Russian Mathematical Surveys, 2025, Volume 80, Issue 1, Pages 177–182 DOI: https://doi.org/10.4213/rm10230e (Mi rm10230)

DOI: https://doi.org/10.4213/rm10230e

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International Mathematical Olympiads (IMO) for high school students have been held annually since 1959. The first was organized in Romania, on an initiative of the Romanian mathematical and physical society and the Ministry of Education of Romania. Initially, olympiads involved only European countries from the ‘Soviet block’ schoolchildren from Bulgaria, Czechoslovakia, East Germany, Hungary, Poland, Romania, and the Soviet Union took part in the first olympiad. Beginning with the 5th Olympiad (Poland, 1963), Yugoslavia and, beginning with the 6th (Moscow, 1964), Mongolia also participated. The 7th Olympiad (East Germany, 1965) involved Finland, and the 9th (Yugoslavia, 1967) was the first at which teams from the ‘Western block’, Great Britain, England, France, and Sweden, also took part. Participation in olympiads has extended since then: students from more than 100 countries take part every year, although some national teams are incomplete and poorly prepared. The information about all olympiads can be found at the official WWW-portal of IMO.^1[x]1https://www.imo-official.org/

Each olympiad is held on two consecutive days: every day the participants receive three problems to be solved in 4.5 hours. The solution of each problem is rated on the basis of seven points, so that the maximum score of a participant can be 42. Problems are selected in two steps: at the first step each country can propose up to six problems, and at the second the Problem Selection Committee selects a short list from all these problem, the list of the best problems, grouped into four classic topics: algebra, combinatorics, geometry, and number theory. Problems in the short list are arranged in the ascending order of their complexity. A few days before the opening of an olympiad the leaders of all national teams (perhaps with their assistants; see below on the composition of a team) arrive at the host country and vote for problems in the short list. Usually, in the final list of problems ‘simpler’ ones (the first two problems for each day, that is, the first, second, fourth, and fifth problems) are related to different areas. This procedure for selecting problems has long been established and was violated only in 2020 and 2021, because of the pandemic, when the final list of problems was compiled by the Problem Selection Committee in association with a select group of team leaders.

The Problem Selection Committee is formed by the host country for a particular olympiad. It is a great honour to be in it and an even greater one to be its guest member (not representing the host nation). From 2007 to 2022 Il’ya Bogdanov from Russia was a guest member of the Problem Committee. He was at the head of the Committee in 2020 and 2021, when the olympiad (in the online/offline mode) was held in St Petersburg.

The host country is selected from the list of applications, 3–5 years prior to the olympiad in question, by a vote of team leaders.

An International Mathematical Olympiad is an individual contest, and the results of each participant are shown on the IMO web-portal, but there is also an unofficial team standing. Before 1979 each team included eight students, and after that six. Each team is accompanied by a Leader, their assistant (Observer A), a Deputy Leader and their assistant (Observer B), and an assistant for participants with special needs (Observer C). In principle, the number of assistants can be greater. Till the end of the second round of the contest leaders and their assistants are accommodated apart from the participants, since they were involved in the selection of problems. During the contest students are accompanied by deputy leaders with assistants. After the second round national teams normally reunite.

Students solve problems in their native languages. Their scorings are determined by way of the coordination procedure, a dialogue between the jury and the leaders and deputy leaders of teams and their assistants. Coordinators have specially been selected by the host country from leading experts in mathematics and pedagogues, participants of former olympiads. A ‘marking scheme’ is created for each problem, indicating the points due for each significant part of the solution of the problem. These schemes must have been developed in advance by the coordinators and approved by the grand jury (including the team leaders) before the students attack the problems,— so the coordinators must foresee all possible ways of their solution.

At the first International Olympiad of 1959 the team from the Soviet Union was incomplete and not quite successful, after which it missed the next two years. Since the fourth olympiad our team has been a permanent participant. The history of the first international olympiads was described in the book^2[x]2The fourth revised and augmented edition, Prosveshchenie, Moscow, 1976, 288 pp. (in Russian). International Mathematical Olympiads: problems, solutions, results by E. A. Morozova, I. S. Petrakov, and V. A. Skvortsov, whose authors were leaders of the Soviet team at the first olympiads. (One of the authors, Elena Aleksandrovna Morozova, was an important figure on the Faculty of Mechanics and Mathematics at Moscow State University: she was an assistant of P. S. Alexandroff and A. N. Kolmogorov, lived a long life, and taught exercises in analytic geometry to many students.) Apart from them, in different tears the Sovied tema was lead by V. V. Vavilov, A. P. Savin, and A. A. Fomin. In 1992, as a consequence of transformations in our country, two teams, from Russia and the Council of Independent States, participated in the olympiad held in Moscow. (This had its benefits: Pavel Kozhevnikov, a member of the second team who won a gold medal, is currently one of the leading coaches of our team.) In the period from 1992 to 2017 the Russian team was led by N. L. Agakhanov, and since the fall of 2017, K. A. Sukhov is the head coach.

Up to 1992 the USSR team was formed of winners of the final round of the All-Union Olympiad of schoolchildren (see the book mentioned above), taking account also of their results at previous olympiads. The team consisted mainly of students in the last (that is, 10th, at that time) grade, but occasionally students in the 9th grade that were very successful at the All-Union Olympiad were also included (the first Soviet schoolboy who participated twice at International Mathematical Olympiads was the Saratov student S. V. Konyagin, who won gold medals in 1972 and 1973). In the inofficial team standing the Soviet team was mostly among the top three: it was the first 14 times, the second seven times, the third three times, the fourth twice, the sixth twice (including at the first olympiad); however, it was only ninth in 1981.

In the period from 1992 to 2017 the Russian team was formed of winners of the last round of the All-Russian Olympiad of schoolchildren. Training camps were organized twice a year, the main camp was in winter (four rounds of contest in six days) and an accessory one in summer (four rounds of contest in 21 days). The final decision on the inclusion in the team was made by the coach staff at the end of the All-Russian Olympiad, on the basis of the results in camps, at All-Russian Olympiads, and at intermediate contests. The standing of the Russian team was as follows: the first place twice (in 1999 and 2007), the second place six times (in 2000–2002, 2006, 2008, and 2010), the third four times (in 1994, 1995, 2004, and 2005). The least successful performance was in 2017, when the team dropped out of the top ten and was only the 11th. In that period of time a large part of the work on the preparation of the national team was performed by the head of the Methodological Commission on Mathematics of the All-Russian Olympiad of schoolchildren Nazar Khangel’dyevich Agakhanov.

Since 2017/2018, the selection to the team has been based on formal criteria. Each training season begins and ends with a summer camp in June–July (since 2023, a season begins, in fact, in May).

As a novation, a student in any grade who is a winner or a ‘top ranker’ of the final round (organized in April for students in the 9th–11th grades) of the All-Russian Olympiad of schoolchildren can get to the camp. Prior to 2023 a ‘top ranker’ could only occur there on a recommendation (the current procedure is described below). The summer camp lasts 21 days and accomodates 40 students, including six members of the national team. For students not in the team the camp includes four rounds of contests and 30 thematic seminars. In the evening students and teachers play volleyball and soccer, listen occasionally to popular science lectures, and one day is reserved for a sight-seeing tour.

Depending on the results of the summer camp, 25–30 students are selected for the fall camp (at the end of October) and also participate in the winter camp (in mid-January). The fall and winter camps are similar: eight days each, when students go through 2 rounds of contests and ten 4-hour lessons. All lessons in seasonal camps are taught in two groups, A for experienced students, and B for newcomers. However, the qualifying competitions are common for all. After the fall and winter camps 12–17 candidates for the national team are selected, who then take part in further competitions.

The next step is the contest Romanian Master of Mathematics, held in Bucharest at the end of February–the beginning of March. A four-person Russian team goes to Romania, while the other candidates participate online, from Sochi. After the contest all candidates meet in the Educational Centre “Sirius”, where in six days they have ten lessons of four hours each.

In April al candidates, independently of their grades, take part in the final round of the All-Russian Olympiad for 11th graders, and in the middle of May they have to go through the final test, the May camp with just two rounds of a qualifying competition.

The sum of the points obtained at five two-round contests makes up the total score of a participant: the contests in the fall and winter camps, Romanian contest, the final part of the All-Russian Olympiad, and the May contest. In accordance with the ratings achieved, six members of the Russian team for the International Olympiad of high-school students are selected. For borderline cases a detailed formalized algorithm for selecting a team has been composed. Currently, in borderline cases we add (at least 18) bonus points to students who are able to complete the assignments of an olympiad round for a higher score (of at least 15 points out of 21).

In the summer camp coaches work separately with the students selected for the team: for them this camp is a kick-off meeting, and the team moves to the olympiad venue without returning home.

We conclude this brief description of a selection season by pointing out that, in comparison to the scheme that existed before 2017, apart from greater numbers of selection events and students involved, the number of training sessions has also increased greatly, owing to the lessons taught in camps and to online lessons, with lists of problems sent to the candidated during the year.

The training camps, including contests and lessons, are managed by the coach staff and guest instructors. The list of regular participants includes S. L. Berlov, I. I. Bogdanov, N. Yu. Vlasova, P. A. Kozhevnikov, P. Yu. Kozlov, A. S. Kuznetsov, A. Yu. Kushnir, and F. V. Petrov. Camps are organized by the Ministry of Education of the Russian Federation, and many of them are held on the basis of the Herzen Pedagogical University, which, in particular, was the organizer of the International Olympiad of 2020–2021 itself. Intermediate camps are usually held in the Educational Centre “Sirius”.

Now we describe in greater detail the international contests in which our team participates.

The contest Romanian Master of Mathematics has been organized since 2008 for teams from countries with the highest standing according to the result of the last IMO. Four students from each country are members of the main team, and in the team competition the top three scores are added. The best team is awarded the passing prize, which is a plate. Five times this plate went to the USA (in 2011, 2013, 2016, 2018, and 2019), four times to Russia (in 2010, 2015, 2020, and 2021), three times to China (in 2009, 2012, and 2014), once to Great Britain (in 2008), once to Korea (in 2017), and in 2012 it stayed in Romania. Since 2020 this plate stays in Russia: there was no contest in 2022, and in 2023 the organizers acquired a new plate.

Our team participates (except in the pandemic years of 2020–2022) at the Chinese Mathematical Olympiad. In response, the Chinese team often participates at the final round of the All-Russian Olympiad. This participation is out of classification.

Another event at which Russian team was involved from 2016 to 2024 was the European Girls Mathematical Olympiad, organized since 2012. As a team, we participated at this Olympiad in 2016–2018 and 2020–2021, while in the events of 2022–2024 out girls took part as individual participants. The team is selected by the coach staff. In 2021 our team scored in total 167 points out of 168 (four participants with six problems worth seven points each), while in 2023 all our participants got the full score. In fact, not so many girls participate at IMO, but in 2022 our team there included two girls; moreover, one of these, Galiya Sharafetdinova, got the full score, which was a rare case for the Russian team: the previous case of a participant with full score was in 2006. Unfortunately, the EGMO has now become very politicized, and the coach staff has decided that the Russian team will not participate at it any further.

The system of selection for the Russian team for International Mathematical Olympiads is constantly being improved. For example, it became clear by 2023 that selection for summer camps needs to be improved: not all winners of the final round of the All-Russian Olympiad want and are ready to learn heavily; on the other hand many guys who scored slightly worse are ready to learn, although a number of these do not have a long history of participation at contests. Thus, we have decided to expand the scope of the May camp. Now the 80 top rankers in the 9th and 10th grades are invited, who participate in a qualifying contest. Taking account of their results and the final round of the All-Russian Olympiad, we select participants of the summer camp.

It is a rare case that a participant is selected to the team in his first season, most students in the team made a second attempt. The coach staff strives to provide favourable conditions for students from distant regions so that they could learn without moving to Moscow or St Petersburg.

Since 2018 the team has included hight school students from Kirov, Novosibirsk, Chelyabinsk, and Krasnodar regions, Tatarstan, Udmurtia, Moscow, and St Petersburg. In 2024 the team consisted of students from St Petersburg (four persons), and also Moscow and Novosibirsk regions (one student from each).

In the cycle of 2024/2025 the summer camp, opening the season, welcomed eight students from St Petersburg, five from Moscow, five from Chelyabinsk region, three from Tatarstan, two students from Mordovia and each of Kurgan, Moscow, and Novosibirsk regions, and also students from Stavropol’, Primorsky, Kirov, Nizhny Novgorod, Pskov, Sverdlovsk, Tomsk, and Yaroslavl’ regions. Candidates for the national team, as of January 2025, are students from St Petersburg (two students), Moscow (two), Chelyabinsk region (two), and also ones from Kirov, Kurgan, Moscow, Tomsk, Yaroslavl’, and Primorsky regions.

In conclusion, we note that participation at olympiads and doing mathematics are certainly related, but not directly. Moreover, both talents to mathematics and contest skills can manifest themselves in different ages: it is not reasonable to train children for winning mathematical contests and, in particular, for participation at international olympiads from an early age. As an illustration, for members of our teams at the International Mathematical Olympiads of the last five years we collect in a single table their standings at the most representative mass contest, the Leonhard Euler Olympiad, in the period when they were in the 7th and 8th grades. These results are arranged in the decreasing order of the scores of the participants at international olympiads.

We wish our students great successes at olympiads and, more importantly, successes in life, on the ways they choose themselves!

Citation in format AMSBIB

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\by K.~A.~Sukhov
\paper Preparing the Russian team to the International Mathematical Olympiad for high school students
\jour Russian Math. Surveys
\yr 2025
\vol 80
\issue 1
\pages 177--182
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