Math contests help students in a number of ways. They generate a culture of enthusiasm for both mathematics and problem solving. They also expose students to many kinds of problems they may never see even in an advanced classroom setting. These problem types include areas such as number theory, combinatorics, and recursion that are extremely pertinant to the current era of computer science.

High school students and very advanced middle schoolers should try the USA Mathematical Talent Search (USAMTS). The USAMTS is described by some mathematicians as more like what they do for a living than any other math contest because students are given a full month to write detailed solutions to challenging problems. Participation is free.

The American Mathematics Competitions (AMC) and MATHCOUNTS are the two most well-known organizations that administer contests. Their exams are so well respected that many elite universities ask students for their scores or at least pay great attention to the results. MATHCOUNTS is a competition for 6th through 8th graders while the AMC is primary focused on high school and top middle school students. Both promote a problem solving approach to mathematics.

The AoPS Internet Guide includes a thorough listing of other math competitions both nationally and within states and Canadian provinces. There are even listings for some international competitions.