International Mathematical Olympiad

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The International Mathematical Olympiad (IMO) is an annual mathematical olympiad for high school students. It is the oldest of the international science olympiads.

The first IMO was held in Romania in 1959. Since then it has been held every year except 1980. About 90 countries send teams of (at most) six students each (plus one team leader, one deputy leader and observers). Teams are not officially recognized - all scores are given only to individual contestants. Contestants 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 six problems, with each problem being worth seven points. The total score is thus 42 points. The examination is held over two consecutive days; the contestants have four-and-a-half hours to solve three 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 solutions are often short and elegant. 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 six problems from the 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 (and maybe observers as well).

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 decisions of the Chief Coordinator and ultimately the Jury if any disputes cannot be resolved.

Contents

[edit] Selection process

Main article: IMO selection process.

[edit] Awards

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 seven points on at least one problem get an honorable mention.

Not more than half of the participants will receive medals.

Special prizes may be awarded for solutions of outstanding elegance or involving good generalisations of a problem. This last happened in 2005, 1995 and 1988, but was more frequent up to the early 1980s.

[edit] Current and future IMOs

[edit] Past IMOs

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 1 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.

№ Venue Date Web
1 Braşov and Bucharest, Romania 23-31 July, 1959
2 Sinaia, Romania 18-25 July, 1960
3 Veszprém, Hungary 6-16 July, 1961
4 Ceske Budejovice, Czechoslovakia 7-15 July, 1962
5 Warsaw and Wrocław, Poland 5-13 July, 1963
6 Moscow, Soviet Union 30 June-10 July, 1964
7 Berlin, GDR 3-13 July, 1965
8 Sofia, Bulgaria 3-13 July, 1966
9 Cetinje, Yugoslavia 2-13 July, 1967
10 Moscow, USSR 5-18 July, 1968
11 Bucharest, Romania 5-20 July, 1969
12 Keszthely, Hungary 8-22 July, 1970
13 Zilina, Czechoslovakia 10-21 July, 1971
14 Toruń, Poland 5-17 July, 1972
15 Moscow, Soviet Union 5-16 July, 1973
16 Erfurt and East Berlin, GDR 4-17 July, 1974
17 Burgas and Sofia, Bulgaria 1975
18 Lienz, Austria 1976
19 Belgrade, Yugoslavia 1-13 July, 1977
20 Bucharest, Romania 1978
21 London, United Kingdom 1979
22 Washington, DC, United States 8-20 July, 1981
23 Budapest, Hungary 5-14 July, 1982
24 Paris, France 1-12 July, 1983
25 Prague, Czechoslovakia 29 June-10 July, 1984
26 Joutsa, Finland 29 June-11 July, 1985
27 Warsaw, Poland 4-15 July, 1986
28 Havana, Cuba 5-16 July, 1987
29 Sydney and Canberra, Australia 9-21 July, 1988
30 Brunswick, FRG 13-24 July, 1989
31 Beijing, PRC 8-19 July, 1990
32 Sigtuna, Sweden 12-23 July, 1991
33 Moscow, Russia 10-21 July, 1992
34 Istanbul, Turkey 13-24 July, 1993
35 Hong Kong 8-20 July, 1994
36 Toronto, Canada 13-25 July, 1995 [1]
37 Mumbai, India 5-17 July, 1996 [2]
38 Mar del Plata, Argentina 18-31 July, 1997 [3]
39 Taipei, Republic of China 10-21 July, 1998 [4]
40 Bucharest, Romania 10-22 July, 1999 [5]
41 Taejon, South Korea 13-25 July, 2000 [6]
42 Washington, DC, United States 1-14 July, 2001 [7]
43 Glasgow, United Kingdom 19-30 July, 2002
44 Tokyo, Japan 7-19 July, 2003 [8]
45 Athens, Greece 6-18 July, 2004 [9]
46 Mérida, Mexico 8-19 July, 2005 [10]
47 Ljubljana, Slovenia 6-18 July, 2006 [11]

[edit] Results for the 2006 IMO

Results by points for the 2006 IMO

  1. People's Republic of China (214)
  2. Russian Federation (174)
  3. Korea (170)
  4. Germany (157)
  5. United States of America (154)
  6. Romania (152)
  7. Japan (146)
  8. Iran (145)
  9. Moldova (140)
  10. Taiwan (136)
  11. Poland (133)
  12. Italy (132)
  13. Vietnam (131)
  14. Hong Kong (129)
  15. Thailand, Canada (123)

Results by Medals for the 2006 IMO

  1. People's Republic of China | (six gold)
  2. Korea | (four gold, two silver)
  3. Germany | (four gold, two bronze)
  4. Iran, Russia | (three gold, three silver)
  5. Romania| (three gold, one silver, two bronze)
  6. United States of America | (two gold, four silver)
  7. Japan | (two gold, three silver, one bronze)
  8. Italy | (two gold, two silver, one honourable mention)
  9. Moldova, Vietnam | (two gold, one silver, three bronze)
  10. Taiwan | (one gold, four silver, one bronze)
  11. Thailand, Hong Kong | (one gold, three silver, two bronze)
  12. Slovakia (one gold, two silver, three bronze)

[edit] Notable achievements

  • Ciprian Manolescu from Romania managed to write a perfect paper (42/42) three times (1995-1996-1997).
  • Reid Barton (USA) was the first participant to obtain a gold medal four times (1998-1999-2000-2001).
  • Christian Reiher (Germany) is the only other participant to have won four gold medals (2000-2001-2002-2003); Reiher also obtained a bronze medal in 1999.
  • In 1994, all six members of the USA team wrote a perfect paper. This accomplishment was noted in TIME Magazine.
  • Terence Tao from Australia won a gold medal at the age of thirteen in 1988, being the youngest person to have a gold medal. In 2006 he received the Fields medal.

[edit] Notable past participants

  • Grigori Perelman from USSR who wrote a perfect paper in IMO 1982 receiving a gold medal. He was offered but declined to accept a Fields medal in August 2006 for his work on proving the Poincaré conjecture, posed in 1904 and regarded as one of the most important and difficult open problems in mathematics. For that, he is eligible for a share of the U$ 1,000,000 Millennium Prize.
  • Terence Tao from Australia who participated in IMO 1986, 1987 and 1988, winning bronze, silver and gold medal respectively. He received a Fields medal in August 2006.

[edit] Sources

  • Steve Olson. Count Down. Houghton Mifflin, 2004. ISBN 0-618-25141-3. Describes the IMO (based on IMO 2000) from the viewpoint of the contestants, with general background information on various related issues (such as competitiveness).
  • Tom Verhoeff. The 43rd International Mathematical Olympiad: A Reflective Report on IMO 2002. Computing Science Report 02-11, Faculty of Mathematics and Computing Science, Eindhoven University of Technology. August 2002. PDF Describes the IMO (based on IMO 2002) from the viewpoint of the leaders, with a comparison to the International Olympiad in Informatics.

[edit] See also

[edit] External links

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