A New Logic
Like Plato, Descartes was impressed with mathematics. Both saw mathematics as a discipline of certainty. For instance, that squares have four sides is not subject to refutation. Mathematics contains what philosophers call a priori truths—truths independent of the world. Mathematics also has proper foundations for systematic expansion.
If you could have a growing body of certain knowledge in mathematics, perhaps you could achieve analogous knowledge growth in the natural sciences. What was the relation between science and mathematics? Could all of science be like mathematics? When Descartes was in his late twenties, the astronomer Galileo stated in The Assayer (Galileo 1623) that the book of nature is written in mathematics. Whether Descartes read this text or not, he did set out to decipher nature according to mathematical physics, seeing the world as being composed of geometrical shapes.
Natural philosophers of the time saw nature in light of mathematics. It was assumed that God had created a mathematical universe. But Descartes was so radical in his thinking that he chose to distrust even mathematics.