Leibniz–Newton calculus controversy
Public dispute between Isaac Newton and Gottfried Leibniz (beginning 1699) / From Wikipedia, the free encyclopedia
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In the history of calculus, the calculus controversy (German: Prioritätsstreit, lit. 'priority dispute') was an argument between the mathematicians Isaac Newton and Gottfried Wilhelm Leibniz over who had first invented calculus. The question was a major intellectual controversy, which began simmering in 1699 and broke out in full force in 1711. Leibniz had published his work first, but Newton's supporters accused Leibniz of plagiarizing Newton's unpublished ideas. Leibniz died in 1716, shortly after the Royal Society, of which Newton was a member, found in Newton's favor. The modern consensus is that the two men developed their ideas independently.
Newton said he had 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[1]). 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,[2] did not explain his eventual fluxional notation for the calculus[3] in print until 1693 (in part) and 1704 (in full).
The prevailing opinion in the 18th century was against Leibniz (in Britain, not in the German-speaking world). Today the consensus is that Leibniz and Newton independently invented and described the calculus in Europe in the 17th century.
It was certainly Isaac Newton who first devised a new infinitesimal calculus and elaborated it into a widely extensible algorithm, whose potentialities he fully understood; of equal certainty, differential and integral calculus, the fount of great developments flowing continuously from 1684 to the present day, was created independently by Gottfried Leibniz.
— Hall 1980: 1
One author has identified the dispute as being about "profoundly different" methods:
Despite ... points of resemblance, the methods [of Newton and Leibniz] are profoundly different, so making the priority row a nonsense.
— Grattan-Guinness 1997: 247
On the other hand, other authors have emphasized the equivalences and mutual translatability of the methods: here N Guicciardini (2003) appears to confirm L'Hôpital (1696) (already cited):
the Newtonian and Leibnizian schools shared a common mathematical method. They adopted two algorithms, the analytical method of fluxions, and the differential and integral calculus, which were translatable one into the other.
— Guicciardini 2003, at page 250[4]