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This one thing [analytic geometry] is of the highest order of excellence, marked by the sensuous simplicity of the half dozen or so greatest contributions of all time to mathematics. Descartes remade geometry and made modern geometry possible. Rene Descartes was the third child of a well off noble family. His mother died a few days after his birth, and he was a frail child. Because of this poor health, his father mostly let Ren do as he wished, but at the age of 8 he was sent to a Jesuit "college" for formal schooling in the classics.
The rector of the school was sensitive to the boy's health and allowed Descartes to stay in bed until he felt ready to attend class. Descartes used these quiet mornings to think, and, later in life, he said that they were the real source of his philosophy and mathematics. By 18 Descartes was quite healthy, and he left school to begin leading the life of a "gentleman" in Paris. He seems to have found wine, women and gambling amusing for awhile, but he soon retired to a quiet suburb for 2 years to think. When his wilder friends finally found him, he decided to find another quiet place -- a war in Germany. On November 10, 1619 while the army was at its winter quarters near the Danube, Descartes had the most remarkable "dream" in the history of science.
He reported a number of episodes in the dream, and one of them is usually believed to be the application of algebra to geometry and the beginning of analytic and coordinate geometry. Descartes remained a soldier for another 2 years and was even offered a lieutenant generalship. He then retired to Paris to think about the problems of "What can we know?" and "How can we know it?" . His first knowable fact was that of is own existence: "Cogito ergo sum. " ("I think, therefore I am. ") Until then Descartes had published nothing, but he had shared his discoveries and philosophical conclusions with others.
One of these, Cardinal De Berulle, convinced Descartes that he had a sacred duty to share them with the world in writing, so he went to Holland to think and write. He spent the next 20 years roaming around Holland and corresponding with the brightest minds of Europe through the only person who knew his whereabouts, Father Mersenne, an old friend from school and a mathematician. While he was finishing his great book, Le Monde, he got word that Galileo had been forced to recant the Copernican doctrine that the Earth revolves around the sun. Descartes now had a real problem: like Galileo, he believed that the Earth revolved around the sun and used it in his book, but he also believed that the Pope was infallible. His "solution" was simply to not have La Monde published until after his death. But friends, including some influential Cardinals, changed his mind, and Le Monde was published in 1637.
A few theologians condemned his work as atheistic, but nothing happened. Descartes was still in Holland happily gardening, thinking and writing when 19 year-old Queen Christina of Sweden decided that she must have him as a tutor in philosophy and mathematics. She sent a ship to fetch him to the court, but he kept the admiral waiting for several months before finally leaving for Sweden in the Fall of 1649. Christina was one of those people who did everything at a gallop. She ate little, needed little sleep, and was not bothered by the cold -- and she expected those around her to do likewise. Descartes managed to not live at the court, but Christina scheduled their philosophy class for 5 am each day, even in the cold, dark northern Winter.
Descartes died the next February of an inflammation of the lungs. Soon after Descartes' death, Le Monde was placed on the list of forbidden reading by the Catholic Church, but a powerful and useful idea is not stopped that easily. Descartes' marriage of geometry and algebra was elegantly simple and extremely powerful. It reinvigorated both algebra and geometry and was a necessary ingredient for the development of calculus 30 years later. Descartes developed techniques for some of the problems of calculus, but they were overshadowed by the simpler and more powerful techniques of Newton and Leibniz.
In 1667, Descartes' bones were taken back to France and entombed in the Pantheon in Paris. Bibliography: None
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