Calculus is the branch of mathematics that studies the rates of change of objects in the universe. There are two main branches of calculus, differentiation and integration, which focus on limits, functions, derivatives, and integrals. Calculus has widespread applications in science, business, and engineering and can solve many problems for which algebra alone is not sufficient. The history of calculus is perhaps one of the most controversial topics in the history of mathematics. Calculus was officially invented in the 17th century by two mathematicians Sir Isaac Newton and Gottfried Leibniz. The controversy lies in who first invented calculus and whether anyone plagiarized their peers. However, although arguments were ubiquitous at the time, this one was so infamous due to the prestigious nature of the men involved. Newton is said to have invented calculus in 1665 in his personal books, but was too afraid to publish it due to the prediction of negative reactions. He later published it in his famous book titled “Philosophiæ Naturalis Principia Mathematica”, published in 1687, which is also considered the most influential book in the history of science. Say no to plagiarism. Get a tailor-made essay on "Why Violent Video Games Shouldn't Be Banned"? Get an original essay Furthermore, the argument that Newton plagiarized Leibniz is incorrect since when it was written in 1655, Leibniz was 20 years old and therefore knew little about mathematics. However, before that, the idea of ​​infinitesimal calculus had already been invented by the ancient Greeks, in particular by Archimedes. He had many great inventions that help the development of mathematics, science and philosophy, but among them was, according to some, his greatest invention. This is the invention of “integral calculus”. Using it, he measured the section of the areas surrounded by geometric figures. He divided the sections into a series of rectangles and then added the areas. This principle is known as 'integration'. Also part of the discovery of 'integral calculus' is 'differential calculus'. He calculated ways to approximate the slope of the tangent lines of his figures. Later in the Middle East, a mathematician named Alhazen derived a formula for the sum of fourth powers. He then used these results to perform calculations that are now known as integration. Furthermore, in the 14th century, the Indian mathematician Madhava of Sangamagrama declared components of calculus such as infinite series and Taylor series approximations. However, Madhava was unable to combine two different ideas under the two main branches of calculus, integral and derivative. Furthermore, he was unable to show a distinct connection between the two and transform calculus into what it is today. Interestingly, there are mathematicians, scientists and philosophers in Europe who precede Newton and Leibniz, including Isaac Barrow, René Descartes, Pierre de Fermat, Blaise Pascal and John Wallis. In particular, Fermat invented an adequacy method for determining the maxima, minima, and tangents of various curves that were closely related to differentiation. This led Isaac Newton to admit that his first ideas about calculus came directly from Fermat's adequacy. Furthermore, the first complete proof of the fundamental theorem of calculus was devised by Isaac Barrow. Newton and Leibniz both thought differently about the fundamental concepts of calculus. Furthermore, while Leibniz thought that the variables x and y spanned sequences or were infinitely close, Newton considered variables that changed.