A number of myths about mathematically gifted students, mathematics itself, and programs designed to serve these students tend to inhibit educators, parents and students themselves from developing students' mathematical creativity, expertise and enjoyment. This paper discusses some of the myths that can discourage students' mathematical development, restrict their understanding of mathematics, and/or are well-intentioned solutions with unintended consequences and includes research results from a few mathematics programs and other studies designed to counteract these myths and maximize students' mathematical achievement, engagement and innovation.