What motivates high school students to persist with challenging mathematics? The current investigation examined this important question using the concept of mathematics self-schema, that is, students' cognitive generalizations of their selves in learning mathematics. Mathematics self-schemas are important sources of motivation. It was hypothesized that students who hold contrasting mathematics self-schemas would learn challenging mathematics and formulate their subject choice intention differently. Study 1 surveyed 373 Year 10 Australian students and classified them into 3 schematic groups based on their survey responses. The results showed that positive, average, and negative schematics held contrasting goals, strategies, and performance expectation when dealing with challenging mathematics. More positive schematics compared with the other groups intended to take advanced mathematics in senior high school. Study 2 used an experimental design to compare positive and negative schematics' contrasting responses when dealing with difficult tests. Seventy-one students drawn from Study 1 joined Study 2. The findings confirmed the differences between these 2 groups. Study 3 randomly assigned 106 average schematics located in Study 1 to positive schematic, negative schematic, and control conditions. Students in the positive and negative conditions were primed to think and act like a schematic corresponding to their assigned condition before completing a challenging test. The results showed that average schematics in the induced conditions acted and responded to the challenging test in a way similar to corresponding positive and negative schematics. The article discusses mathematics self-schemas as a source of motivation for understanding students' engagement in and subject choice intention for challenging mathematics.