This paper reports a study aimed at characterizing the conditions that lead to high achievement in mathematics in India. The study involved eight schools in the greater Mumbai region. The main result of the study is that the notion of high achievement itself is problematic, as reflected in the reports about mathematics achievement within and outside India as well as the complexities of a school system which, despite democratic ideals, has difficulty serving the needs of all students. This study provides snapshots of three mathematics classes that embody some of these complexities to provide a balanced account of conditions that either support or detract from the goal of high achievement in India.