The United States of America Mathematical Olympiad (USAMO) is one of the most prestigious proof-based mathematics competitions for high school students in the United States. It is the culmination of the American Mathematics Competitions (AMC) series, and is open **by invitation only** to top scorers on the AMC 10/12 and the American Invitational Mathematics Examination (AIME), via an index-based selection process. USAMO consists of two days of examinations, each with three challenging proof-based problems and a 4.5-hour time limit. The contest tests deep problem-solving ability, creativity, and rigorous mathematical reasoning rather than routine calculation. High scorers may be invited to the Mathematical Olympiad Program (MOP), which trains students for the International Mathematical Olympiad (IMO). Participation in USAMO is a significant distinction in college admissions, especially for STEM fields, and helps students develop advanced skills in mathematical thinking and written communication.