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It is significant that Descartes should choose mathematics to study according to this method. Mathematics has had far more success than any other field (except logic) with deductive reasoning. Math is built upon simple, self-evident axioms that are then used, along with some rules of inference, to derive proofs of more complex propositions.

Descartes is not only one of the greatest philosophers of the modern world, he is also one of its greatest mathematicians. His discussion of algebra and geometry alludes to his discovery of analytic geometry that brought those two fields together. Until Descartes, algebra and geometry were two totally separate fields of study. He invented the Cartesian co-ordinate system that every math student knows and loves. That's the co-ordinate system with the x-axis and the y-axis that allows you to plot lines and curves and whatever other shapes you please. Geometrical figures could be plotted onto the co-ordinate grid, and since every line and curve on the grid corresponds to an equation, geometrical figures can be expressed as equations. Geometrical figures become algebraic equations, and algebraic equations can be graphed as geometrical figures. This all seems pretty commonplace to us today, but if you try to imagine solving math problems without graphing anything you'll begin to understand the colossal contribution Descartes made to mathematics.