This paper contains a brief description of the founding and early years of the Study of Mathematically Precocious Youth (SMPY) from 1968 to the present. Several of the guiding principles behind SMPY are discussed. SMPY led to the formation of strong regional, state, and local centers that now blanket the United States with annual talent searches and academic summer programs. Among their main tools are the assessment tests of the College Board including the SAT, high school achievement tests, and Advanced Placement Program (AP) examinations. Identifying, via objective tests, youths who reason exceptionally well mathematically and/or verbally is the initial aim of SMPY and its sequels. The 12- or 13-year-old boys and girls who score high are then provided the special, supplemental, accelerative educational opportunities they sorely need. (Contains 42 references.) (Author/NB)