Mathematics is a very broad topic and has a lot of different topics, some of which you may not even know is related to mathematics. Rene Descartes is a very big part of the mathematical world, and he made many big contributions that changed the way mathematics is looked at today. Although some people might think of Descartes as a philosopher more than a mathematician, that is not true in any sense he made many contributions both to physics and mathematics, some of the areas he affected the most are geometry and calculus. Rene Descartes was a very intelligent man who was able to influence and impact many different aspects of the world and still have an impact on us today.

First I will start out with the basics about Rene Descartes, Rene was a French philosopher and mathematician who made many outstanding discoveries in the field. Rene Descartes was born on March 31st in 1596 in France and he died at the age of 53 on February 11th, 1650 in Stockholm, Sweden. Descartes had a sister and two brothers, and his mother passed away at a very young age, later in life he had a daughter as well. Early on in his life, his father sent Rene and his siblings to live with their grandmother. Descartes would then go on to attend the boarding school Jesuit college of Henri IV, and later on in life would attend the University of Poitiers. Over the span of his career, he managed to be named a mathematician, a scientist, and a philosopher, as he was able to impact all of those fields with his findings.

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One of the more outstanding feats that Rene Descartes was able to achieve during his time of being a mathematician was being able to discover the Cartesian Coordinates. This is something that everyone has used during some part of their life, whether it be in middle school or in college you have used this in a math class at some point. The Cartesian Coordinates is basically graphing a point on a grid, and you are able to graph that point because it has a location that is described by a vertical and horizontal number, for example (3,2) these numbers make it unique to where the location of the point is. In the article 17th Century Mathematicians- Descartes it states “He used perpendicular lines (or axes), crossing at a point called the origin, to measure the horizontal (x) and vertical (y) locations, both positive and negative, thus effectively dividing the plane up into four quadrants.”(17th Century Mathematicians- Descartes). This describes how the grid is split up, it is divided into four sections, which determine whether the point is positive or negative. All points are based on the origin, which is (0,0) on the plane. Not only are you able to plot points on the plane, but you can also graph lines or shapes, which are represented by equations. For example in the article 17th Century Mathematicians- Descartes it states “y = x yields a straight line linking together the points (0,0), (1,1), (2,2), (3,3), etc. The equation y = 2x yields a straight line linking together the points (0,0), (1,2), (2,4), (3,6), etc.”(17th Century Mathematicians- Descartes). These are only some of the things that can be graphed on the Cartesian Coordinate Plane, there are numerous other equations that can be represented on the plane. Descartes made it possible to solve equations both graphically and algebraically, which is a huge accomplishment in the world of mathematics, I believe that this is possibly the most notable thing that Descartes was able to contribute to the world of mathematics, he changed the way we look at equations and graphing and made it much easier and less of a hassle.

It may seem like the discovery of the Cartesian Coordinate System would be Rene Descartes most significant accomplishment, but that is not necessarily the case. He also has helped in other areas of math too, one of the main areas being calculus. As stated by Anirudh in Rene Descartes 10 Major Accomplishments “Descartes developed his rule of signs, a technique for determining the number of positive or negative real roots of a polynomial.”(Anirudh). Descartes developed a rule to help distinguish what is positive and negative roots, this is useful in math where you have to use polynomials. These rules became important for future mathematicians who studied and did research in the field of calculus.

One of the many things that he was known for over his career would be his discoveries in philosophy. He was able to become the “Father of Modern Philosophy” with the outstanding findings he had in the field. The main thing that he was able to find in the field of philosophy was the idea of Mind-Body Dualism. This was basically being able to distinguish the differences between the physical being of the body and the mental state of the mind. In Gary Hatfield’s Encyclopedia, it states “He has merely relied on the fact that he can doubt the existence of matter to conclude that matter is distinct from the mind.”(Gary Hatfield). This is basically showing the mind and body are two separate beings, thus forming the basis of his philosophy.

Since I have only studied bits and pieces of things about Rene Descartes, I was unaware of many of the things that he has accomplished. There are a few things that I found to be the most notable things about Rene Descartes, his contributions to mathematics changed the way that we look at mathematics and solve problems. The main things that I found to be the most outstanding thing that he has done would be founding the Cartesian Coordinate Plane, this opened up a whole new way of solving equations, and made mathematics much more diverse. Another piece that is not talked much about in this essay would be his influence and findings in the field of philosophy as he is known to be the “Father of Modern Philosophy” he had many breakthrough findings in that field which would make him very notable in that field as well.

Rene Descartes was a very smart man as he made many discoveries in many different fields, some in math some not. One of these fields he happened to impact would be physics. Descartes would end up being one of the people who helped Isaac Newton develop the law of motion, he set some of the laws of motion prior to Isaac Newton. As stated by Anirudh in Rene Descartes 10 Major Accomplishments “His first law states “that each thing always remains in the same state; and consequently, when it is once moved, it always continues to move”(Anirudh). while his second law holds that “all movement is, of itself, along straight lines.” These two laws were Rene Descartes contribution to the law of motion. Not only did Descartes discover a part of the law of motion, but he discovered many other laws as well. Some of these laws include the law of reflection, the law of refraction, and part of the law of conservation of mechanical momentum. Rene Descartes was able to influence our society in many ways that I didn't think were possible, when I looked at math I did not once think of Rene Descartes, after doing my research and seeing all the fields and areas of mathematics he was able to reach out and influence my view has changed.

## Works Cited

- Anirudh. “Anirudh.” Learnodo Newtonic, 11 Sept. 2018, https://www.learnodo-newtonic.com/rene-descartes-contribution.
- Descartes - 17th Century Mathematics - The Story of Mathematics, https://www.storyofmathematics.com/17th_descartes.html.
- Hatfield, Gary. “René Descartes.” Stanford Encyclopedia of Philosophy, Stanford University, 16 Jan. 2014, https://plato.stanford.edu/entries/descartes/.