Rene Descartes Essay, Research Paper

Ren Descartes

Over the course of approximately sixty years, Ren Descartes set a precedent for mathematic excellence in the fields of algebra, geometry, and calculus. His findings lay the foundation for modern math and became a turning point between medieval and modern mathematics.2 The product of these findings was a mixture of mathematics and science that would later be created by Newton and Leibniz. This new form of mathematics would become known as Calculus.

Ren Descartes was born near Tours, France on March 31, 1596. He was born to a family of moderate wealth and was the second in a family of two sons and one daughter. At the age of eight, a young Ren Descartes found himself attending the Jesuit school of La Fl che in Anjou. There, he realized how little he actually knew, except for one subject mathematics. It was also there that Descartes developed the habit of staying in bed late due to his delicate health. Upon graduating from school, he began studying law at the University of Poitiers from which he later graduated. But, Descartes never practiced law. In 1618, he enlisted in the service of Prince Maurice of Nassau with the intentions of initiating a military career. During this time, though, Descartes found himself thinking about mathematics, so much so that it is said that his mathematical ideas came to him in his dreams on November 10th, 1619 when stationed on the Danube. This Descartes considered one of the most critical days of his life affecting him so much that he left the service.

Descartes spent the next five years traveling during which he continued to refine his mathematical concepts. He finally settled in Holland where some of his greatest mathematical theories were created. Over the following years, Descartes would write books pertaining to physics, meteorology, and, within his most famous book, La G om trie, geometry.

The ideas expressed in the latter emphasized algebra s importance in geometry. This book was the first to look at linking the two subjects together, offering the creation of coordinate geometry. This basic mathematical idea, introduces a pair of axes in a plane from which you can label any point with a pair of numbers for which there are an x and a y where all solutions lie on the same line. A problem existing with such can be solved algebraically thus, tying the two subjects together.

La G om trie was the only book related to the topic of mathematics written by Descartes. Divided into three books, the first begins with an explanation of the principles of analytical geometry. Some of this included the finding of a point where the perpendiculars on given straight lines shall be in a constant ration to the product of the perpendicular on other given straight lines.

In the second book, Descartes divided curves into two major classes. These were geometrical and mechanical curves. Descartes only expanded on the idea of geometrical curves which he defined as those which can be generated by the intersection of two lines moving parallel to one coordinate axis. Basically, he stated that dy/dx is an algebraical function.

The third book contained an analysis of the then current algebra. He noticed that mathematicians generally denoted known quantities with letters at the beginning of the alphabet and unknown quantities were denoted with letters at the end of the alphabet.

In 1649, Queen Christina of Sweden persuaded Descartes to visit Stockholm. The Queen wanted to draw tangents with him at the early hour of 5 a.m.daily. It only took a few months of walking back in forth to the palace in the cold climate to eventually catch pneumonia and die. But, Descartes story does not yet end. Seventeen years after his death, Descartes bones, except for his right hand, were returned to France, the land of his birth. The French Treasurer-General, however, secured his right hand, as a souvenir.

Over the course of his lifetime, Ren Descartes made a profound impact on many subjects, but most of all, mathematics. The ideas that Descartes pioneered led way to new forms of math including Calculus. An example of this was his intense involvement with functions. Today, students are finding the limits of functions such as Descartes had described. Calculus also deals with the area under curves- curves upon which Descartes had studied and theorized. Though Descartes did not affect Calculus at the time, the theories and ideas that he had discovered pioneered the way for further mathematicians to come.

Endnotes

1. Quotations by Ren Descartes. Feb. 2000. School of Mathematics and Statistics, University of St. Andrews, Scotland. 15 Jan. 2001. http://www-groups.dcs.st-andrews.ac.uk/ history/Quotations/Descartes.html

2. Descartes Method and Coordinate Geometry. Department of Mathematics and Computer Information Science, Mansfield University, Mansfield Pennsylvania. 15 Jan. 2001. http://www.mnsfld.edu/ rwalker/Descartes.html

References

Descartes Method and Coordinate Geometry. Department of Mathematics and Computer Information Science, Mansfield University, Mansfield Pennsylvania. 15 Jan. 2001. http://www.mnsfld.edu/ rwalker/Descartes.html

Descartes, R. 15 Jan. 2001. http://library.thinkquest.org/22584/temh3010.htm

Descartes, Ren . Microsoft Encarta Online Encyclopedia 2000. 15 Jan. 2001. http://encarta.msn.com

Quotations by Ren Descartes. Feb. 2000. School of Mathematics and Statistics, University of St. Andrews, Scotland. 15 Jan. 2001. http://www-groups.dcs.st-andrews.ac.uk/ history/Quotations/Descartes.html

Ren Descartes. School of Mathematics, Trinity College, Dublin. 15 Jan. 2001. http://www.maths.tcd.ie/pub/HistMath/People/Descartes/RouseBall/RB_Descartes.html