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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