Gottfried Leibniz had begun working on the calculus in 1674; the earliest evidence of its use in his surviving notebooks is 1675.

He had had a coherent system in hand by 1677, but has waited seven years to publish it.

A German philosopher of Sorbian origin, educated in law and philosophy and writing primarily in Latin and French, Leibniz serves as factotum to the House of Hanover.

The Brunswicks have tolerated the enormous effort Leibniz has devoted to intellectual pursuits unrelated to his duties as a courtier, pursuits such as perfecting the calculus, writing about other mathematics, logic, physics, and philosophy, and keeping up a vast correspondence.

Being able to calculate rates of change also allows one to determine where maximum and minimum values occur—the title of Leibniz's first calculus publication, in the recently founded journal Acta Eruditorum, is “ova Methodus pro Maximis et Minimis, Itemque Tangentibus, qua nec Fractas nec Irrationales Quantitates Moratur, et Singulare pro illi Calculi Genus (“A New Method for Maxima and Minima, as Well as Tangents, Which Is Impeded Neither by Fractional nor by Irrational Quantities, and a Remarkable Type of Calculus for This”).

A branch of mathematics that includes the study of limits, derivatives, integrals, and infinite series, calculus constitutes a major part of modern university education.