Gottfried Wilhelm Leibniz was a philosopher, mathematician, physicist, jurist, and contemporary of Newton.  He is considered one of the great thinkers of the 17th century. He believed in a universe which followed a "pre-established harmony" between mind and matter, and attempted to reconcile the existence of a material world with the existence of a supreme being.

The twentieth century philosopher and mathematician Bertrand Russell considered Leibniz's greatest claim to fame to be his invention of the infinitesimal calculus -- a remarkable achievement considering that Leibniz was self-taught in mathematics.

Leibniz is portrayed overlaid with integral notation from his calculus which he developed coincident with but independently of Newton's development of calculus.

Although the historical record suggest that Newton developed his version of calculus first, Leibniz was the first to publish.  Unfortunately, what emerged was not fruitful collaboration, but a rancorous dispute that raged for decades and pitted English continental mathematicians supporting Newton as the true inventor of the calculus, against continental mathematicians supporting Leibniz.

Today, Leibniz and Newton are generally recognized as 'co-inventors' of the calculus.

But Leibniz' notation for calculus was far superior to that of Newton, and it is the notation developed by Leibniz, including the integral sign and derivative notation, that is still in use today.

Leibniz considered symbols to be critical for human understanding of all things. So much so that he attempted to develop an entire 'alphabet of human thought', in which all fundamental concepts would be represented by symbols which could be combined to represent more complex thoughts. Leibniz never finished this work.

Leibniz, who had strong conceptual differences with Newton in other areas, notably with Newton's concept of absolute space, also develop bitter conceptual differences with Descartes over what was then referred to as the "fundamental quantity of motion", a precursor of the Law of Conservation of Energy.

Much of Leibniz' work went unpublished during his lifetime. He died embittered, in ill health, and without achieving the considerable wealth, fame, and honor accorded to Newton.  

Leibniz' diverse writings -- philosophical, mathematical, historical, and political -- were resurrected and published in the late 19th and 20th centuries.

But calculus -- with Leibniz notation still in use today -- remains his towering legacy.