THE Great Sulk
Although they worked independently, the discovery of calculus is credited to these two men, Sir Isaac Newton and Gottfried Wilhelm von Leibniz. It is important to realize that there were other mathematicians whose work dealt with many of the fundamentals of calculus. For example, Archimedes (287-212 B.C.), one of the greatest mathematicians of all time, understood the concept of limits, calculated pi, and found the area under a curve. Pierre Fermat also found a method of finding maxima and minima, something that we recognize as setting the derivative equal to zero.
When Newton was a student at Cambridge, the institution was forced to close due to an outbreak of the Plague; after which Newton developed 'fluxions' (his term for differential calculus) at the age of 22. During this time, Newton also created his famous three laws of motion and a universal theory for gravity. In fact, 'fluxions' were the means by which Newton was able to find these physics principles. Drawing upon the work of Fermat, Newton figured out how to find the slope of the tangent for a point on a parabolic curve; this is the derivative. After this, he saw that finding the area under the curve (the integral) was the reverse of finding the derivative. This concept is the fundamental theorem of calculus. With this, Newton was able to find the velocity, accerleration, and position of an apple. Today, we apply these equations to a number of things, including the orbit of planets around the sun, the rate that food cools, or how much interest accumulates in a savings account.
Preferring not to publish his work immediately, Newton contrasted with Leibniz, who was very vocal about his discoveries. When Newton presented his work on calculus by publishing an essay in 1704 called "On the Quadrature of Curves", Leibniz was already known for his work on calculus. As you can imagine, the confusion over who truly discovered calculus led to a feud between the two men that was later called the "Great Sulk". The Royal Society of England credited Newton with the discovery in 1715, and Leibniz wasn't given joint credit until his death in 1716.
Today, we know that Newton and Leibniz worked independently and that Newton developed calculus about 8 years prior to Leibniz. Still, much of the notation ( such as 'dy/dx' ) that is used in calculus is the sole contribution of Leibniz. He also came up with the term 'calculus'. Apparently, he is even responsible for the universalization of the '=' symbol. He was also very accomplished, and was a philosopher, scientist, logician, diplomat and a lawyer. Newton went on to be a internationally known scientist and mathematician as well, and today he is considered to be the father of modern physics due to his work in the Principia and Opticks.