Development of Calculus

Calculus, being a difficult subject, therefore requires much more than the intuition and genius of one man. It took the work and ideas of many great men to establish the advanced concepts now known as calculus. Of the many mathematicians involved in the discovery of calculus, Gottfried Wilhelm von Liebniz and Sir Isaac Newton were the most important. Together, they established the basic principles of calculus, and, with the help of other mathematicians, it was refined using the concept of the limit. The developemtn of calculus can be thought of as being in three periods; Anticipation, Development, and Rigorization. During the Anticipation, various mathematicians provided the stepping stones to build the concepts of calculus. During the Development, Newton and Liebniz developed the main concepts and prinicples used today. In the Rigorization, various mathematicians used the concept of the limit to give concrete meaning to the principles developed my Leibniz and Newton.

The Anticipation of calculus started way back in the time of ancient Greece, when, at around 450BC, the philosopher Zeno of Elea made this conjecture:

If a body moves from A to B then before it reaches B it passes through the mid-point, say B1 of AB. Now to move to B1 it must first reach the mid-point B2 of AB1. Continue this argument to see that A must move through an infinite number of distances and so cannot move.