René Descartes (1596–1650) was a creative mathematician of the first order, an important scientific thinker, and an original metaphysician. During the course of his life, he was a mathematician first, a natural scientist or “natural philosopher” second, and a metaphysician third. In mathematics, he developed the techniques that made possible algebraic (or “analytic”) geometry. In natural philosophy, he can be credited with several specific achievements: co-framer of the sine law of refraction, developer of an important empirical account of the rainbow, and proposer of a naturalistic account of the formation of the earth and planets (a precursor to the nebular hypothesis). More importantly, he offered a new vision of the natural world that continues to shape our thought today: a world of matter possessing a few fundamental properties and interacting according to a few universal laws. This natural world included an immaterial mind that, in human beings, was directly related to the brain; in this way, Descartes formulated the modern version of the mind–body problem. In metaphysics, he provided arguments for the existence of God, to show that the essence of matter is extension, and that the essence of mind is thought. Descartes claimed early on to possess a special method, which was variously exhibited in mathematics, natural philosophy, and metaphysics, and which, in the latter part of his life, included, or was supplemented by, a method of doubt.

Descartes presented his results in major works published during his lifetime: the Discourse on the Method (in French, 1637), with its essays, the Dioptrics, Meteorology, and Geometry; the Meditations on First Philosophy (i.e., on metaphysics), with its Objections and Replies (in Latin, 1641, 2nd edn. 1642); the Principles of Philosophy, covering his metaphysics and much of his natural philosophy (in Latin, 1644); and the Passions of the Soul, on the emotions (in French, 1649). Important works published posthumously included his Letters (in Latin and French, 1657–67); World, or Treatise on Light, containing the core of his natural philosophy (in French, 1664); Treatise on Man (in French, 1664), containing his physiology and mechanistic psychology; and the Rules for the Direction of the Mind (in Latin, 1701), an early, unfinished work attempting to set out his method.

Descartes was known among the learned in his day as a top mathematician, as the developer of a new and comprehensive physics or theory of nature (including living things), and as the proposer of a new metaphysics. In the years following his death, his natural philosophy was widely taught and discussed. In the eighteenth century aspects of his science remained influential, especially his physiology, as did his project of investigating the knower in assessing the possibility and extent of human knowledge; he was also remembered for his failed metaphysics and his use of skeptical arguments for doubting. In the nineteenth century he was revered for his mechanistic physiology and theory that animal bodies are machines (that is, are constituted by material mechanisms, governed by the laws of matter alone). The twentieth century variously celebrated his famous “cogito” starting point, reviled the sense data that some alleged to be the legacy of his skeptical starting point, and looked to him as a model of the culturally engaged philosopher. He has been seen, at various times, as a hero and as a villain; as a brilliant theorist who set new directions in thought, and as the harbinger of a cold, rationalistic, and calculative conception of human beings.