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.