USA Mathematical Talent Search (USAMTS)

USAMTS is a free, take-home competition where students get over a month to solve one puzzle and four proof-based problems per round, with no time pressure and reference materials allowed. Every entrant receives personalized written feedback on their proof-writing alongside a numeric score, and a high combined score is one way to qualify directly for the AIME. It's run by the nonprofit Art of Problem Solving Initiative and open to US middle and high schoolers.

Who can apply

FieldsMathematics

Logistics

AwardsTop ~45% receive prizes (books, T-shirts, Wolfram software); high scores can qualify a student for the AIME.

Applying

You submitRegister free online, download each round's problems, and submit written solutions by the round deadline.