This article records tradition as it has been passed down and reported. Its sources are not yet part of the atlas's verified catalogue.
Two men invented calculus, roughly at the same time, without knowing what the other had done, and then spent the rest of their lives, and enlisted most of learned Europe, arguing about which one of them really did it. Isaac Newton worked it out first, privately, in 1665 and 1666, while Cambridge was closed against the plague and a twenty-three year old had nothing to do but think. He wrote almost none of it down for publication. Gottfried Wilhelm Leibniz, a German philosopher and diplomat working independently in Paris nearly a decade later, developed his own version between 1672 and 1676, and did the opposite of Newton's silence: he wrote it up, gave it a systematic notation, the integral sign and the dy/dx that every calculus student still learns, and published it, in 1684, years before Newton put his own methods into print. For a while this looked like an ordinary case of two people converging on the same idea, which happens constantly in mathematics and is rarely a scandal. It became one because, in 1711, a paper appeared in the Royal Society's own journal accusing Leibniz outright of plagiarizing Newton. Leibniz, understandably furious, demanded the Society investigate and clear his name. It did investigate. It did not clear his name. The committee never asked Leibniz for his own account of events, and the resulting report, the Commercium Epistolicum, published in 1713, found decisively for Newton. What the committee's findings did not say, and what Leibniz never lived to learn for certain, is that Newton was the Royal Society's president at the time, and substantially wrote the supposedly independent report against his own rival himself. Leibniz answered in kind, with an anonymous pamphlet of his own, Charta Volans, and the two camps kept fighting for years after both men were dead, refusing for a generation to so much as read one another's mathematical papers out of national loyalty. Here is the part the shouting obscured. Both men were right to think they had found something real, and both were wrong to think there could only be one discoverer. They had built the same machine from different starting materials: Newton thought in terms of things in motion, quantities flowing and changing over time, which is why his version is called the method of fluxions; Leibniz thought in terms of infinitely small differences accumulating into sums, which is why his notation still shows up, quite literally, as a sum sign stretched into a curve. The Fundamental Theorem of Calculus, the single result that ties differentiation and integration together as two faces of one operation, falls out of either approach, which is exactly why a priority dispute over it was always going to be unsatisfying to actually settle: the two men were not racing toward the same finish line so much as tunneling toward each other from opposite ends of the same mountain, and both broke through. Modern historians of mathematics do not hand the trophy to either side. They treat Newton and Leibniz as independent co-discoverers, and note, a little ruefully, that most of what a student now learns, the notation itself, came from the side the Royal Society ruled against.