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A mathematical olympiad is a mathematical competition where participants are examined by problem solving [1] and may win medals depending on their performance. Usually aimed at pre-university students, much of olympiad mathematics consists of elementary mathematics, though solutions may involve the use of calculus or higher-level mathematics. The biggest mathematics olympiad is the International Mathematical Olympiad. [2] Among their objectives, they serve the purpose of identifying talented or gifted students in mathematics, who often receive opportunities for scholarships at universities. [3] [4] In a sense, they measure some mathematical abilities of the students. [3]
The concept of mathematics competitions dates back to the late 19th century. A one-off competition for 70 primary school students was held in Bucharest in May 1885, but little is known about it. [5] A better-documented Eötvös Competition in Hungary became one of the earliest organized contests in 1894. [5] [6] Romania followed with another competition, this time for secondary school students, in June 1898. [5] USSR introduced regular math olympiads in the 1930s, and the predecessor of the Putnam Competition started in 1938 in the US. [5]
The success of these national competitions eventually led to the establishment of the International Mathematics Olympiad, which has grown from 7 participating countries in 1959 to over 100 countries in recent years. [7]
Modern olympiad mathematics can be split into four categories: algebra, combinatorics, geometry, and number theory. Algebra is restricted to elementary algebra, number theory is restricted to elementary number theory, and geometry is usually restricted to Euclidean plane geometry. [8] While never required, the use of non-elementary techniques like calculus, linear algebra, algebraic number theory, algebraic geometry and projective geometry is allowed, and can often lead to more elegant solutions.