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 1 Selection process 2 Awards 3 Current and future IMOs 4 Past IMOs 5 Results for the 2006 IMO 6 Notable past participants 7 Notable achievements 8 Multiple IMO winners 9 Sources 10 See also 11 External links

[edit] Selection process

Main article: IMO selection process.

[edit] Awards

The participants are ranked based on their individual scores.

• The total number of awarded medals is as close as possible to but not more than half the total number of contestants.
• Subsequently the number of gold, silver and bronze medals is chosen such that their ratio approximates 1:2:3.
• Participants who don't win a medal but who score seven points on at least one problem 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 2005, 1995 and 1988, but was more frequent up to the early 1980s.

The rule that at most half the contestants win a medal is sometimes broken if adhering to it causes the number of medals to deviate too much from half the number of contestants. This last happened in 2006 when the choice was to give either 188 or 253 of the 498 contestants a medal.

[edit] Current and future IMOs

• The 48th IMO will be held in Hanoi, Vietnam in 2007.
• The 49th IMO will be held in Granada, Spain in 2008.
• The 50th IMO will be held in Bremen, Germany in 2009.

[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 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.

№	Venue	Date	Web site
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, Soviet Union	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, China	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, Taiwan	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

Place	Team	Points
1	China	214
2	Russia	174
3	South Korea	170
4	Germany	157
5	United States	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 past participants

• Grigory Margulis (USSR) received IMO 1962 Silver medal. He became only the seventh mathematician ever to receive both a Fields Medal in 1978 and a Wolf Prize in Mathematics in 2005.
• Grigori Perelman (USSR) wrote a perfect paper in IMO 1982 and received a Gold medal. He was awarded but declined to accept a Fields medal in 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 $1,000,000 Millennium Prize offered by Clay Mathematics Institute.
• Vladimir Drinfel'd (USSR) at the age of 15 wrote a perfect paper in IMO 1969 and received a Gold medal. He was awarded a Fields Medal in 1990.

Complete list of Fields Medal winners who also received IMO medals with corresponding years and medals received noted (G for Gold, S for Silver, and B for Bronze medal):

Name	Team	IMO medal(s)	Fields medal	Wolf Prize
Grigory Margulis	Soviet Union	IMO 1962 S	1978	2005
Vladimir Drinfel'd	Soviet Union	IMO 1969 G	1990
Jean-Christophe Yoccoz	France	IMO 1974 G	1994
Richard Borcherds	United Kingdom	IMO 1977 S IMO 1978 G	1998
Timothy Gowers	United Kingdom	IMO 1981 G	1998
Grigori Perelman	Soviet Union	IMO 1982 G	2006
Laurent Lafforgue	France	IMO 1984 S IMO 1985 S	2002
Terence Tao	Australia	IMO 1986 B IMO 1987 S IMO 1988 G	2006

[edit] Notable achievements

• Reid Barton (USA) was the first participant to win a Gold medal four times (1998-1999-2000-2001). Barton is also one of only seven four-time Putnam Fellow (2001-2002-2003-2004).
• Christian Reiher (Germany) is the only other participant to have won four Gold medals (2000-2001-2002-2003); Reiher also received a Bronze medal (1999).
• Wolfgang Burmeister (GDR) and Martin Harterich (FRG) are the only other participants besides Reiher 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 history of competition. He did it all three times he participated in IMO (1995-1996-1997). Manolescu is also a three-time Putnam Fellow (1997-1998-2000).
• Eugenia Malinnikova (USSR) is the best 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 repeat 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 at the age of thirteen in IMO 1988, becoming the youngest person to receive a Gold medal. He received a Fields medal in 2006.
• Team USA won IMO 1994 in unique style when all six members of the team wrote a perfect paper and thus received six Gold medals. This accomplishment has never been repeated and earned a mention in TIME Magazine.
• Other teams that won IMO and had all members receive Gold medals are China 8 times (1992-1993-1997-2000-2001-2002-2004-2006) and Bulgaria once (2003).
• Team Hungary won IMO 1975 in completely opposite and totally unorthodox way when none of the eight team members received a Gold medal (5 Silver, 3 Bronze). Second place team GDR also did not have a single Gold medal winner (4 Silver, 4 Bronze).

[edit] Multiple IMO winners

The following table lists all IMO Winners who have won at least three Gold Medals, with corresponding years and non-Gold Medals received noted (S for Silver medal, B for Bronze medal).

Name	Team(s)	Years
Christian Reiher	Germany	2000	2001	2002	2003	1999 B
Reid Barton	United States	1998	1999	2000	2001
Wolfgang Burmeister	GDR	1968	1970	1971	1967 S	1969 S
Martin Harterich	FRG	1986	1987	1989	1988 S	1985 B
Laszlo Lovasz	Hungary	1964	1965	1966	1963 S
Jozsef Pelikan	Hungary	1964	1965	1966	1963 S
Nikolai Nikolov	Bulgaria	1992	1993	1995	1994 S
Kentaro Nagao	Japan	1998	1999	2000	1997 S
Vladimir Barzov	Bulgaria	2000	2001	2002	1999 S
Iurie Boreico	Moldova	2004	2005	2006	2003 S
Simon Norton	United Kingdom	1967	1968	1969
John Rickard	United Kingdom	1975	1976	1977
Sergey Ivanov	Soviet Union	1987	1988	1989
Theodor Banica	Romania	1989	1990	1991
Eugenia Malinnikova	Soviet Union	1989	1990	1991
Serguei Norine	Russia	1994	1995	1996
Yuly Sannikov	Ukraine	1994	1995	1996
Ciprian Manolescu	Romania	1995	1996	1997
Ivan Ivanov	Bulgaria	1996	1997	1998
Nikolai Dourov	Russia	1996	1997	1998
Tamas Terpai	Hungary	1997	1998	1999
Stefan Hornet	Romania	1997	1998	1999
Vladimir Dremov	Russia	1998	1999	2000
Mihai Manea	Romania	1999	2000	2001
Tiankai Liu	United States	2001	2002	2004
Oleg Golberg	Russia '02, '03   United States '04	2002	2003	2004
Bela Racz	Hungary	2002	2003	2004
Andrey Badzyan	Russia	2002	2003	2004
Rosen Kralev	Bulgaria	2003	2004	2005

[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

• International Science Olympiad

[edit] External links

• Central IMO web site
• Introduction to the IMO Business, including information on IMO ShortLists/LongLists by Orlando Döhring
• IMO Resources - IMO problems and solutions, IMO Shortlists, IMO Longlists and one of the largest collection of Olympiad problems in the world.
• IMO problems and solutions
• Complete IMO results
• IMO scores (since 1980's) with Statistical analysis
• IMO winners Hall of Fame - IMO winners who have won Fields Medal or Nevanlinna Prize
• IMO contestants who have won three or more gold medals
• MathLinks IMO Forums - discuss the latest developments in the IMO with former, current or future contestants, leaders and other people involved in the IMO
• The IMO Compendium - the most complete collection of shortlisted and long listed problems for the IMO's; huge collection of problems from other contests.