Newton and Leibniz Both Invent Calculus, Then Fight Over Who Was First
Two different notations, two independent paths to the same tool, and a priority war that outlived them both
Quick facts
- Newton's fluxions tract
- Written 1666, published 1711/1736
- Leibniz's publications
- 1684 and 1686
- Royal Society report
- Commercium Epistolicum, 1713, written by Newton
- Modern consensus
- Independent, parallel discovery
What happened
Isaac Newton wrote a tract on fluxions, his term for what would become calculus, in October 1666, but the work was not published at the time, though it circulated privately among mathematicians, and his fuller treatments written in 1669 and 1671 were not formally published until 1711 and 1736. Gottfried Wilhelm Leibniz developed his own version independently, working out the core ideas during a period in Paris starting in 1672 and publishing his results in 1684 and 1686, using the integral symbol and differential notation still standard today. In 1711 the mathematician John Keill publicly accused Leibniz of deriving his calculus from letters Newton had sent years earlier, prompting Leibniz to demand a retraction and insist he had never even heard of Newton's fluxions until reading the work of John Wallis. The Royal Society convened a committee in 1713 that, in a report actually written by Newton himself, the Commercium Epistolicum, ruled in Newton's favor without properly hearing Leibniz's side.
Why it matters
Modern historians treat Newton and Leibniz as having developed calculus independently, arriving at the same tool through genuinely different conceptual routes, Newton through changing quantities over time and Leibniz through infinitesimals and a superior symbolic notation that became the worldwide standard. The dispute, driven as much by national rivalry between English and Continental mathematicians as by the mathematics itself, split European mathematical communities for a generation and delayed British mathematicians' adoption of Leibniz's more workable notation for decades.
How we know
Newton's unpublished 1666 tract and subsequent manuscripts, along with Leibniz's 1684 and 1686 publications and his correspondence defending his independent discovery, all survive and have been examined by historians, and the Royal Society's 1713 Commercium Epistolicum report, now known to have been written by Newton rather than by a neutral committee, is itself a primary document in the dispute.
Sources
- MacTutor History of Mathematics, University of St Andrews. The rise of calculus · Reputable sourcemathshistory.st-andrews.ac.uk · The domain "mathshistory.st-andrews.ac.uk" is on our Reputable source registry. · Link is live and its text matches the event's key terms (Jul 2026)
- MacTutor History of Mathematics, University of St Andrews. Gottfried Wilhelm Leibniz · Reputable sourcemathshistory.st-andrews.ac.uk · The domain "mathshistory.st-andrews.ac.uk" is on our Reputable source registry. · Link is live and its text matches the event's key terms (Jul 2026)
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Related timelines
- The Scientific Revolution → · See the Scientific Revolution timeline for how Newton's Principia and the broader mechanical universe he described depended on the calculus developed in this dispute.