Leibniz–Newton calculus controversy

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".

Today the consensus is that Leibniz and Newton independently invented and described the 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".

They adopted two algorithms, the analytical method of fluxions, and the differential and integral calculus, which were translatable one into the other.In the 17th century, as at the present time, the question of scientific priority was of great importance to scientists.

However, during this period, scientific journals had just begun to appear, and the generally accepted mechanism for fixing priority by publishing information about the discovery had not yet been formed.

The first of them occurred at the beginning of 1673, during his first visit to London, when in the presence of the famous mathematician John Pell he presented his method of approximating series by differences.

To Pell's remark that this discovery had already been made by François Regnaud and published in 1670 in Lyon by Gabriel Mouton, Leibniz answered the next day.

Leibniz, who learned about this, returned to Paris and categorically rejected Hooke's claim in a letter to Oldenburg and formulated principles of correct scientific behaviour: "We know that respectable and modest people prefer it when they think of something that is consistent with what someone's done other discoveries, ascribe their own improvements and additions to the discoverer, so as not to arouse suspicions of intellectual dishonesty, and the desire for true generosity should pursue them, instead of the lying thirst for dishonest profit."

To illustrate the proper behaviour, Leibniz gives an example of Nicolas-Claude Fabri de Peiresc and Pierre Gassendi, who performed astronomical observations similar to those made earlier by Galileo Galilei and Johannes Hevelius, respectively.

[12] Newton's approach to the priority problem can be illustrated by the example of the discovery of the inverse-square law as applied to the dynamics of bodies moving under the influence of gravity.

Based on an analysis of Kepler's laws and his own calculations, Robert Hooke made the assumption that motion under such conditions should occur along orbits similar to elliptical.

The Dutchman Simon Stevin (1548–1620), the Italian Luca Valerio (1553–1618), the German Johannes Kepler (1571–1630) were engaged in the development of the ancient "method of exhaustion" for calculating areas and volumes.

This evidence, however, is still questionable based on the discovery, in the inquest and after, that Leibniz both back-dated and changed fundamentals of his "original" notes, not only in this intellectual conflict, but in several others.

[16] If good faith is nevertheless assumed, however, Leibniz's notes as presented to the inquest came first to integration, which he saw as a generalization of the summation of infinite series, whereas Newton began from derivatives.

It is known that a copy of Newton's manuscript had been sent to Ehrenfried Walther von Tschirnhaus in May 1675, a time when he and Leibniz were collaborating; it is not impossible that these extracts were made then.

It is, however, worth noting that the unpublished Portsmouth Papers show that when Newton went carefully into the whole dispute in 1711, he picked out this manuscript as the one which had probably somehow fallen into Leibniz's hands.

Those who question Leibniz's good faith allege that to a man of his ability, the manuscript, especially if supplemented by the letter of 10 December 1672, sufficed to give him a clue as to the methods of the calculus.

In 1696, already some years later than the events that became the subject of the quarrel, the position still looked potentially peaceful: Newton and Leibniz had each made limited acknowledgements of the other's work, and L'Hôpital's 1696 book about the calculus from a Leibnizian point of view had also acknowledged Newton's published work of the 1680s as "nearly all about this calculus" ("presque tout de ce calcul"), while expressing preference for the convenience of Leibniz's notation.

I have enjoyed little leisure, being so weighted down of late with occupations of a totally different nature.In any event, a bias favouring Newton tainted the whole affair from the outset.

The Royal Society, of which Isaac Newton was president at the time, set up a committee to pronounce on the priority dispute, in response to a letter it had received from Leibniz.

[21] At the end of 1715, Leibniz accepted Johann Bernoulli's offer to organize another mathematician competition, in which different approaches had to prove their worth.

His next study, entitled "Observations upon the preceding Epistle", was inspired by a letter from Leibniz to Conti in March 1716, which criticized Newton's philosophical views; no new facts were given in this document.