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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!).
René Descartes believed that every human us a "noble savage" when in the state of nature.
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Descartes did not invent polynomials.
Philosophically, Descartes was concerned with the existence of reality.