# The Development of Calculus and My Routinary Activities Connected with Calculus

Calculus - A subject that has amassed over different concepts, theorems, and the like. Its complex structure is that of a key figure in the world of mathematics. As far as history goes, the invention of calculus was a great advancement; a marvelous achievement to be added to the world of science. Calculus was big at the time for its breakthrough in the field of research, physics, and science overall. So, with all this talk of calculus there is one question that comes to mind: who came up with it? Obviously for something to be discovered, there should be someone behind it; every invention has its inventor. Therefore, we would have to assume in one way or another that calculus has an inventor. But, who exactly? Well, with further research into the topic, there are top two names – both of which have prominent roles in the early stages of calculus. These two names are also well known in the scientific world for each of their contributions to the field. These two prominent names are none other than Sir Isaac Newton and Gottfried Leibniz themselves.

As mentioned earlier, these two individuals are well known and have solidified positions in the field of science and the latter. They are both highly respected for their works and contributions. With that, it has always been an ongoing debate for which person was solely responsible for the creation (rather, discovery) of calculus. Why is that, exactly? I, for one, am not sure. I honestly do not care if calculus must have only one inventor or discoverer. However, I have indeed read about how Sir Isaac Newton tried to expose his colleague Gottfried Leibniz for plagiarism of his own works at one point. Perhaps that is the reason why the debate exists in the first place – it started as a controversy between these two prominent names of which one or the other deserves the rightful credit. I will, of course, get back to that later on but for now, let us get an overview of the situation of both these characters. This long-running debate is alternatively termed the “calculus controversy” for its overall importance in the subject matter itself. To start this off, we must take a look at each of these two contributors and their background in order to come up with a hypothesis on which one comes on top and triumphant.

First, let us take a look at the famous and critically acclaimed Sir Isaac Newton. Now, Sir Isaac Newton was a well-known and highly reputable English mathematician. Sir Isaac Newton is responsible for the discovery of gravity, the creation and establishing of the three laws of motion, and the formulation of the color spectrum through the scattering of white visible light as we know of it today. Isaac Newton has also developed an empirical law of cooling, discovered the universally revered binomial theorem, and moved the British pound into the gold standard. To add to this, of course, Newton provided the field of science with calculus, a study that he proposed in his famous book Principia Mathematica, which is considered to be one of the greatest books ever written for the field of mathematics, physics, and science.

Now, how about Leibniz? Do not take this man lightly, either; he, too, has had some major contributions to the field of science on his own accord. Gottfried Wilhelm Leibniz was a German mathematician who developed the binary system that serves as the basis of all modern electronic devices we use today, contributed some of his ideas and thoughts to the theory of everything (also known as the monadology), and invented modern formal logic. Gottfried Leibniz is also known for anticipating the discoveries of Albert Einstein with his own metaphysical theory of dynamism, theorized about an early computer to solve algebraic expressions, and explored the field that is now known as the field of topology. In addition to all of his marvelous works and contributions, Leibniz is known to have provided the field of science with calculus in his own different method and way.

Strangely enough, both of these two men invented calculus in their own methods until they died and the two individuals left the world believing that only one man can claim all the credit for the discovery or invention of calculus. In 1666, Sir Isaac Newton was one of the countless and many students at Cambridge University who were sent home on account of the great plague at the time. In his spare time, Newton developed what we now know as calculus in order to solve physics problems. However, he called calculus the method of fluxions at first. Fluxion is his term for a derivative of a continuous function. Sir Isaac Newton mainly used geometric proofs for his new theory and relied on limits and concrete reality rather than concepts in theory. However, as was typical with Newton, he withheld his extraordinary findings for many years refusing to publish them for the rest of the world. Meanwhile, Gottfried Leibnitz began working on his form of calculus in 1674 while staying in Paris. On November 11th of 1675, he made a breakthrough finding the area under the graph of the function y equals f of x (or written as y=f(x)). He invented a whole new system of notation for his discovery using an elongated letter S for the latin word “summa” for integration and D for the latin word “differentia” for differentials. Leibniz published his first account of differential calculus in 1684 and then published an explanation of integral calculus in 1686. A year later, Newton finally got around to publishing his findings and produced the Principia Mathematica. In the book, he described his famous law of motion, his law of universal gravitation, and a derivation of Kepler’s laws of planetary motion. Throughout the book, Newton used calculus to back up his physical theories. However, since Leibniz had published first, it was he who took sole credit for this amazing new field of mathematics. In the big picture, both of these men are responsible for calculus. Newton simply lacked a standard notation and heavily relied on geometric proofs of infinitesimals. Leibniz and Newton both based their work on this concept. Infinitesimals were (as stated) quantities that were not zero yet smaller in absolute value than any real number. They were necessary because the concept of the limit was not fully flourished. Infinitesimals were on ungrounded philosophical and mathematical bases and many refused to accept calculus based on these infirm ideas. By this time, Newton set out on a mission to expose Leibniz for plagiarism. He argued that Leibniz had connections to him and some of Newton’s unpublished writings may have found a way into Leibniz’s hands. The two men have also corresponded through letters quite recently through sharing ideas about mathematics. In the end, Newton was presumed to have won over the debate, since he had amassed more friends and supporters compared to Leibniz. So, even though Newton was more circulated as the prime creator of calculus, it is still reasonable to suggest that both men have developed calculus in their own different and special methods.

To keep this essay brief, I shall deliver my three routinary activities in a few sentences. The first routinary activity that involves calculus is setting my alarm at 5:55 am. The trick here is I do not usually get up and out of bed right after the alarm goes. In order to counter this and the potential waste of time, I set the alarm at 5:55 so that I do not have to get up after 6 am. I can be aware that I am awake before 6 since that is the time when I should get ready for school. The limit that I want to set is 6 but I should try not to wake up exactly at 6 since I want to be early. The second activity is the amount of rice I put on my plate. Of course, moderation of food should always be observed. The number of rice cups should be reflective of the person, as is the method done by people in a diet. For me, my moderation should limit to about 4 cups of rice. This should be my limit and it must not go over that number. The last activity is my time on the computer. For some time now, my eyes have become strained from the long exposure I endure at night. In order to remedy this, I have decided to limit my use of the computer to 3 hours at maximum. Now, that is my limit for my moderation.

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