Several hundred thousand intellectually talented 12-to 13-year-olds have been tested nationwide over the past 16 years with the mathematics and verbal sections of the Scholastic Aptitude Test (SAT). Although no sex differences in verbal ability have been found, there have been consistent sex differences favoring males in mathematical reasoning ability, as measured by the mathematics section of the SAT (SAT-M). These differences are most pronounced at the highest levels of mathematical reasoning, they are stable over time, and they are observed (...) in other countries as well. The sex difference in mathematical reasoning ability can predict subsequent sex differences in achievement in mathematics and science and is therefore of practical importance. To date a primarily environmental explanation for the difference in ability has not received support from the numerous studies conducted over many years by the staff of Study of Mathematically Precocious Youth (SMPY) and others. We have studied some of the classical environmental hypotheses: attitudes toward mathematics, perceived usefulness of mathematics, confidence, expectations/ encouragement from parents and others, sex-typing, and differential course-taking. In addition, several physiological correlates of extremely high mathematical reasoning ability have been identified (left-handedness, allergies, myopia, and perhaps bilateral representation of cognitive functions and prenatal hormonal exposure). It is therefore proposed that the sex difference in SAT-M scores among intellectually talented students, which may be related to greater male variability, results from both environmental and biological factors. (shrink)