Who invented calculus

Calculus is a branch of mathematics that deals with the study of limits, infinite series, continuity, derivatives and integrals. In the 17th Century, Isaac Newton and Gottfried Wilhelm Leibniz developed the theory of calculus independently.  However, there exists controversy as to who invented calculus? since both the scientists put forth their thoughts in different ways using the fundamental concepts. 

Newton explained calculus as the change in variables with time, while Leibniz defined the variables x and y as traversing over sequences of values that exist infinitely close. He stated that dx and dy are the differences between the consecutive values of the sequence. Leibniz didn’t use the concept of dy / dx that gives the tangent as the defining property. On the other hand, Newton used x’ and y’ as finite velocities to calculate the tangent. Both of them thought in terms of graphs than in terms of functions. Newton’s theory was geometrical whereas Leibniz was analytical. 

The 3 stages involved in the development of calculus involves: 

Anticipation: Areas under the curves or maximisation of certain quantities were found using the infinite processes. 

Development: Both the mathematicians curated the foundations of calculus and together brought them under the umbrella of derivative and integral calculus. 

Rigoriztion: To justify them and project it as Calculus being a concept of mathematical foundation.

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