Answer:
The author of this proverbial saying isn't known. It is sometimes ascribed to Plato and it does appear in translations of Plato's Republic. Those translations weren't made until much later than the phrase was in common use in English and are more likely to be the work of the translator than being a literal version of Plato's words. The proverb was known in England by the 16th century, although at that point it must have been known to very few as it was then documented in its Latin form rather than in English. Many well-known proverbs appeared first in Latin and were transcribed into English by Erasmus and others, often as training texts for latin scholars.
William Horman, the headmaster of Winchester and Eton, included the Latin form 'Mater artium necessitas' in Vulgaria, a book of aphorisms for the boys of the schools to learn by heart, which he published in 1519.
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