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, these focus on limits, functions, derivatives and integrals. Calculus has many applications in science, economics, 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 invented calculus first and whether anyone plagiarized their contemporaries. However, although feuds were ubiquitous at the time, this one was so infamous because of the high profile of the men involved. Newton is said to have invented calculus in 1665 in his personal books, but he was too afraid to publish it due to his anticipation 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 Should Not Be Banned”? Get the original essay Additionally, the argument that Newton plagiarized Leibniz is flawed because when this article was written in 1655, Leibniz was 20 years old and therefore knew little about mathematics. However, before this, the idea of ​​calculation had already been invented by the ancient Greeks, notably Archimedes. He had many great inventions that helped in the development of mathematics, science, and philosophy, but among these was, some say, his greatest invention. This is the invention of “integral calculus”. Thanks to this, he measured the section of the areas surrounded by geometric figures. He divided the sections into a number of rectangles and then added up the areas. This principle is known as “integration.” “Differential calculus” is also part of the discovery of “integral calculus”. He calculated ways to approximate the slope of the tangent lines in his figures. Further back in the ages, in the Middle East, a mathematician called Alhazen derived a formula for the sum of fourth powers. He then used these results to perform calculations now known as integration. Additionally, in the 14th century, the Indian mathematician Madhava of Sangamagrama enunciated components of calculus such as infinite series and approximations of Taylor series. However, Madhava was not able to combine two different ideas under the two main branches of calculus, integrals and derivatives. Moreover, he was not able to show a distinct connection between the two and transform the calculus as it is today. Interestingly, there are mathematicians, scientists and philosophers in Europe who predate Newton and Leibniz, including Isaac Barrow, René Descartes, Pierre de Fermat, Blaise Pascal and John Wallis. Fermat notably invented a method of adequacy to determine the maxima, minima and tangents to various curves closely linked to differentiation. This led Isaac Newton to admit that his early ideas about calculus came directly from Fermat's adequacy. Additionally, the first complete proof of the Fundamental Theorem of Calculus was devised by Isaac Barrow. Both Newton and Leibniz had different views on the fundamental concepts of calculus. Furthermore, while Leibniz considered the variables x and y to extend.