H. I. Marrou, A History Of Education in Antiquity, Translated by George Lamb, New American Library, 1964
Part One, Section 6, “The Masters of the Classical Tradition, I. Plato”, pp. 111-112
But the essential point is that the function of these mathematical studies was not simply to provide technical training: however practical they might be, they nevertheless had a much deeper function. Fully accepting, and enlarging, Hippias’s teaching, Plato asserted the supreme educational value of mathematics, and maintained that no other subject was in this respect comparable with it: mathematics awakened the mind, developed its speed and liveliness and its memorizing powers.
Everyone could derive benefit from it: these exercises in applied mathematics sorted out the best pupils and encouraged them in their natural quickness to learn, but even the slower, more stubborn ones were gradually roused from their torpor, and improved, and became quicker to learn than they would have been by nature. This is an original and profound observation. Unlike many of his successors (ancient and modern), who maintain that literature is the only subject that everyone can learn, mathematics being reserved for the fortunate few who have a bent for it, Plato claims that anyone can learn mathematics because the only thing that is needed for it is the reasoning faculty, a thing that everybody possesses.
This is true at this elementary stage at least, though only a few specially gifted minds will be able to complete the study of mathematics, and these will have to be carefully chosen. We must stress the historical importance of this idea of selection, which is still the basis of our own competitive system of examinations. Plato believed that mathematics provided the test for the “best minds,” the people who would one day be ready to study philosophy: mathematics would discover their learning ability, their perceptiveness, their powers of memory, their capacity for hard work despite the aridity of such gruelling study. And in the very process of being selected, the future philosophers would at the same time be undergoing training and preparation for their future work. The essential element in this “preparatory education”–προπαίδεια–was mathematics.