The calculus studied today is defined as the mathematical study of limits, functions, derivatives, integrals, and infinite series, but; calculus was not always as advanced and complex. The long history of calculus traces all the way back to ancient Greece. The ancient Greeks were extremely advanced in their mathematical skills. The Greeks invented calculus to solve the values of “holes”. They understood numbers as ratios of integers. This understanding caused the Greeks to believe that there were “holes” in the number line. To solve for the unknown “holes,” the Greeks developed a system of lengths and volumes, which became the foundation of the calculus we know today.

In 450 BC, Greek philosopher, Zeno of Elea advanced ancient calculus, by developing a series of problems based on the infinite. Zeno’s paradoxes argued that motion is impossible. His work articulated the idea of paradoxes and the infinitesimals they create, thus advancing the ideals behind calculus.

In 370 BC, calculus developed further with the method of exhaustion. Greek mathematicians, Antiphon and Exodus formulated the method of exhaustion. The method of exhaustion calculates the area and volume of regions and solids by categorizing them into an infinite number of common shapes. Archimedes of Syracuse improved this method by inventing heuristic methods, which are still resembled in today’s methods.

The most decisive step towards current day calculus was developed independently by both Isaac Newton and Gottfried Leibniz. Prior to Newton and Leibniz, the term calculus was a general term, referring to any form of mathematics.

Both mathematician studied calculus during the Hellenistic period. When they were living, Newton and Leibniz were rivals, fighting for the title over who first invented calculus. Though they were rivals, the men understood calculus in differing ways, each offering equally essential contributions to the development of modern calculus. Read the rest of this entry »