Leibniz–Newton calculus controversy

The calculus controversy (often referred to with the German term Prioritätsstreit, meaning "priority dispute") was an argument between 17th-century mathematicians Isaac Newton and Gottfried Leibniz (begun or fomented in part by their disciples and associates) over who had first invented the mathematical study of change, calculus. It is a question that had been the cause of a major intellectual controversy, one that began simmering in 1699 and broke out in full force in 1711.

Newton claimed to have begun working on a form of calculus (which he called "the method of fluxions and fluents") in 1666, at the age of 23, but did not publish it except as a minor annotation in the back of one of his publications decades later (a relevant Newton manuscript of October 1666 is now published among his mathematical papers). Gottfried Leibniz began working on his variant of calculus in 1674, and in 1684 published his first paper employing it, "Nova Methodus pro Maximis et Minimis". L'Hôpital published a text on Leibniz's calculus in 1696 (in which he recognized that Newton's Principia of 1687 was "nearly all about this calculus"). Meanwhile, Newton, though he explained his (geometrical) form of calculus in Section I of Book I of the Principia of 1687, did not explain his eventual fluxional notation for the calculus in print until 1693 (in part) and 1704 (in full).

The last years of Leibniz's life, 1710–1716, were embittered by a long controversy with John Keill, Newton, and others, over whether Leibniz had discovered calculus independently of Newton, or whether he had merely invented another notation for ideas that were fundamentally Newton's. Newton manipulated the quarrel. The most remarkable aspect of this struggle was that no participant doubted for a moment that Newton had already developed his method of fluxions when Leibniz began working on the differential calculus. Yet there was seemingly no proof beyond Newton's word. He had published a calculation of a tangent with the note: "This is only a special case of a general method whereby I can calculate curves and determine maxima, minima, and centers of gravity." How this was done he explained to a pupil a full 20 years later, when Leibniz's articles were already well-read. Newton's manuscripts came to light only after his death.

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