A Julia Robinson Mathematics Festival offers students advanced and thought-provoking mathematics in a social and cooperative atmosphere. Students choose among several tables offering problem sets, games, or puzzles with mathematical themes. They work as long as they wish, while a facilitator provides support and encouragement. Motivation comes from the social interaction, rather than from any prize, grade, medal, or ranking. Festivals are run locally and supported by a national network. They can address any level of student, from those struggling with mathematics to those soaring in achievement.