History and Background of Rene Descartes

Published: 2021-03-15 13:33:40
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Rene Descartes, a French mathematician and a philosopher, was born on March 31, 1596. He was born in the beautiful city of the south of France (Touraine, France). Rene Descartes had a father named Joachim Descartes. Additionally, his father was a counselor of Congress. His fathers desire was to ensure that his son had an enabling environment for studying. Rene Descartes was admitted to Jesuit College of Henry IV to pursue his education at a tender age of eight years. He studied grammar, literature, science and mathematics at that institution for eight years.It is with great interest that he delved in mathematics studies and found it pleasurable despite his ill health (Boyer and Merzbach).

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In the year 1614, Descartes left Jesuit College of Henry IV to study civil and canon law at Poitiers. In 1616, he acquired two titles- licentiate and baccalaureate. He did spend time pursuing philosophy, health and theology. He was recruited a soldier (basically as a mercenary in the both Protestant and Catholic (Boyer and Merzbach) when he was a young man. However, his passion was deeply rooted in mathematics, and thats the reason as to why he spent many years studying the same in Paris. This was coupled with motivation from friends such as Ditch philosopher and scientist Beckham who urged him to pursue mathematics and natural science. He, therefore, concluded that his true career path in his life was the quest for real insight and natural science (Domski).

Descartes Contribution to calculus

Rene has established famous and notable contributions to mathematics, calculus in particular. Firstly, it is worth noting that, his contribution chiefly in geometry. This massive contribution earned him a name that is popular today as the father of analytical geometry. His primary interest was to bridge the gap that existed between algebra and geometry. He is, therefore, widely celebrated as being the first mathematician-cum-scientist who established the foundation of modern geometry that facilitated the development of analysis and calculus. Regarding algebra, he expressed intensively how algebraic equations can be illustrated by use of geometrical shapes and also shown in details (Domski).

While staying at Holland, he wrote the Discours de la methode (1637). In the final chapters, of the Discours, he wrote a one hundred and six paged essay in which he provided what is termed today as analytical geometry or coordinate geometry. This enhanced the learning of geometry with calculus after it was republished in Latin alongside supportive writings. Many innovations were introduced primarily in mathematics notation. These innovations are used even in the modern days (Descartes). Descartes posited that, small alphabetical letters near the beginning of the alphabet show constants, on the other hand, those towards the end stands for variables. Additionally, Rene introduced the application of numerical superscripts to denote the power of the particular quantity or number (Descartes). Symbols such as the plus sign (+), the square root sigh ( ) and the square sign (a2 ) He, however, denoted the second power as aa that is not so common in modern-day calculus (Knobloch).

Renes contribution in calculus was also predominant in the shifting of attention from curves to their actual equations. Descartes emphasized the use of tools of algebra to derive solutions of several geometric problems. Take, for instance, in finding tangents to curve. He introduced this solution by initiating a procedure that is followed to construct the normal to the curve at any particular point. Basically, in such cases, the tangent is perpendicular to the normal (Knobloch).

Descartes also contributed in part of the calculus that deals with the theory of equations. He stated that x - a is a factor of a polynomial if and only if a is a root. It is true if that the maximum number of roots is equivalent to the degree of the polynomial.

Descartes contribution in Infinitesimal Calculus

This is a branch of mathematics that entails the calculation and finding of the slope or the gradient of a given line. Infinitesimal calculus is important in calculating maxima and minima and the area covered by the curve among other importance. Earlier on, calculus was just complicated, and it was involved with integration and differentiation (Boyer and Merzbach). Descartes among other scholars like Isaac Newton contributed in this field a great deal. Descartes helped in this area by simplifying the derived formulas by expanding on the notion of the infinite variables. Additionally, he further aided in the understanding of the Cartesian plane and how infinite variables were indicated on them (Boyer and Merzbach). A great contribution in this same area is the fact that he developed functions such as horizontal and vertical Asymptotes. He made this possible by applying the infinite trait of numeric divided by zero.

To conclude, it is remarkable that Descartes contribution to mathematics and calculus particularly has helped solve problems in the modern days. The great mathematician and philosopher believed that it was only through mathematics that we can be certain and true. On the same note, he felt that it is only by learning mathematics that can help us solve complex ideas in the world into easier ideas. It is through his contribution that today we find it easy applying various concepts of analytical geometry in calculus.

Works cited

Descartes, Rene. The Geometry Of Rene Descartes. New York: Dover, 1954. Print.

Knobloch, Eberhard. ':Redefining Geometrical Exactness: Descartes Transformation Of The Early Modern Concept Of Construction.'. ISIS 96.3 (2005): 431-432. Web.

Boyer, Carl B, and Uta C Merzbach. A History Of Mathematics. New York: Wiley, 1991. Print.

Domski, Mary. 'Descartes' Mathematics'. Stanford Encyclopedia of Philosophy. N.p., 2011. Web. 9 Dec. 2015.

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