What is the origin of calculus, and who invented it?

While calculus was systematically developed in the 17th century, its core ideas have roots that stretch back to ancient times. However, the creation of a unified, powerful system is credited to two mathematicians who worked independently: Sir Isaac Newton and Gottfried Wilhelm Leibniz.

This led to one of the most famous intellectual disputes in history.

• Sir Isaac Newton (England): Newton began developing his version of calculus in the 1660s to solve problems in physics. He needed new mathematical tools to describe his laws of motion and universal gravitation. He thought in terms of "fluxions" (which we now call derivatives) to describe the rate at which quantities change. However, he was hesitant to publish his work.
• Gottfried Wilhelm Leibniz (Germany): A decade later, Leibniz developed his own version of calculus to tackle geometric problems, such as finding the tangent to a curve. His great contribution was creating the elegant notation that we still use today, including the dy/dx notation for derivatives and the long 'S' symbol (∫) for integrals. He published his work before Newton.

The Controversy: Because Leibniz published first, but Newton's work was technically earlier, a bitter dispute arose over who invented it. Today, historians agree that they both deserve credit for inventing calculus independently.