International Mathematical Olympiad
The International Mathematical Olympiad (IMO) is an annual contest for high school students. It is the oldest of the science olympiads.
The first IMO was held in Romania in 1959. Since then it has been held every year except 1980. About 80 countries send teams of (at most) 6 students each (plus one team leader, one deputy leader and observers). Teams are not officially recognized - all scores are given only to individual contestants. Constestants must be under the age of 20 and must not have any post-secondary school education. Subject to these conditions, an individual may participate any number of times in the IMO.
The paper consists of 6 problems, with each problem being worth 7 points. The total score is thus 42 points. The examination is held over two consecutive days; the contestants have 4.5 hours to solve 3 problems on each day. 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, and often admit of short and elegant solutions. Finding them, however, requires exceptional ingenuity and mathematical ability.
Each participating country other than the host country may submit suggested problems to a Problem Selection Committee provided by the host country, which reduces the submitted problems to a shortlist. The team leaders arrive at the IMO a few days in advance of the contestants and form the IMO Jury which is responsible for all the formal decisions relating to the contest, starting with selecting the 6 problems from that shortlist. As the leaders know the problems in advance of the contestants, they are kept strictly separated from the contestants until the second examination has finished; the contestants are accompanied to the IMO by their deputy leaders.
Each country's marks are agreed between that country's leader and deputy leader and Co-ordinators 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 ultimate decision of the Jury if any disputes cannot otherwise be resolved.
In the United States, all high school students may opt to take the American Mathematics Competition 10 or 12 (AMC). The highest possible score on this examination is 150. Those who score over 100 or in the top 5% of the AMC 12, or those who score in the top 1% in the AMC 10 are invited to take the American Invitational Mathematics Examination (AIME). This consists of 15 questions, each worth 10 points.
Unlike the AMC, which has five possible answers to each question, questions on the AIME are stuctured so that the answers will always be whole integers from 1-999. This makes obtaining points by guessing randomly much less likely, although it has sometimes been rumored that the number 17 appears as an answer with disproportionate frequency.
The total score a student achieves on the AIME is added to the total on the AHSME. Those who score over 200 (?) points collectively then take the USAMO. The top six scorers on the USAMO then represent the United States at the IMO.
The participants are ranked based on their individual scores.
- Gold medals will be awarded to the top 1/12 of the contestants.
- Silver medals will be awarded to the next 2/12.
- Bronze medals will be awarded to the next 3/12.
- Participants who don't win a medal but who score 7 points on at least one problem will get 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 and 1988, but was more frequent up to the early 1980s.
Current and Future IMOs
- The 46th IMO will be held in Mérida, Mexico in 2005. 
- The 47th IMO will be held in Slovenia in 2006.
- The 48th IMO will be held in Viet Nam in 2007.
- The 49th IMO will be held in Spain in 2008.
- The 50th IMO will be held in Bremen, Germany in 2009.
Sources differ about the cities hosting some of the early IMOs. This may be partly because leaders are generally housed well away from the students, and partly because after the competition the students did not always stay based in one city 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.
- The 1st IMO was held in Brasov and Bucharest, Romania in 1959.
- The 2nd IMO was held in Sinaia, Romania in 1960.
- The 3rd IMO was held in Veszprem, Hungary in 1961.
- The 4th IMO was held in Ceske Budejovice, Czechoslovakia in 1962.
- The 5th IMO was held in Warsaw and Wroclaw, Poland in 1963.
- The 6th IMO was held in Moscow, USSR in 1964.
- The 7th IMO was held in Berlin, German Democratic Republic in 1965.
- The 8th IMO was held in Sofia, Bulgaria in 1966.
- The 9th IMO was held in Cetinje, Yugoslavia in 1967.
- The 10th IMO was held in Moscow, USSR in 1968.
- The 11th IMO was held in Bucharest, Romania in 1969.
- The 12th IMO was held in Keszthely , Hungary in 1970.
- The 13th IMO was held in Zilina, Czechoslovakia in 1971.
- The 14th IMO was held in Torun, Poland in 1972.
- The 15th IMO was held in Moscow, USSR in 1973.
- The 16th IMO was held in Erfurt and East Berlin, German Democratic Republic in 1974.
- The 17th IMO was held in Burgas and Sofia, Bulgaria in 1975.
- The 18th IMO was held in Linz, Austria in 1976.
- The 19th IMO was held in Belgrade, Yugoslavia in 1977.
- The 20th IMO was held in Bucharest, Romania in 1978.
- The 21st IMO was held in London, United Kingdom in 1979.
- The 22nd IMO was held in Washington, DC, United States in 1981.
- The 23rd IMO was held in Budapest, Hungary in 1982.
- The 24th IMO was held in Paris, France in 1983.
- The 25th IMO was held in Prague, Czechoslovakia in 1984.
- The 26th IMO was held in Joutsa, Finland in 1985.
- The 27th IMO was held in Warsaw, Poland in 1986.
- The 28th IMO was held in Havana, Cuba in 1987.
- The 29th IMO was held in Canberra, Australia in 1988.
- The 30th IMO was held in Brunswick, Federal Republic of Germany in 1989.
- The 31st IMO was held in Beijing, China in 1990.
- The 32nd IMO was held in Sigtuna, Sweden on 12-23 July, 1991.
- The 33rd IMO was held in Moscow, Russia on 10-21 July, 1992.
- The 34th IMO was held in Istanbul, Turkey on 13-24 July, 1993.
- The 35th IMO was held in Hong Kong on 8-20 July, 1994.
- The 36th IMO was held in Toronto, Canada on 13-25 July, 1995. 
- The 37th IMO was held in Mumbai, India on 5-17 July, 1996. 
- The 38th IMO was held in Mar del Plata, Argentina on 18-31 July, 1997. 
- The 39th IMO was held in Taipei, Taiwan on 10-21 July, 1998. 
- The 40th IMO was held in Bucharest, Romania on 10-22 July, 1999. 
- The 41st IMO was held in Taejon, South Korea on 13-25 July, 2000. 
- The 42nd IMO was held in Washington, DC, United States on 1-14 July, 2001. 
- The 43rd IMO was held in Glasgow, United Kingdom on 19-30 July, 2002.
- The 44th IMO was held in Tokyo, Japan on 7-19 July, 2003. 
- The 45th IMO was held in Athens, Greece on 6-18 July, 2004. 
- Central IMO web site
- IMO problems and solutions
- IMO scores
- IMO winners Hall of Fame - IMO winners who have won Fields Medal or Nevanlinna Prize
- IMO contestants who have won 3 or more gold medals