HCSSiM is an intensive six-week encounter with college-level mathematics for talented and highly motivated high school students. It is demanding and expanding. Participants spend a major portion of each day actively engaged in doing mathematics (not simply learning the results of mathematics). HCSSiM students live in the dorms at Hampshire College in Massachusetts for six summer weeks, and study and play in its fields, woods, and academic buildings (not typically in that order). The daily schedule includes 4 hours of morning classes (Mon-Sat), the pre-supper Prime Time Theorem, and evening problem sessions. Afternoons are devoted to reading, rest, recreation, occasional trips to town, and informal study. Participants have unparalleled access to faculty members in classrooms, at meals, and in the program dorm. Productive collaborations continue long after the program, and many lifelong friendships are forged.