He has been dubbed the "Father of Modern Philosophy", and much of subsequent Western philosophy is a response to his writings, which continue to be studied closely to this day. In particular, his Meditations on First Philosophy continues to be a standard text at most university philosophy departments. Descartes' influence in mathematics is also apparent, the Cartesian coordinate system allowing geometric shapes to be expressed in algebraic equations being named for him. He is credited as the father of analytical geometry.
Descartes was also one of the key figures in the Scientific Revolution. Descartes frequently sets his views apart from those of his predecessors. In the opening section of the Passions of the Soul, a treatise on the Early Modern version of what are now commonly called emotions, he goes so far as to assert that he will write on his topic "as if no one had written on these matters before". Many elements of his philosophy have precedents in late Aristotelianism, the revived Stoicism of the 16th century, or in earlier philosophers like St. Augustine.
In his natural philosophy, he differs from the Schools on two major points: First, he rejects the analysis of corporeal substance into matter and form; second, he rejects any appeal to ends—divine or natural—in explaining natural phenomena. In his theology, he insists on the absolute freedom of God’s act of creation. Descartes was a major figure in 17th-century continental rationalism, later advocated by Baruch Spinoza and Gottfried Leibniz, and opposed by the empiricist school of thought consisting of Hobbes, Locke, Berkeley, and Hume. Leibniz, Spinoza and Descartes were all well versed in mathematics as well as philosophy, and Descartes and Leibniz contributed greatly to science as well. As the inventor of the Cartesian coordinate system, Descartes founded analytic geometry, the bridge between algebra and geometry, crucial to the discovery of calculus and analysis. His most famous statement is "Cogito ergo sum" (French: Je pense, donc je suis; English: I think, therefore I am; or I am thinking, therefore I exist), found in §7 of part I of Principles of Philosophy (Latin) and in part IV of Discourse on the Method (French).
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