International Mathematical Olympiad
[4] The content ranges from extremely difficult algebra and pre-calculus problems to problems in branches of mathematics not conventionally covered in secondary or high school and often not at university level either, such as projective and complex geometry, functional equations, combinatorics, and well-grounded number theory, of which extensive knowledge of theorems is required.
Supporters of this principle claim that this allows more universality and creates an incentive to find elegant, deceptively simple-looking problems which nevertheless require a certain level of ingenuity, often times a great deal of ingenuity to net all points for a given IMO problem.
[8] Several students, such as Lisa Sauermann, peter scholze Reid W. Barton, Nicușor Dan 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.
[10] 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.
In some countries, especially those in East Asia, the selection process involves several tests of a difficulty comparable to the IMO itself.
[15] In others, such as the United States, possible participants go through a series of easier standalone competitions that gradually increase in difficulty.
[18] Special prizes may be awarded for solutions of outstanding elegance or involving good generalisations of a problem.
[19] The special prize in 2005 was awarded to Iurie Boreico, a student from Moldova, for his solution to Problem 3, a three variable inequality.
[28] 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.
[85] Hungary won IMO 1975 in an unorthodox way when none of the eight team members received a gold medal (five silver, three bronze).
[77] Second place team East Germany also did not have a single gold medal winner (four silver, four bronze).
[90] 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.
[93] Terence Tao (Australia) participated in IMO 1986, 1987 and 1988, winning bronze, silver and gold medals respectively.
[95] Representing the United States, Noam Elkies won a gold medal with a perfect paper at the age of 14 in 1981.
Both Elkies and Tao could have participated in the IMO multiple times following their success, but entered university and therefore became ineligible.
[99] This gender gap in participation and in performance at the IMO level led to the establishment of the European Girls' Mathematical Olympiad (EGMO).
