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Descartes, René

geometry philosophy familiar cartesian

[daykah®t] (1596–1650) French philosopher and mathematician: creator of analytical geometry.

Descartes has a dominant position in shaping modern philosophy, but this is not our concern here. With enough modest inherited wealth to live as he chose, he spent his life in travel, on his work in philosophy, mathematics, physics and physiology and as a soldier serving in Holland, Bohemia and Hungary. In 1621 he left the army and in 1629 settled in Holland for some 20 years, before being persuaded to become tutor to Queen Christina of Sweden, a headstrong and athletic 19-year-old. From childhood Descartes had risen late and claimed to do his best thinking in a warm bed; the Queen’s insistence on tutorials in philosophy at 5 am in a freezing library either hastened or produced the lung disease which killed him within 5 months of arrival.

Although Descartes theorized extensively in physics and physiology, his lasting influence outside philosophy is in mathematics, where he created analytical or coordinate geometry, also named (after him) Cartesian geometry. This translates geometrical problems into algebraic form, so that algebraic methods can be applied to their solution; conversely he applied (for the first time) geometry to algebra. His methods made a massive change in mathematical thought and remain familiar today, as in the equation of the straight line, y = mx + c and the equations of familiar curves such as the conic sections. The thinker J S Mill (1806–73) claimed that Cartesian geometry ‘constitutes the greatest single step ever made in the progress of the exact sciences’.

Although Descartes’s ideas on the nature of consciousness were valuable, they have been overtaken by modern work. Curiously, despite being fond of his pet dog, since he believed that animals have no rational soul it followed that they lacked consciousness or feelings of any kind.

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