The purposes of this study were to determine whether mathematically gifted boys and girls in secondary schools were significantly different in cognitive abilities and personality factors and to determine whether these cognitive abilities and personality factors were accurate predictors of mathematical achievement. Mathematically gifted boys (n=77) and girls (n=62) who enrolled in two summers of an accelerated mathematics program completed a mathematics reasoning test (SAT-M), a verbal reasoning test (SAT-V), a measure of spatial ability (Group Embedded Figures Test), and a Personality Test (California Psychological Inventory). At the end of each summer program, students received mathematics achievement ratings depending on the number of courses completed. The only significant difference found indicated that boys have higher mathematical reasoning ability than girls. Also, mathematical reasoning ability was determined to be the single best predictor of mathematical achievement for the mathematically gifted boys, while verbal ability was the best predictor of mathematical achievement for the girls. For both the girls and the boys, neither spatial reasoning ability nor personality factors significantly predicted mathematical achievement. (Author)