René Descartes has been dubbed the "Father of Modern Philosophy", but he was also one of the key figures in the Scientific Revolution of the 17th Century, and is sometimes considered the first of the modern school of mathematics. As a young man, he found employment for a time as a soldier (essentially as a mercenary in the pay of various forces, both Catholic and Protestant). But, after a series of dreams or visions, and after meeting the Dutch philosopher and scientist Isaac Beeckman, who sparked his interest in mathematics and the New Physics, he concluded that his real path in life was the pursuit of true wisdom and science. Back in France, the young Descartes soon came to the conclusion that the key to philosophy, with all its uncertainties and ambiguity, was to build it on the indisputable facts of mathematics. To pursue his rather heretical ideas further, though, he moved from the restrictions of Catholic France to the more liberal environment of the Netherlands, where he spent most of his adult life, and where he worked on his dream of merging algebra and geometry. In 1637, he published his ground-breaking philosophical and mathematical treatise "Discours de la méthode" (the “Discourse on Method”), and one of its appendices in particular, "La Géométrie", is now considered a landmark in the history of mathematics. Following on from early movements towards the use of symbolic expressions in mathematics by Diophantus, Al-Khwarizmi and François Viète, "La Géométrie" introduced what has become known as the standard algebraic notation, using lowercase a, b and c for known quantities and x, y and z for unknown quantities. It was perhaps the first book to look like a modern mathematics textbook, full of a's and b's, x2's, etc. It was in "La Géométrie" that Descartes first proposed that each point in two dimensions can be described by two numbers on a plane, one giving the point’s horizontal location and the other the vertical...
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