Theformal study of calculus had begun from the 17th century by well-known mathematiciansand scientists in the world, Isaac Newton and Gottfried Leibniz.
The historyitself of the calculus didn’t begin with Newton’s and Leibniz’s findings buttheir calculuswas the culmination of centuries of work by other mathematicians andcontributors; it is possible that it has been at useas early as the Greek era since its elements have appeared in ancient Greece, then in Chinaand the Middle East, and still later again in medieval Europe and in India. Einstein’s andLeibniz’s Some of the ideas that had led to integral calculus were presentedand introduced in the ancient times. These ideas seemed to be that they werenot developed systematically and rigorously. Though some of the formulas lackedmajor concepts and components and were simple to begin with, calculations ofvolume and area were introduced and could be found in the Egyptian Moscowpapyrus. From the periodof Greek mathematics, the method ofexhaustion was used by Eudoxus, which foreshadows the concept of thelimit, to calculate areas and volumes, eventually made Archimedes develop this ideafurther, inventing heuristics which resemble the methods of integralcalculus.
The method ofexhaustion was thendiscovered in China by Liu Hui and Zu Gengzhi independently. Pierre de Fermat,the first credited mathematician because of his discovery of the process andpower rule for differentiation, had made a more logically enough way forcalculating integrals. He was one of the many that had noticed the polarrelationship between derivatives and integrals, but not the importance of thisrelationship.
By the early seventeenth century, here came the said two well-knownmathematicians and scientists that made everything in place in calculus.The controversy incalculus came up largely due to these men’s publications. While Newton had madehis discoveries and researches, his findings were not published until 1693.Meanwhile, on the other hand, Leibniz made his discoveries after Newton and hisworks were published in 1684 and 1686, before Newton. The mathematicalcommunity discovered the differences between the dates of their discoveries andtheir publications, that eventually led them asking their selves if Leibniztruly stole Newton’s ideas and made them as if those were his own, or if they discoveredit independently.People from thetwo nations where Newton and Leibniz lived in realized that credit for thediscovery of calculus was at stake, and each party wanted their nation to be creditedfrom this. In 1711, this controversy was brought to court. After countlessfeedbacks, reviews, findings, reasoning, and critical judgments, themathematical community had now realized that Newton and Leibniz had made theirdiscoveries independently.
After Leibniz’s death, Europe continued to useLeibniz’s notation and methods that are easy, while on the other hand, Englandremained loyal to the complicated methods and notation of Newton. Because ofthis, England became far behind the rest of the countries in the entire 18thcentury.