# Gottfried Wilhelm Leibniz: the (other) godfather of calculus

Whilst many associate fellow mathematician Sir Isaac Newton with development of calculus, Leibniz independently developed differential and integral calculus.

To this day his notation on the subjects is still used. To celebrate such an important figure in the world of mathematics, we are going to take a look at some of Gottfried Wilhelm Leibniz's achievements.

**Calculus**

Leibniz, alongside Newton, was at the forefront of the development of calculus. Amongst the other theories and rules he developed, Leibniz also introduced several important notations that are still used to this day. For example, the integral sign '?'. His notations for calculus are considered to be his most enduring mathematical legacy.

The rule of differential calculus is still called "Leibniz's law", and the theorem that tells how and when to differentiate under the integral sign is known as the "Leibniz integral rule".

**The calculator and other mechanical devices**

In 1671, Leibniz began work on an invention that would be able to do all four maths operations (addition, subtraction, multiplication, and division). His invention was called the "stepped reckoner", and he continued to work on it and improve it over a number of years.

Leibniz also devised a cipher machine, a tool that used a method of secret writing using substitution or transposition of letters according to a key. His model has since been reproduced.

In 1693, Leibniz released a design of a machine to the general public that could, in theory, integrate differential equations.

**The binary number system**

Leibniz is referred to by many as the first computer scientist and information theorist; early in his career, he developed the binary number system, and often revisited it throughout his life.

In 1679, while working on his binary number system, Leibniz came up with the idea of a machine in which binary numbers were represented by marbles. Modern computers have since replaced Leibniz's marbles, however they still run as Leibniz envisioned.

Throughout his life, Leibniz made major contributions to maths, physics and technology, and anticipated notions that surfaced much later in philosophy, probability theory, biology, medicine, geology, psychology, linguistics, and much more.

Students who study the Kumon Maths Programme are able to continue the legacy of Leibniz, as they come face-to-face with calculus in the later levels. The calculus sections of the programme allow them to understand and learn about the notions and notations that Leibniz developed, and to apply these to their studies.