Leibniz' final years were overshadowed by a priority fight with the powerful president of the Royal Society, Isaac Newton, who said he had invented calculus before Leibniz, without publishing it, and who made friends sign texts he wrote to support this claim. Today's historians give credit not only to Leibniz and Newton but also to the much earlier Indian Kerala School, in particular, Madhava of Sangamagrama. All of them extended the pioneering work on infinitesimals and special cases of calculus by Archimedes.

Leibniz, sometimes called the last universal genius, invented at least two things that are essential for the modern world: calculus, and binary arithmetics based on bits. Modern physics, math, engineering would be unthinkable without the former: the fundamental method of dealing with infinitesimal numbers. Leibniz was the first to publish it. He developed it around 1673. In 1679, he perfected the notation for integration and differentiation that everyone is still using today. Binary arithmetics based on the dual system he invented around 1679, and published in 1701. This became the basis of virtually all modern computers.