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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!).
Claude Mydorge, and Father Marin Mersenne
Descartes did not invent polynomials.
Philosophically, Descartes was concerned with the existence of reality.
Rene Descartes was a French mathematician who created coordinated geometry.