Since 1971 the Study of Mathematically Precocious Youth (SMPY) at Johns Hopkins University has pioneered in discovery of and provision of educational help for 12-year-old boys and girls who reason better mathematically than 99% of other 12-year-olds. SMPY originated widespread searches for such youths and special academic classes for them outside the regular school system. A regional talent search, verbal as well as mathematical, now covers all 50 states of the USA, and many varied residential summer programmes are offered across the country. These have provided educational facilitation for many thousands, and have encouraged greater curricular flexibility in schools and better articulation of in-school with out-of-school learning experiences. From the first talent search conducted by SMPY in 1972, it became obvious that boys tend to score considerably higher than girls on the College Board Scholastic Aptitude Test-Mathematical (SAT-M), a test intended mainly for college-bound 17- and 18-year-olds. This difference was reported in 1974 but attracted little attention until a controversial report in 1980 stimulated research on sex differences in various aspects of mathematics. Here I describe a study of sex differences over 10 years on 14 College Board high school achievement tests, which are taken (three usually) by bright 17- and 18-year-olds seeking admission to the USA's selective colleges and universities. Among the high scores on the European history test the ratio of males to females was greatest, 6:1. The next most sex-differentiating test was physics, 2.9:1, followed by elementary-level mathematics (mainly algebra and geometry), 2.5:1. Other ratios favouring males were, in 1991, chemistry (2.4:1), American history (2.1:1), biology (1.8:1), precalculus mathematics (1.6:1), Latin (1.6:1), French (1.4:1), modern Hebrew (1.1:1) and German (1.02:1). Tests in which more females were high scorers were literature (1.26:1), English composition (1.05:1) and Spanish (1.01:1). The largest sex differences on other standardized tests, for mechanical reasoning and spatial rotation, favour males. There are even larger differences for self-reported evaluative attitudes, with the theoretical value high for boys and the aesthetic high for girls. Such value scores correlated strangely with scores on achievement and aptitude tests. By 12 or younger, bright boys and girls already show many of the cognitive sex differences found in 18-year-olds.