In talent searches for gifted junior high school youth, those who score in the top two to five percent on a standardized achievement test are eligible to take the Scholastic Aptitude Test (SAT) which is regarded as a high-level ability test. While no important sex differences on the SAT verbal test have been observed, substantial sex differences in several statistics (including average scores) have consistently favored boys on the SAT mathematics test. A theory is provided which accounts for and provides an explanation of the SAT mathematics sex differences data. The proposed model based on this theory assumes that a recessive X-linked gene facilitates high mathematical score performance. It is pointed out that: (1) predictions from the theory are in precise order agreement with empirical data; (2) new testable predictions have been made; and (3) published data enables bounds on the putative recessive facilitative gene to be given (which may be less than 0.07). It is also pointed out that the model does not "prove" genetic factors are at the root of high mathematical test score sex differences; but until an alternative is proposed and the current model is clearly falsified, it should be regarded as a viable testable explanation. (Author/JN)