Both Newton and Leibniz independently developed their own versions of calculus. Newton's method of fluxions was developed earlier but remained largely unpublished. Leibniz's notation and approach, published later, proved more influential in the development of the field.

Leibniz published "Nova Methodus pro Maximis et Minimis", which presented his differential calculus. This was the first published account of calculus, using a notation that is still widely used today.

Rumors and indirect accusations of plagiarism began to circulate, with some suggesting that Leibniz had derived his calculus from Newton's unpublished work. However, direct confrontation was still absent.

The controversy escalated as supporters of Newton and Leibniz began to publicly defend their respective candidates. Accusations became more direct and personal.

The Royal Society, under Newton's presidency, appointed a committee to investigate the priority dispute. The committee, unsurprisingly, concluded that Newton had invented calculus first. The impartiality of this investigation was widely questioned.

The Royal Society published the "Commercium Epistolicum", a collection of letters and documents intended to support Newton's claim of priority. The publication was heavily biased in Newton's favor and further inflamed the controversy.

The controversy created a deep rift between British and Continental mathematics for many years. British mathematicians largely adhered to Newton's notation and methods, while Continental mathematicians adopted Leibniz's. This slowed the development of mathematics in Britain for a significant period, and created an environment of scientific nationalism. Modern scholars generally recognize that both Newton and Leibniz independently developed calculus.