Argument

Leibniz–Newton calculus controversy

Overview

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 invented 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 (having learned the rudiments from Erhard Weigel starting in 1663), but Newton's supporters accused Leibniz of plagiarizing Newton's unpublished ideas.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 arguably "the greatest advance in mathematics that had taken place since the time of Archimedes."

Newton began working on a form of calculus, which he called "The Method of Fluxions and Infinite Series," in 1666 at the age of 23. Although a surviving manuscript from October 1666 records this early work, it was not published until decades later in 1737 as a minor annotation in the back of one of his works. He further developed his ideas in De analysi per aequationes numero terminorum infinitas, written in 1669, and Method of Fluxions, written in 1671. Gottfried Leibniz began developing his own variant of calculus in 1674 and published his first paper on the subject, "Nova Methodus pro Maximis et Minimis," in 1684. In 1696, Guillaume de l'Hôpital published a text on Leibnizian calculus, in which he recognized that Newton's Principia of 1687 was "nearly all about this calculus." Meanwhile, Newton had presented a geometrical form of calculus in Section I of Book I of the Principia of 1687, but did not publish his eventual fluxional notation for the calculus in print until 1693 in partial form and 1704 more fully.

Today, the consensus is that Leibniz and Newton independently invented and described calculus in Europe in the 17th century. Their work was 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.

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.

On the other hand, other authors have emphasized the equivalences and mutual translatability of the methods; here Niccolò 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.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

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That gives rise to these eternal, and usually mistaken, contentions on necessity and contingency, on the possible and the impossible. But provided that it is understood that necessity and possibility, taken metaphysically and strictly, depend solely upon this question, whether the object in itself or that which is opposed to it implies contradiction or not; and that one takes into account that contingency is…
Gottfried Wilhelm Leibniz, Theodicy Essays on the Goodness of God, the Freedom of Man and the Origin of Evil
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They are, therefore, two translations of one and the same original, or, as Spinoza says, two attributes of one and the same substance, which we must call God. And these two translations, as also an infinity of others into languages which we know not, are called up and even forced into existence by the original, just as the essence of the circle is translated automatically, so to speak, both by a figure and by an…
Henri Bergson, Creative Evolution
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_That of Newton._ Passing now to the conception of Newton, it is evident that by its nature it is not exposed to the fundamental logical objections which are called forth by the method of Leibnitz. The notion of _limits_ is, in fact, remarkable for its simplicity and its precision. In the transcendental analysis presented in this manner, the equations are regarded as exact from their very origin, and the general…
Auguste Comte, The philosophy of mathematics
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Philosophers who discussed Leibniz–Newton calculus controversy

Gottfried Wilhelm Leibniz

Related ideas

Place in the tradition

Part of German philosophy.

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