Mathematical olympiad

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]^[5] In a sense, they measure some mathematical abilities of the students.^[4]

History

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.^[6] A better-documented Eötvös Competition in Hungary became one of the earliest organized contests in 1894.^[6]^[7] Romania followed with another competition, this time for secondary school students, in June 1898.^[6] USSR introduced regular math olympiads in the 1930s, and the predecessor of the Putnam Competition started in 1938 in the US.^[6]

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.^[8]

Curriculum

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.^[9] 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.