The German mathematician Gottfried Wilhelm Leibniz published the first
paper on calculus in 1684. Most historians agree that Isaac Newton
invented calculus eight to ten years earlier, but he was typically very
late in publishing his works. The invention of calculus marked the
beginning of higher mathematics. It provided scientists and
mathematicians with a tool to solve problems that had been too
complicated to attempt previously
No actually greeks and egyptians invented first part of it
The person who invented calculus was named Karl Weierstrass!!!
In the late seventeenth century, calculus was invented independently around the same time by two separate people : the German mathematician Gottfried Leibniz, and the English scientist Isaac Newton. It is not completely clear who first discovered it. It may well have been Newton but his work was not published for some time after he made his discovery. Certainly, Leibniz's work was the first to come to public light. Both men used different notations to describe the same concepts and it is Leibniz's notation which is in widespread use today in colleges and universities.
In the early eighteenth century, a bitter controversy erupted over who exactly had first discovered calculus. Leibniz was accused of plagiarising Newton's work. Leibniz had corresponded with Newton, and had seen some of his manuscripts. He argued, however, that these had no influence on him and that he had developed the concept independently. The Royal Society of London investigated the issue and determined that Newton had invented the calculus first. Since Newton was British, however, some suspected it of nationalistic bias.