The independent development of calculus by Newton and Leibniz arose from a need to be able to solve problems that involved continuous change and motion which traditional mathematics was unable to do. This need resulted in the emergence of calculus as a distinct field of study which provided a means of analyzing continuous quantities and their changes especially in scientific fields, such as physics and astronomy.

Regarding its application and impact, Calculus became the fundamental language to describe change and motion which lead to a better understanding of how the natural world functions.

The evolution of Calculus from an emergent mathematical  field to a foundation tool allowed it to become the basis for solving problems that involve continuous change.