The

formal study of calculus had begun from the 17th century by well-known mathematicians

and scientists in the world, Isaac Newton and Gottfried Leibniz. The history

itself of the calculus didn’t begin with Newton’s and Leibniz’s findings but

their calculus

was the culmination of centuries of work by other mathematicians and

contributors; it is possible that it has been at use

as early as the Greek era since its elements have appeared in ancient Greece, then in China

and the Middle East, and still later again in medieval Europe and in India. Einstein’s and

Leibniz’s

Some of the ideas that had led to integral calculus were presented

and introduced in the ancient times. These ideas seemed to be that they were

not developed systematically and rigorously. Though some of the formulas lacked

major concepts and components and were simple to begin with, calculations of

volume and area were introduced and could be found in the Egyptian Moscow

papyrus. From the period

of Greek mathematics, the method of

exhaustion was used by Eudoxus, which foreshadows the concept of the

limit, to calculate areas and volumes, eventually made Archimedes develop this idea

further, inventing heuristics which resemble the methods of integral

calculus. The method of

exhaustion was then

discovered in China by Liu Hui and Zu Gengzhi independently.

Pierre de Fermat,

the first credited mathematician because of his discovery of the process and

power rule for differentiation, had made a more logically enough way for

calculating integrals. He was one of the many that had noticed the polar

relationship between derivatives and integrals, but not the importance of this

relationship. By the early seventeenth century, here came the said two well-known

mathematicians and scientists that made everything in place in calculus.

The controversy in

calculus came up largely due to these men’s publications. While Newton had made

his discoveries and researches, his findings were not published until 1693.

Meanwhile, on the other hand, Leibniz made his discoveries after Newton and his

works were published in 1684 and 1686, before Newton. The mathematical

community discovered the differences between the dates of their discoveries and

their publications, that eventually led them asking their selves if Leibniz

truly stole Newton’s ideas and made them as if those were his own, or if they discovered

it independently.

People from the

two nations where Newton and Leibniz lived in realized that credit for the

discovery of calculus was at stake, and each party wanted their nation to be credited

from this. In 1711, this controversy was brought to court. After countless

feedbacks, reviews, findings, reasoning, and critical judgments, the

mathematical community had now realized that Newton and Leibniz had made their

discoveries independently. After Leibniz’s death, Europe continued to use

Leibniz’s notation and methods that are easy, while on the other hand, England

remained loyal to the complicated methods and notation of Newton. Because of

this, England became far behind the rest of the countries in the entire 18th

century.