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For the mathematicians and scientists of ancient Greece, the motive was intellectual recreation more than the solving of practical problems. Later in history a great many practical problems have been solved by the use of mathematical and scientific knowledge developed in ancient Greece (and greatly expanded in subsequent eras) but at the time no one knew or anticipated that such uses would ever be found for abstract knowledge. It was just interesting.

They built upon the earlier Greek, Babylonia and Egyptians knowledge.

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