An article written by Simon Harding and Paul Scott titled “The History of Calculus” explains the very beginnings and evolutions of calculus. Harding and Scott begin their article by explaining how important calculus is to almost every field, claiming that “…in any field you could name, calculus… can be found,” (Harding, 1976). I agree with this statement completely, and can even support it with examples of its uses in various fields like engineering, medicine, management, and retail. All of these utilize calculus in some way, shape, or form, even if it is a minute.
The authors of this article also pose a few questions at the end of their introduction, regarding the “who what and when’s” of the founding of calculus. In an attempt to satisfy their questions, Harding and Scott take look at the history of the famous philosopher, and one of the founders of calculus, Archimedes.
The subsection about Archimedes describes Ancient Greece, and how countless citizens of the area yearned to know how their world functioned. They depended on mathematicians and philosophers to inform them of the structure of the universe. One of the most renowned philosophers of the time, Archimedes of Susa, became one of the forefathers of calculus with his method of finding the area of shapes that were previously impossible to figure (Harding, 1976). Harding and Scott focused mainly on this method of Archimedes, which was known as the “method of exhaustion,” (Harding, 1976). By his method, Archimedes could calculate the areas of formerly impossible figures by using infinitely smaller, possible shapes within the impossible one. An example that the authors claim to be extremely well-known was his approximation of the area of a circle using tangent lines and polygons. Archimedes found that the more sides that a polygon had, the closer it was to the true area of the circle. This eventually led to the fundamental theory of limits. The authors extend into more detail about Archimedes’ theories and calculations, including the discovery of pi, and differences between his geometric style and our more algebraic one (Harding, 1976).
After Harper and Scott further discuss the works of Archimedes, they jump ahead to the sixteenth century, when astronomy and rapid mechanical inventions that required calculus were prevalent. During this time, there were multiple mathematicians who made substantial contributions to the field, but the two that are referred to as the fathers of modern calculus are Sir Isaac Newton and Gottfried Leibniz. What makes these two so intriguing and noteworthy is that both of them separately came to the same answers at the same time, but neither could show the beginnings of his work, only that it did work every time. The authors said that this coincidence caused a rivalry between the two, each thinking that the other stole his work. Eventually, Newton was given a position on London’s Royal Society, where he was said to have used his prestige to sway the public...