential to preserve the original aspect of the challenge posed to each IMO participant and therefore are submitted in a secure fashion. Ideally each country should submit problems each year but this is never the case. Fortunately, some of the IMO community are committed to creating problems or compiling problems to keep the IMO operational and its standards high. In fact, former Olympiad participants can sometimes reserve a special problem they find for the IMO. Of all these problems submitted a short list must be compiled. In order to make the selection process efficient, the short list must filter out submissions that are inadequate for the IMO be it because they are known or the arguments used to solve them are known and it is easily recognizable that they can be used, or because the level does not correspond to the level of the IMO.
One of the alternatives of reducing the group in charge of problem selection for the IMO is to form a very good committee to compile the short list. This committee, called the problem selection committee, must have ample knowledge of existing problems, standard mathematical arguments and in general, each member must be an outstanding problem-solver. This is why throughout the years certain former Olympiad participants have become experts at choosing a short list and are invited over and over again to the IMO as such. The first filter of the problems becomes very academic and professional. The second filter, that of the International Jury, further allows for problems used locally to be singled out and discarded.
The compilation of the short list is a long process. Many problems are submitted and of them a great number must be rejected. Those that are not must be solved and discussed and then ranked, formatted and printed by the problem selection committee. Since the problems are kept confidential because they are the core of the IMO, the committee is generally asked to meet for many weeks at the host country before the IMO. This meant that its members had to request the time from their jobs to travel to the host country to work on the problems. Generally they returned home before traveling again to attend the IMO. To make this process more efficient a secure forum was requested from the website developer, so at least the initial filter of the inadequate problems could be done at home. In 2013, to avoid the time and costs of multiple visits to the country the committee was invited to Colombia some weeks before the IMO to finish the discussion, formatting, ranking and printing of the short list. They were concentrated in the small town of Villa de Leyva, several hours by car from Bogota where they had intense working hours producing the short list, and the version with solutions, in time for confidential printing in Bogota. The short lists themselves were carried personally by the IMO organizers. It is no exaggeration to emphasize the importance of the short list for the IMO. There lies the quality of the IMO, the real challenge to its students and producing it in such a professional manner simplifies the work of the International Jury.
In recent years it has become evident that since the problem selection committee has more time to ponder the problems of the short list, their reflections on the adequacy and purpose of each problem are very helpful when the International Jury is selecting the problems for the IMO. Nevertheless, reflections from experienced leaders that have just tackled the problems are also important. Not only because they might recognize problems used locally, but because they give the selection process the expert opinion of what it entails to solve the problems under time constraints.
In general the IMO procedures see the importance of having observers from future host countries attend the IMO to gain experience and this is reflected in the general regulations which state that these observers are financially supported. This is limited to two observers from the following IMO and one from the one after.
Exam implementation
To preserve the prestige of the IMO, the implementation of its exams must ensure that no student is given any advantage over the others. This means that careful procedures of invigilation are put in effect to avoid cheating from others or from items taken to the exam. The sheer number of the participants makes the implementation a logistical challenge.
Contestants are first screened before they enter the exam site so that they do not bring more than the required tools. Invigilators help control entrance and attendance into rooms and then the actual seating. Each participant can request the exam in many languages so in order to be able to accommodate such a diversity of exam packages, fixed seating must be used. The IMO system is programmed to print out the exam papers in a specific seating order according to the language requests. For this the seating must be established beforehand together with coding of the rooms. This information is printed on the name tags given to each participant, directly from the IMO system. Logistical work like this is part of what organizers must do in advance to prepare for the IMO. At the IMO all of this helps the processes to run smoothly, especially for the student who is already nervous when taking the exam. Preparing each exam room with rows of seats containing each exam package takes at least half a day.
In the first 30 minutes of each of the four and a half hour exams, participants may ask for clarifying questions on problem formulation for any of the questions. These questions are written on a piece of paper and relayed to the jury (usually via the internet) and the jury will decide whether and how to respond to each.
In order to aid the correction process and to avoid cheating from those correcting the papers, all examination scripts and a lot of the scratch paper is photocopied or scanned at every IMO.
After scanning all the papers are taken from the scanning site to the purposely confidential International Jury site on the first day; the second day they are handed to the jury wherever they had moved for the remainder of the IMO.
Coordination and medals
The just and homogeneous correction or acknowledgement of each participant’s contribution to a solution of each problem is another part of the transparent organization of an IMO which contributes to the prestige of the medals awarded. For this a special correction procedure has been created called coordination.
In order to efficiently grade or award points to each participant’s solutions, the leaders and deputy leaders of each participating country first read each of their contestants’ papers and allot a number of points to them according to previously agreed upon criteria. This does not only offer the benefit of distributed work but also helps with the actual reading of the paper which is written in each contestant’s language.
A group of select mathematicians capable of distinguishing solutions to each problem of the IMO, or the equivalence between mathematical arguments that contribute towards a solution to these problems, form a group called the coordinators. Each coordinator is assigned a problem to work on and there are four different groups of coordinators for each of the six problems of the IMO.
Once the leaders of each country have assigned points to the solutions of each contestant, they must present each solution to a problem to a group of coordinators of the problem with the proposed points in order to agree on the number of points that must be awarded to the solution. The coordinators are the body of judges that ensure that all contestants are awarded the correct points for their work.
The coordination process is complex and requires a lot of logistical organization. Its existence relieves each country and everyone outside the IMO of any doubt that points may be awarded in a prejudiced or unjust fashion. In this way it preserves the prestige of the IMO and becomes necessary.
Coordinators have a lot of work like anyone else that attends an IMO. They must read the solutions or attempted solutions to one exam problem of all the contestants belonging to a fourth of the participating countries, that is, around 150 papers. They must assign points according to criteria which they have helped to make. And then they must meet with the leaders of their assigned countries to agree upon the official scores. Added to this are the procedures they must follow for when they cannot agree with a group of leaders. All of this in about two days!
To aid the coordination process the IMO system schedules the meetings and keeps a careful control of their implementation. Official results are also recorded there for further consideration and communication. Coordinators are given copies of the papers so they can work in parallel with the leaders.
Once the scores of each contestants papers have been agreed on the medals are awarded according to the total of points obtained by each contestant. Roughly half the contestants are awarded a medal. The proportion of Gold, Silver and Bronze medals awarded is 1:2:3. This means that at each IMO Gold medals are awarded to about 50 of the most talented contestants worldwide.
Mathematical exchange
One of the important functions of the IMO is to allow participants to exchange important ideas about themselves, their culture and their education. To a great extent the IMO helps countries share their ideas on competition but more importantly it helps to exchange ideas about mathematics education and practices and to a lesser extent mathematics itself.
This exchange is in fact one of the IMO’s goals and thereby is an important basis for allowing every country to assist in the IMO’s processes. Contestants get the very important opportunity of meeting people like themselves, with great talent in solving mathematical problems and in understanding mathematical arguments. Before attending the IMO they already have had a chance to meet their own country’s peers and turn the competition to be one of the team into patriotic camaraderie. But once at the IMO they have a chance to meet people like them from all over the world and measure up to international standards in a competition which ends up being against themselves. The friendships created at the IMO often last a lifetime and turn into professional collaboration. This is a unique chance to meet people like themselves that will in high probability contribute to the academic development of humankind. This contribution to the motivation of these talented students in the study of mathematics and other sciences is perhaps the greatest reason for the IMO to be organized at a venue, and not by correspondence.
After the exams students have some free time whilst the papers are being marked. This is an excellent opportunity get to know each other and to see a bit of the host country. It is also a great moment to provide motivation to pursue their interest in mathematics.