International Mathematical Olympiad

Mathematical competitions have played important roles in the tradition of many countries for centuries, surely dating as far back as the Greeks competing to solve geometry problems. In the XVI century, the Italians competed to resolve cubic polynomials, the French held competitions in the XVIII century, and Hungary organized the Eotvos competitions since 1894, which is most likely the closest antecedent to the Mathematical Olympiad held today. The first Mathematical Olympiad took place in Leningrad (now Sankt Petersburg) in 1934, organized by B. N. Delone and G. M. Frijtengolts. The International Mathematical Olympiad (IMO) was first held in 1959, hosted by Romania, to which Hungary, Bulgaria, Poland, Czechoslovakia, East Germany, and USSR were invited. Since then, it has been held, with each participating country hosting it by turns. As time went by, the number of participating countries has been increasing, with 73 countries in the 34^th IMO in Istanbul, Turkey (in 1993, this was the year when Slovenia first took part). It has now become the well-known competition for young mathematics enthusiasts all over the world.

When the IMO first began, each country was allowed up to eight participants. In 1982, this was scaled back to four members, but in 1983 the number was increased to six, which is where it still stands. The contestants must be no more than 20 years old and must not have any post secondary-school education. There is no limit to how many times a person may participate in the IMO, provided the individual meets the age and schooling requirements. The usual size of an official delegation to an IMO is (a maximum of) six students, along with the Leader and Deputy Leader. The student competitor writes two papers, on consecutive days, each paper consisting of three questions. Each question is worth seven marks. Only a whole number of marks are given, so there can be no half mark score.

Each invited country can send in up to six questions for consideration for the final competition papers. These submissions are reviewed by the host country's competitions committee, and a short list of about thirty questions is made. In recent years, there has also been a list of twelve preferred questions. The choice of the questions on the actual competition papers is made by the International Jury. The International Jury consists of the Chief Delegate (Leader) from each participating country, together with the Chairman named by the host country. Decisions are made by a simple majority vote. The official languages of the IMO are English, French, German and Russian. Since Spanish is spoken in a large number of participating countries, it has become an unofficial “official” language. In recent years, English has been the working language of the International Jury, with the other official languages available whenever required.

The International Jury members receive the short list of questions on arrival at the sequestered site. They have little time to review these problems before meeting to discuss which problems will be included. An honor system requires delegates to identify any suggested problems that are well known, in text books, or have been used in training programs. Some problems are eliminated as too easy or too hard. After considerable debate, the six problems are chosen, and their wording in all the official languages is agreed. The leaders of countries, whose students require other languages, then translate the questions into the required language. All papers, in all languages, are then inspected by all members of the International Jury, to ensure that all translations are appropriate.

When all paper are prepared the Deputy Leaders and Contestants will arrive at the venue. The Opening Ceremony is held, and the Contest begins the following day to last for two days. Each Contestant has to answer 3 questions in each of the two days in his/her own language in for 4 and a half hours. After the Contest, the programme shifts to entertaining activities such as sightseeing and games, for three days. During this period, the Contestants will have good opportunities to develop international friendship, through sharing talks and entertainment with each other. Meanwhile, the Leaders and Deputy Leaders mark the exam papers, and have Coordination sessions to discuss whether the marking has been done fairly and correctly.

The last day is for the Closing Ceremony, and the Gold, Silver, and Bronze medals will be awarded for excellent performances. The International Mathematical Olympiad is an individual competition. Only individuals compete. There is no team competition. Medals are awarded to approximately the top half of the participating students. Gold, Silver and Bronze medals are awarded in the ratio of 1:2:3, with no more that 1/12 of the students getting a Gold Medal, no more that 1/4 of the students getting either a Gold or a Silver Medal and no more that 1/2 of the students getting a medal of any kind. In order to encourage more students, and to encourage students to solve complete problems, recent practice has awarded a Certificate of Honorable Mention to any student (not receiving a medal) who obtained full marks for at least one problem.

IMO Timeline
#	Year	Country	City	Participating countries	Number of contestants	Country with the highest score
1	1959	Romania	Brasov	7	52	Romania
2	1960	Romania	Sinaia	5	39	CSSR
3	1961	Hungary	Veszprem	6	48	Hungary
4	1962	CSSR	Ceske Budejovice	7	56	Hungary
5	1963	Poland	Wroclaw	8	64	USSR
6	1964	USSR	Moscow	9	72	USSR
7	1965	GDR	Berlin	10	80	USSR
8	1966	Bulgaria	Sofia	9	72	USSR
9	1967	Yugoslavia	Cetinje	13	99	USSR
10	1968	USSR	Moscow	12	96	GDR
11	1969	Romania	Bucharest	14	112	Hungary
12	1970	Hungary	Keszthely	14	112	Hungary
13	1971	CSSR	Zilina	15	115	Hungary
14	1972	Poland	Torun	14	107	USSR
15	1973	USSR	Moscow	16	125	USSR
16	1974	GDR	Erfurt	18	140	USSR
17	1975	Bulgaria	Burgas	17	135	Hungary
18	1976	Austria	Lienz	18	139	USSR
19	1977	Yugoslavia	Belgrade	21	155	USA
20	1978	Romania	Bucharest	17	132	Romania
21	1979	Great Britain	London	23	166	USSR
22	1981	USA	Washington	27	185	USA
23	1982	Hungary	Budapest	30	119	Germany
24	1983	France	Paris	32	186	Germany
25	1984	CSSR	Prague	34	192	USSR
26	1985	Finland	Joutsa	38	209	Romania
27	1986	Poland	Warsaw	37	210	USA, USSR
28	1987	Cuba	Havanna	42	237	Romania
29	1988	Australia	Canberra	49	268	USSR
30	1989	Germany	Braunschweig	50	291	China
31	1990	China	Peking	54	308	China
32	1991	Sweden	Sigtuna	56	318	USSR
33	1992	Russia	Moscow	56	322	China
34	1993	Turkey	Istanbul	73	413	China
35	1994	Hong Kong	Hong Kong	69	385	USA
36	1995	Canada	Toronto	73	412	China
37	1996	India	Mumbai	75	424	Romania
38	1997	Argentina	Mar del Plata	82	460	China
39	1998	Taiwan	Taipeh	76	419	Iran
40	1999	Romania	Bucharest	81	450	China, Russia
41	2000	South Korea	Taejon	82	461	China
42	2001	USA	Washington	83	473	China
43	2002	Great Britain	Glasgow	84	479	China
44	2003	Japan	Tokyo	82	457	Bulgaria
45	2004	Greece	Athens	85	486	China
46	2005	Mexico	Merida	91	513	China
47	2006	Slovenia	Ljubljana	90	498	China
48	2007	Viet Nam	Hanoi
49	2008	Spain	Granada
50	2009	Germany	Bremen