Descartes did not invent polynomials.
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The first polynomials went as far back as 2000 BC, with the Babylonians.
He didn't invent mathematics.
False
He developed the concepts which were set out by Archimedes.
Short answer: Descartes' doubt was like WWI - the doubt to end all doubt. Only by doubting everything could Descartes hope to find anything that was certain (even if the only certainty is that nothing else is certain!).