Modern physics, math, engineering would be unthinkable without the former: the fundamental method of dealing with infinitesimal numbers. Leibniz developed it around 1673. In 1679, he perfected the notation for integration and differentiation that everyone is still using today.

Binary arithmetics is based on the dual system he invented around 1679, and published in 1701. This became the basis of virtually all modern computers.

In 1671 he developed a non-programmable computer (shown on the right), the step reckoner.