Leibniz–Newton calculus controversy

In the history of calculus, the calculus controversy (German: Prioritätsstreit, lit. 'priority dispute') was an argument between mathematicians Isaac Newton and Gottfried Wilhelm Leibniz over who had first discovered calculus. The question was a major intellectual controversy, beginning in 1699 and reaching its peak in 1712. Leibniz had published his work on calculus first, but Newton's supporters accused Leibniz of plagiarizing Newton's unpublished ideas. The modern consensus is that the two men independently developed their ideas. Their creation of calculus has been called "the greatest advance in mathematics that had taken place since the time of Archimedes."

Newton stated he had begun working on a form of calculus (which he called "The Method of Fluxions and Infinite Series") in 1666, at the age of 23, but did not publish it until 1737 as a minor annotation in the back of one of his works 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 prevailing opinion in the 18th century was against Leibniz (in Britain, not in the German-speaking world). Today, the consensus is Leibniz and Newton independently invented and described calculus in Europe in the 17th century, with their work noted to be more than just a "synthesis of previously distinct pieces of mathematical technique, but it was certainly this in part".

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, on page 250