Portrait of Gottfried Wilhelm Leibniz, Newton's rival in the calculus priority dispute — Gottfried Wilhelm Leibniz — portrait (public domain). His differential notation is the one mathematics still uses.

The Calculus Dispute

Newton invented his method first and published it last. Leibniz published first — and his notation is the one the world still uses. The full story, told from both sides.

Newton’s side

Newton developed his method of fluxions by the mid-1660s and had a working calculus by 1671, when he wrote (but did not publish) De Methodis Serierum et Fluxionum. In 1676 he sent two long letters to Leibniz through Henry Oldenburg, secretary of the Royal Society — letters that contained, in coded anagram form, his claim to the method. Newton’s lifelong position was simple: he had it first, and the 1676 correspondence proved it. The second edition of the Principia (1713) carried his General Scholium; privately, Newton regarded Leibniz’s later publication as, at best, a rediscovery.

Leibniz’s side

Gottfried Wilhelm Leibniz developed his differential calculus independently around 1675–76 and published first: the Nova Methodus appeared in the Acta Eruditorum in 1684 — three years before the Principia. His notation — dy/dx, the integral sign ∫ — was a genuine innovation in symbolic thinking, and it is the notation mathematicians still use, because it works better for the problems calculus actually solves. Leibniz always acknowledged Newton’s correspondence but insisted, plausibly, that his route was his own.

The escalation

1708: John Keill, Newton’s ally, wrote in the Philosophical Transactions that Leibniz had taken his calculus from Newton — the first public accusation of plagiarism.
1711: Leibniz appealed to the Royal Society for justice.
1712: The Society appointed a committee. Its members were Newton’s London circle; Leibniz was not invited to testify. The report, Commercium Epistolicum, concluded Newton was first — and implied Leibniz’s work was derivative.
1715: An anonymous review of the report in the Philosophical Transactions declared Leibniz a plagiarist with finality.

What the committee did not advertise: Newton, as president of the Royal Society, had overseen the process — and he wrote the report’s substance himself, anonymously, then anonymously reviewed his own verdict in the Society’s journal. The manuscript of the anonymous review survives in Newton’s hand; his authorship was confirmed in the twentieth century.

The verdict of history

Modern historians generally conclude independent invention: Newton first in private, Leibniz first in print, with a genuinely different and more fertile notation. The dispute’s real casualty was English mathematics, which clung to Newton’s dot-notation and fluxions while the Continent advanced with Leibniz’s symbols — a self-imposed isolation that lasted over a century. Leibniz died in 1716, his English reputation destroyed; Newton, three years later, was still defending the verdict.

What we don’t know

Whether any specific line of Leibniz’s work derives from the 1676 letters is unprovable either way; the documents admit both readings, and honest historians say so. What is not in doubt is the institutional conduct of 1712–15.

Source notes

The 1676 letters via Oldenburg: H. W. Turnbull (ed.), The Correspondence of Isaac Newton, vol. 2.
Keill’s 1708 accusation: Philosophical Transactions, 1708.
Commercium Epistolicum (1712); Newton’s authorship of the anonymous 1715 Account: the manuscript survives; see the transcription at Trinity College Dublin’s History of Mathematics archive.
Leibniz’s 1684 Nova Methodus: Acta Eruditorum (1684).
For the standard modern account: R. S. Westfall, Never at Rest (1980), ch. 14; A. R. Hall, Philosophers at War (1980).