If it takes two to make a quarrel, it takes two men of genius to make a famous quarrel. If Newton is one of the half-dozen mightiest figures in the history of science, Gottfried Wilhelm Leibniz enjoys an equal eminence in the history of philosophy. And though in the folk culture of the Germans Leibniz may stand as a lesser man than Goethe, just as in Anglo-Saxon eyes Newton must bow to Shakespeare, by more formal standards each appears as the dominant figure of an aspect of European intellectual life. It is perhaps not accidental that they were contemporaries, Newton's life-span exceeding Leibniz's by a few years at either end, for this was the moment when European intellectual development toward freedom and maturity offered the highest opportunity for creativity. This was the point of flexure on its growth curve. Of course, both Newton and Leibniz were men of transition, thinking for the future with minds conditioned by the past. It might be imagined, perhaps, that Newton the scientist, the man of numbers rather than words, belonged more decisively to the new age than did Leibniz, of whom it has been written that “he is, in relation to the new scientists [of the seventeenth century], a man sunk deep in medieval conceptions, a weaver of metaphysical systems, a believer in the necessary unity of theology, philosophy and science.”

In telling this story of the bitter quarrel between two of the greatest men in the history of thought, the most notorious of all priority disputes, I have not attempted to enter into the technical details of the evolution of the differential and integral calculus and have tried rather to trespass as little as may be into the province of the professional historian of mathematics. My interest has been in the course of the quarrel, rather than in the technical nature of its subject, in mathematicians rather than in mathematics.

So far as I am aware, there is no earlier history of the calculus dispute of any size, though it is discussed in general histories of mathematics and in biographies of the participants, nor has there been any reissue of the Commercium Epistolicum since that edited by J–B. Biot and F. Lefort in 1856 (Paris: Mallet-Bachelier); a Spanish version of its documents was published by J. Babini in 1972 (Gotifredo Guillermo Leibniz, Isaac Newton. El cálcula infinitesimal. Origen. Polemica, Buenos Aires) and an Italian one by G. Cantelli in 1958 (La disputa Leibniz-Newton sull'analysi, Turin and Florence: P. Boringhieri). Older works such as F. Cajori's History of the Conceptions of Limits and Fluxions in Great Britain from Newton to Woodhouse (Chicago and London: Open Court Publishing Co., 1919) and J. M. Child's Early Mathematical Manuscripts of Leibniz (London: Open Court, 1920) are very out of date.

Leibniz's idea of the basic structure of the universe was, within the context of his era, far more conventional than that which Newton developed and regarded as alone consistent with a mathematical science of mechanics. Newton conceived upon the foundations laid by the Greek atomists one of the grandest generalizations of modern science: the idea that all the matter in the universe consists of particles, of which the smallest are atoms, which are impelled or retained by the forces mutually acting between them into a myriad of different configurations and an endless variety of motions, from which by successive stages all the observed manifestations of nature result. The idea of particles, or atoms, was by no means new; the novelty lay in the idea of fundamental forces, forces of attraction and repulsion, operating directly between the atoms, or particles. The prevailing theory of Leibniz and Newton's time, originating with Descartes, was that what we may ordinarily call a “force,” like magnetism or gravity, was only apparent, a kind of optical illusion; the reality lay in the movement of invisible, indetectable particles whose pressures on bodies cause the movements we attribute to forces. To this Newton's thoughts were completely opposed; forces, he thought, were real and prior, though he recognized that there might be still deeper explanations of the way the force worked. The first thing was to find out the nature of the force itself, the laws it obeyed, not to imagine hypotheses about streams of invisible particles.

In march 1693 Fatio de Duillier had been invited by Newton to rejoin him in Cambridge at Newton's expense, and on 11 April (apparently in reply to this invitation) Fatio wrote:

Thereafter, the intimate and frequent correspondence between the two men ceases; the following summer was that of Newton's mental illness. We have no evidence as to what passed when Newton admitted his friend, at Cambridge, to the privacy of his manuscripts, nor subsequently do we have any record of how he reacted to Fatio's dramatic displays, first in private and finally in public, of his admiration for Newton and his conviction that Leibniz had stolen the calculus from Newton. If letters were exchanged between the two men, or if (as is unlikely enough, in fact) Newton disclosed his personal judgment of Fatio to others, the documents have failed to survive.