Descartes was the son of a counselor of the Britanny parlement; his mother, who died shortly after his birth, left him sufficient funds to make him financially independent. Born at La Haye in France, he was educated by the Jesuits of La Flèche (1604–12) and at the University of Poitiers, where he graduated in law in 1616. For the next decade Descartes spent much of his time in travel throughout Europe and in military service, first with the army of the Prince of Orange, Maurice of Nassau, and later with the Duke of Bavaria, Maximilian, with whom he was present at the battle of the White Mountain outside Prague in 1620. In the years 1628–49 Descartes settled in the freer atmosphere of Holland. There, living quietly, he worked on the exposition and development of his system. Somewhat unwisely, he allowed himself to be enticed into the personal service of Queen Christina of Sweden in Stockholm in 1649. Forced to indulge the Queen's passion for philosophy by holding tutorials with her at 5 a.m. on icy Swedish mornings Descartes, who normally loved to lie thinking in a warm bed, died within a year from pneumonia and the copious bleeding inflicted by the enthusiastic Swedish doctors.

Descartes is in many ways, in mathematics, philosophy, and science, the first of the moderns. The moment of modernity can be dated precisely to 10 November, 1619, when, as later described in his Discours de la méthode (1637; Discourse on Method), he spent the whole day in seclusion in a poêle (an overheated room). He began systematically to doubt all supposed knowledge and resolved to accept only “what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.”

Descartes thus managed to pose in a single night the problem whose solution would obsess philosophers for the next 300 years. The same night also provided him with one of the basic insights of modern mathematics – that the position of a point can be uniquely defined by coordinates locating its distance from a fixed point in the direction of two or more straight lines. This was revealed in his La Geométrie (1637; Geometry), published as an appendix to his Discourse, and describing the invention of analytic or coordinate geometry, by which the geometric properties of curves and figures could be written as and investigated by algebraic equations. The system is known as a Cartesian coordinate system.

His theories on physics were published in his Principia philosophiae (1644; Principles of Philosophy). “Give me matter and motion and I will construct the universe,” Descartes had proclaimed. The difficulty for him arose from his account of matter which, on metaphysical grounds, he argued, “does not at all consist in hardness, or gravity or color or that which is sensible in another manner, but alone in length, width, and depth,” or, in other words, extension. From this initial handicap Descartes was forced to deny the existence of the void and face such apparently intractable problems as how bodies of the same extension could possess different weights. With such restrictions he was led to describe the universe as a system of vortices. Matter came in three forms – ordinary matter opaque to light, the ether of the heavens transmitting light, and the subtle particles of light itself. With considerable ingenuity and precious little concern for reality Descartes used such a framework within which he was able to deal with the basic phenomena of light, heat, and motion. Despite its initial difficulties it was developed by a generation of Cartesian disciples to pose as a viable alternative to the mechanics worked out later in the century by Newton. Unlike many less radical thinkers Descartes did not shrink from applying his mechanical principles to physiology, seeing the human body purely in terms of a physicomechanical system with the mind as a separate entity interacting with the body via the pineal gland – the supposed seat of the soul.

The fundamental impact of Descartes's work was basically one of demystification. Apart from the residual enigma of the precise relationship between mind and body, the main areas of physics and physiology had been swept clear of such talk as that of occult powers and hidden forms.