Plato on Why Mathematics is Good for the Soul

In T. Smiley (ed.), Mathematics and Necessity: Essays in the History of Philosophy. pp. 1-81 (2000)
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Abstract
Anyone who has read Plato’s Republic knows it has a lot to say about mathematics. But why? I shall not be satisfied with the answer that the future rulers of the ideal city are to be educated in mathematics, so Plato is bound to give some space to the subject. I want to know why the rulers are to be educated in mathematics. More pointedly, why are they required to study so much mathematics, for so long?
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