Summary.—The structure of mathematical ability in grammar and technical schools was investigated by factorial analysis. The following conclusions were drawn:1There is a close connection between mathematical and general ability; high intelligence is the most important single factor for success in mathematics.2In addition, there exists a clearly identifiable mathematical group factor. The different branches of mathematics are linked together more closely than they would be if a general factor only were in operation.3Verbal, spatial, and numerical group factors were isolated.4Performance in geometry is connected with spatial ability as measured by the spatial factor.5Performance in arithmetic (especially mechanical arithmetic), and to a lesser extent performance in algebra, is in part dependent upon numerical ability as measured by a number factor.6When the influence of general ability is eliminated, verbal ability has little connection with mathematical ability.7No marked differences in factor pattern were observed between different types of school ‘grammar and technical) or between different countries (England and Northern Ireland).8The attainment tests of mathematics, constructed specially for this research, proved to be highly reliable and valid measures of mathematical abil