The Newton–Leibniz Calculus Controversy, 1708–1730

Abstract This article examines the controversy between Isaac Newton and Gottfried Wilhelm Leibniz concerning the priority in the invention of the calculus. The dispute began in 1708, when John Keill accused Leibniz of having plagiarized Newton’s method of fluxions. It will be shown that the mathematicians participating in the controversy in the period between 1708 and 1730—most notably Newton, Leibniz, Keill, and Johann Bernoulli—held different conceptions of mathematical method. The dispute began in a political climate agitated by the Hanoverian succession and was intertwined with tensions dividing the Royal Court. It developed into a discussion of technical issues concerning the relation between mathematics and natural philosophy and the methods of the integral calculus.