History and applications

The discoverers of calculus

Today it is generally believed that calculus was discovered independently in the late 17th century by two great mathematicians: Isaac Newton and Gottfried Leibniz. However, the dispute over who first discovered calculus became a major scandal around the turn of the 18th century.

Like most scientific discoveries, the discovery of calculus did not arise out of a vacuum. In fact, many mathematicians and philosophers going back to ancient times made discoveries relating to calculus.

The ancient Greeks made many discoveries that we would today think of as part of calculus — however, mostly integral calculus, which will be discussed in the module Integration . Indian mathematicians in Kerala had developed Taylor polynomials for functions like \(\sin x\) and \(\cos x\) before 1500. (See the article Was calculus invented in India? listed in the References section.)

In the early 17th century, Fermat developed a method called adequality for finding where the derivative of a function is zero, that is, for solving \(f'(x) = 0\). But it was not until Newton and Leibniz that gradients of tangents to curves could be calculated in general.

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