Mathematics learning requires diverse cognitive functions, even at the primary school level. The current paper presents the results of two studies that focus on the cognitive functions which are associated with mathematic learning and mathematical ability. The objective of the first study was to identify cognitive functions that not only underlie and predict achievements in mathematics, but that are a pre-requisite to these achievements. To achieve these objectives, the performance of 112 fifth graders was studied in seven quantitative and non-quantitative cognitive tests, as well as in a standard mathematics test. Study 2 focuses on the relationships between a large variety of basic quantitative and non-quantitative cognitive functions and general mathematical ability of 600 high school graduates and college students. The results of both studies shed some light on the sources of mathematical learning difficulties and mathematical learning disabilities.