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Rene Descartes
Rene Descartes was born in 1596 A. D. in La Haye, a small town about 200 miles south of Paris. He was considered a gentleman of his time. He went to a college called La Fleche when he was eight years old. He studied the traditional languages and humanities of early times. He then studied logic, philosophy, physics and mathematics there. Because of his poor health in childhood, it was assumed that he would not live long. Taking care of his health, the teacher of the school where he studied was not so strict about attendance. He was advised by his teacher to take extended rest in the morning until he feels rested. He never gave up his habits. He was advised to wake up late during his rest periods, spending his mornings in bed meditating and writing. When he met Pascal in 1647, he was sure that he could do well in mathematics or that he could do a good job in mathematics. But no one allowed her to get up at dawn until she felt comfortable.
When he left school in 1612, he continued to follow the necessary path to a life of health, moving to Paris to enjoy social work, but this did not last long in Paris. Then again he restored the relationship with his school friends. Among them was Mersenne. Mersenne was positive about Descartes' desire to study deeply, and they spent two years studying mathematics in depth. Descartes' father was not well inclined towards the profession when he was a young man. He enrolled in the University of Poitiers to study law. In 1616 he received his degree from the said university. He entered the Army at the age of 21 as a Gate Layman, a volunteer job. He continued his studies when he had free time from his work at that time. When on November 1, 1619 in the army it was known about the risk of his life during the winter. Then during the winter, he took measures to protect himself from the cold, so it is said that the stove was lit above the room. At that time he thought about important work that he liked. Accordingly, he discovered "The foundations of a marvelous science". From this time his lifestyle and work changed as a mathematician and philosopher. He became interested in analytical geometry around this time. He wished to revise the earlier philosophy and to do more in relation to mathematical philosophy. Vartan Russell observes that Socrates meditated on snowy days but Descartes needed warm weather, indicating Descartes' state of health. It is also mentioned that he visited Europe a lot which he called Lakshya Hin. Such a tour includes countries like Holland, Germany, Hungary, Italy. Thus bewildered by Lakshya Hin's visit, he thought it wrong to wander about in his productive years, and then he chose Holland as a place to settle down. In 1621, he resigned from his army mission and devoted himself to the study of mathematics. After that he continued to search for mathematics. He died on February 11, 1650 in Stockholm.
Descartes' mathematical contributions
Descartes contributed not only to mathematics but also to the field of philosophy:
1. Publications in Philosophical Fields:
A collection of Descartes' works on philosophy appeared in 1637. He created "Discourse on the method of rightly conducting the reason in the search for truth in the sciences" which is a work in the field of philosophy which he wrote in his own mother tongue. He also used mathematical style arguments in relation to philosophy.
2. Discovery of Cartesian Geometry:
He also contributed to the development of geometry in mathematics. In the creation of La Geometrie (Geometry) in French, he emphasized three main parts. The first part is created with an emphasis on pure mathematics. Which is considered the main basis of the development of analytical geometry. He gave birth to analytical geometry by incorporating geometry and algebra. In its parts, the first and second parts included the use of algebra in geometry, while the third part included the effects of equations.
Part 1: In the first part, problems which can be constructed by means of circles and straight lines only, x,y,z were included to indicate the coordinates as we do in coordinate geometry today. It also used the exponent notation a.a=a² that we use today. In this geometrical work, he dealt with the generalization of three- and four-line punctuation. It is also known as four line locus problem. Descartes referred to this in an algebraic way. Later in 1687, Newton gave the solution geometrically.
Part 2: The second part of Descartes' work consists of "On the nature of curved lines". In this he mentioned about geometrical and mechanical (transcendental) curve, mechanical curve was later called transcendental curve by Leibniz. It has also studied about line, circle, conic section.
Apart from this his works are mentioned as follows:
• Introduced modernity in analytical geometry.
• Mentioned how area and volume can be calculated according to Algebraic structure and mentioned how it can be indicated.
• Line segments are denoted by algebraic letters.
• Mention that letters represent each area of mathematics.
• Studied about different types of curves and their characteristics in geometry.
• Initiated modernism in philosophy by writing "Principia Philosophiae".
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