Was Pythagoras against traditional/contemporary Greek education?
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At least part of this is rooted in Pythagoras' disdain of those who sold their knowledge, which, as we know from Plato, is something that "sophists" were wont to do. Similarly, schoolmasters, I believe, were paid by students for their knowledge.
From Iamblichus' Life of Pythagoras 34:
The Pythagoreans objected to those who offered disciplines for sale, who open their souls like the gates of an inn to every man that approaches them; and who, if they do not thus get buyers, diffuse themselves through the cities, and in short, hire gymnasia, and require a reward from young men for those things that are without price.
The Pythagoreans thought that those who teach for the sake of reward show themselves worse than scuplors or artists who perform their work sitting.
(Translated by Kenneth S. Guthrie in his The Pythagorean Sourcebook and Library, 1987.)
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