The purpose of this paper is to examine how mathematically talented children in a disadvantaged rural community experience mathematics, both as a discipline and as a school subject. The aim is to find answers to questions such as: "What do these children think mathematics is?" "What value do they attach to the study of mathematics?" and "In what ways do classroom, home, and community experiences shape their thinking about what mathematics is and what it is for?" Information is provided about the county in which the study was conducted, including a brief description of the school district and its gifted program. Then the authors describe the students whose interviews constituted the data on which the findings are based. Finally, the five themes that represent the principal findings of the study are discussed. (Contains 2 footnotes.)