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Although Descartes mistrusted the information received through the senses, he did believe that certain knowledge can be acquired by other means, arguing that the strict application of reason to all problems is the only way to achieve certainty in science. In Rules for the Direction of the Mind, Descartes argues that all problems should be broken up into their simplest parts and that problems can be expressed as abstract equations. Descartes hopes to minimize or remove the role of unreliable sense perception in the sciences. If all problems are reduced to their least sense-dependent and most abstract elements, then objective reason can be put to work to solve the problem.
Descartes’s work combining algebra and geometry is an application of this principle. By creating a two-dimensional graph on which problems could be plotted, he developed a visual vocabulary for arithmetic and algebraic ideas. In other words, he made it possible to express mathematics and algebra in geometric forms. He also developed a method to understanding the properties of objects in the real world by reducing their shapes to formulae and approaching them through reason rather than sense perception.
