The three phases (finding seventh and eighth grade mathematically talented students, studying them, and helping them educationally) of the Study of Mathematically Precocious Youth (SMPY) are detailed, and examples of the superiority of educational acceleration over educational enrichment are pointed out. Results of standardized intelligence tests are seen to be less helpful than scores on the mathematics part of the College Entrance Examination Board's Scholastic Aptitude Test in identifying gifted students for SMPY. Four types of enrichment (busy work, irrelevant academic, cultural, and relevant academic) are described and contrasted with academic acceleration. Presented is the case of 11 1/2-year-old boy who was helped educationally by entering college before completing high school. Stressed is the need for flexibility that makes a variety of educationally accelerative possibilities (such as grade skipping and college courses for credit) available for the student. (SBH)