International Mathematical Olympiad

The competition consists of six problems. The competition is held over two consecutive days with three problems each; each day, the contestants have four-and-a-half hours to solve three problems. Each problem is worth 7 points for a maximum total score of 42 points. Calculators are banned. Protractors were banned relatively recently. Each country's marks are agreed between that country's leader and deputy leader, and coordinators provided by the host country (the leader of the team whose country submitted the problem in the case of the marks of the host country), subject to the decisions of the chief coordinator and, ultimately, a jury if any disputes cannot be resolved. Question type Unlike other science olympiads, the IMO has no official syllabus and does not cover any university-level topics. The problems chosen are from various areas of secondary school mathematics, broadly classifiable as geometry, number theory, algebra, and combinatorics. They require no knowledge of higher mathematics such as calculus and analysis, and solutions are often elementary. However, they are usually disguised so as to make the solutions difficult. The problems given in the IMO are largely designed to require creativity and the ability to solve problems quickly. Thus, the prominently featured problems are algebraic inequalities, complex numbers, and construction-oriented geometrical problems, though in recent years, the latter has not been as popular as before because of the algorithmic use of theorems like Muirhead's inequality, and complex/analytic bashing to solve problems. ==Team selection==

The selection process differs by country, but it often consists of a series of tests that admit fewer students at each test. Contestants must be under the age of 20 and must not be registered at any tertiary institution. Subject to these conditions, an individual may participate any number of times in the IMO. , part of the United States' selection process In some countries, especially those in East Asia, the selection process involves several tests of a difficulty comparable to the IMO itself. The Chinese contestants go through a camp. In others, such as the United States, possible participants go through a series of easier standalone competitions that gradually increase in difficulty. In the United States, the tests include the American Mathematics Competitions, the American Invitational Mathematics Examination, and the United States of America Junior Mathematical Olympiad/United States of America Mathematical Olympiad, each of which is a competition in its own right. For high scorers in the final competition for the team selection, there also is a summer camp, like that of China. In countries of the former Soviet Union and other eastern European countries, a team has in the past been chosen several years beforehand, and they are given special training specifically for the event. However, such methods have been discontinued in some countries. ==Awards==

The participants are ranked based on their individual scores. Medals are awarded to the highest ranked participants; slightly fewer than half of them receive a medal. The cutoffs (minimum scores required to receive a gold, silver, or bronze medal respectively) are then chosen so that the numbers of gold, silver and bronze medals awarded are approximately in the ratios 1:2:3. Participants who do not win a medal but who score 7 points on at least one problem receive an honorable mention. Special prizes may be awarded for solutions of outstanding elegance or involving good generalisations of a problem. This last happened in 1995 (Nikolay Nikolov, Bulgaria) and 2005 (Iurie Boreico), but was more frequent up to the early 1980s. The special prize in 2005 was awarded to Iurie Boreico, a student from Moldova, for his solution to Problem 3, a three-variable inequality. The rule that at most half the contestants win a medal is sometimes broken if it would cause the total number of medals to deviate too much from half the number of contestants. This last happened in 2010 (when the choice was to give either 226 (43.71%) or 266 (51.45%) of the 517 contestants (excluding the 6 from North Korea — see below) a medal), 2012 (when the choice was to give either 226 (41.24%) or 277 (50.55%) of the 548 contestants a medal), and 2013, when the choice was to give either 249 (47.16%) or 278 (52.65%) of the 528 contestants a medal. In these cases, slightly more than half the contestants were awarded a medal. ==History==

The first IMO was held in Romania in 1959. Since then it has been held every year (except in 1980, when it was cancelled due to internal strife in Mongolia). It was initially founded for eastern European member countries of the Warsaw Pact, under the USSR bloc of influence, but later other countries participated as well. Sources differ about the cities hosting some of the early IMOs. This may be partly because leaders and students are generally housed at different locations, and partly because after the competition the students were sometimes based in multiple cities for the rest of the IMO. The exact dates cited may also differ, because of leaders arriving before the students, and at more recent IMOs the IMO Advisory Board arriving before the leaders. Several students, such as Lisa Sauermann, Peter Scholze, Reid W. Barton, Nicușor Dan (notably elected President of Romania in 2025) and Ciprian Manolescu have performed exceptionally well in the IMO, winning multiple gold medals. Others, such as Terence Tao, Artur Avila, Grigori Perelman, Ngô Bảo Châu, Peter Scholze and Maryam Mirzakhani have gone on to become notable mathematicians. Several former participants have won awards such as the Fields Medal. Shortly after the 2016 International Mathematical Olympiad in Hong Kong, North Korean child prodigy Ri Jong-yol made his way to the South Korean consulate general, where he sought refuge for two months. Chinese authorities eventually allowed him to leave Hong Kong on a flight to Seoul. The 61st IMO, scheduled to be held in St. Petersburg, Russia in 2020, was instead held virtually because of the COVID-19 pandemic, the first time this had occurred. The 62nd IMO in 2021 was also held virtually. At the 2025 IMO, both OpenAI and Google DeepMind claimed that their systems could have achieved a gold-medal level performance in the competition. However, mathematicians including Terence Tao and Kevin Buzzard cautioned that these claims were not based on reproducible experimental conditions and reflected neither a fair comparison to the human competitors nor the sort of performance that would be needed for research-level mathematics. Penalties and bans North Korea is the only country to ever be disqualified for cheating, once at the 32nd IMO in 1991 and again at the 51st IMO in 2010. However, the incident in 2010 was controversial. There have been other cases of cheating where contestants received penalties, although these cases were not officially disclosed. (For instance, at the 34th IMO in 1993, a contestant was disqualified for bringing a pocket book of formulas, and two contestants were awarded zero points on second day's paper for bringing calculators.) Russia has been banned from participating in the Olympiad since 2022 as a response to its invasion of Ukraine. Nonetheless, a limited number of students (specifically, 6) are allowed to take part in the competition and receive awards, but only remotely and with their results being excluded from the unofficial team ranking. Slightly more than a half of the IMO 2021 Jury members (59 out of 107) voted in support of the sanction proposed by the IMO Board in an online voting in March 2022. National achievements The following nations have achieved the highest team score in the respective competition: • China, 25 times: in 1989, 1990, 1992, 1993, 1995, 1997, 1999 (joint), 2000–2002, 2004–2006, 2008–2011, 2013, 2014, 2019 (joint), 2020–2023, 2025; • Russia (including Soviet Union), 16 times: in 1963–1967, 1972–1974, 1976, 1979, 1984, 1986 (joint), 1988, 1991, 1999 (joint), 2007; • United States, 9 times: in 1977, 1981, 1986 (joint), 1994, 2015, 2016, 2018, 2019 (joint), 2024; • Romania, 5 times: in 1959, 1978, 1985, 1987, 1996; • West Germany, twice: in 1982 and 1983; • South Korea, twice: in 2012 and 2017; • Iran, once: in 1998; • East Germany, once: in 1968. The following nations have achieved an all-members-gold IMO with a full team: • China, 16 times: in 1992, 1993, 1997, 2000–2002, 2004, 2006, 2009–2011, 2019, 2021–2023, 2025. • South Korea, 3 times: in 2012, 2017, and 2019. • Russia, twice: in 2002 and 2008. • Bulgaria, once: in 2003. The only countries to have their entire team score perfectly in the IMO were the United States in 1994, China in 2022, and Luxembourg, whose 1-member team had a perfect score in 1981. The US's success earned a mention in TIME Magazine. Hungary won IMO 1975 in an unorthodox way when none of the eight team members received a gold medal (five silver, three bronze). Individual achievements at the 2015 IMO Several individuals have consistently scored highly and/or earned medals on the IMO: Zhuo Qun Song (Canada) is the most highly decorated participant with five gold medals (including one perfect score in 2015) and one bronze medal. Reid Barton (United States) was the first participant to win a gold medal four times (1998–2001). Barton is also one of only eight four-time Putnam Fellows (2001–04). Christian Reiher (Germany), Lisa Sauermann (Germany), (Serbia), Nipun Pitimanaaree (Thailand) and Luke Robitaille (United States) are the only other participants to have won four gold medals (2000–03, 2008–11, 2009–12, 2010–13, 2011–14, and 2019–22 respectively); Reiher also received a bronze medal (1999), Sauermann a silver medal (2007), von Burg a silver medal (2008) and a bronze medal (2007), and Pitimanaaree a silver medal (2009). Wolfgang Burmeister (East Germany), Martin Härterich (West Germany), Iurie Boreico (Moldova), and Lim Jeck (Singapore) are the only other participants besides Reiher, Sauermann, von Burg, and Pitimanaaree to win five medals with at least three of them gold. Ciprian Manolescu (Romania) managed to write a perfect paper (42 points) for gold medal more times than anybody else in the history of the competition, doing it all three times he participated in the IMO (1995, 1996, 1997). Manolescu is also a three-time Putnam Fellow (1997, 1998, 2000). Eugenia Malinnikova (Soviet Union) is the highest-scoring female contestant in IMO history. She has 3 gold medals in IMO 1989 (41 points), IMO 1990 (42) and IMO 1991 (42), missing only 1 point in 1989 to precede Manolescu's achievement. Terence Tao (Australia) participated in IMO 1986, 1987 and 1988, winning bronze, silver and gold medals respectively. He won a gold medal when he just turned thirteen in IMO 1988, becoming the youngest person to receive a gold medal (Zhuo Qun Song of Canada also won a gold medal at age 13, in 2011, though he was older than Tao). Tao also holds the distinction of being the youngest medalist with his 1986 bronze medal, followed by 2009 bronze medalist Raúl Chávez Sarmiento (Peru), at the age of 10 and 11 respectively. Gender gap and the launch of European Girls' Mathematical Olympiad Over the years, since its inception to present, the IMO has attracted far more male contestants than female contestants. During the period 2000–2021, there were only 1,102 female contestants (9.2%) out of a total of 11,950 contestants. The gap is even more significant in terms of IMO gold medallists; from 1959 to 2021, there were 43 female (3.3%) and 1295 male gold medal winners. This gender gap in participation and in performance at the IMO level led to the establishment of the European Girls' Mathematical Olympiad (EGMO). ==Media coverage==

• A documentary, "Hard Problems: The Road To The World's Toughest Math Contest" was made about the United States 2006 IMO team. • A BBC documentary titled Beautiful Young Minds aired July 2007 about the performance of British prodigy Daniel Lightwing taking part in the IMO and struggling with Asperger's syndrome. It inspired the BBC film X+Y (2014), a fictionalized version of Lightwing's story. • A book named Countdown by Steve Olson tells the story of the United States team's success in the 2001 Olympiad. ==See also==