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This theorem was not invented so much as evolved. All mathematical proofs and theorems evolve from simple math to more complex math. The related Wikipedia article explores and explains the history of this theorem.

In short...
Pythagoras, whose dates are commonly given as 569-475 BC, used algebraic methods to construct Pythagorean triples, according to Proklos's commentary on Euclid. Proklos, however, wrote between 410 and 485 AD. According to Sir Thomas L. Heath, there was no attribution of the theorem to Pythagoras for five centuries after Pythagoras lived. However, when authors such as Plutarch and Cicero attributed the theorem to Pythagoras, they did so in a way which suggests that the attribution was widely known and undoubted.

Pythagoras was Greek and lived in Greece, so it can be assumed that he completed the theorem in Greece.

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Q: Where was the Pythagorean theorem invented?
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