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The Princeton Companion to Mathematics by Imre Leader, June Barrow-Green, Timothy Gowers

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VI.11 René Descartes

b. La Haye (now “Descartes”), France, 1596; d. Stockholm, 1650

Algebra; geometry; analytic geometry; foundations of mathematics

In 1637 Descartes published La Géométrie as an “essay” appended to his philosophical treatise Discours de la Méthode. It remained his only mathematical publication. No single early modern text shaped the development of mathematics between 1650 and 1700 as strongly as La Géométrie. It was the founding text of analytic geometry and it paved the way for the merging of algebra and geometry that made possible the development of the integral and differential calculus about fifty years later.

Descartes was educated at the Jesuit College at La Flèche. He spent his life mostly outside France, traveling ...

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