1. International Mathematical Olympiad (IMO): This is the highest-level Olympic Mathematical Competition in the world, which is sponsored by the International Mathematical Union every year. Participants come from all over the world and the competition is fierce. Winning a prize in such a competition is very valuable.
2. China Mathematical Olympics (CMO): sponsored by the Chinese Mathematical Society, it is one of the highest-level Olympic Games in China. Participants come from all over the country, and it is very valuable to win the prize in such a competition.
3. American Mathematical Olympiad (AMC): sponsored by the American Mathematical Association, it is one of the highest-level Olympic mathematical competitions in the United States. Participants come from all States in the United States, and it is very valuable to win the prize in such a competition.
4. British Mathematical Olympiad (BMO): sponsored by the Royal Society, it is one of the highest-level Olympic Games in Britain. Participants come from various schools in Britain, and it is very valuable to win prizes in such competitions.
5. Russian Mathematical Olympiad (RMO): sponsored by the Russian Mathematical Association, it is one of the highest-level Olympic mathematical competitions in Russia. Participants come from various schools in Russia, and it is very valuable to win prizes in such competitions.