Gottfried Wilhelm von Leibniz was a German philosopher, mathematician, and logician who invented differential and integral calculus (independently of Sir Isaac Newton) in the 1670s. He introduced several notations used in calculus to this day, for instance the integral sign (representing an elongated S from the Latin word summa) and the d used for differentials from the Latin word differentia. The product rule of differential calculus is still called "Leibniz's law". In addition, the theorem that tells how and when to differentiate under the integral sign is called the Leibniz integral rule. Leibniz is credited with the term "function" (1694), which he used to describe a quantity related to a curve; such as a curve's slope or a specific point of a curve. Leibniz constructed the first mechanical calculator capable of multiplication and division. He also developed the modern form of the binary numeral system that is used in digital computers today.

In philosophy, he is mostly remembered for optimism:  his conclusion that our universe is, in a restricted sense, the best possible one God could have made.

Leibniz contributed a fair amount to the statics and dynamics emerging about him, often disagreeing with Descartes and Newton. Until the discovery of subatomic particles and the quantum  mechanics governing them, many of Leibniz's speculative ideas about aspects of nature not reducible to statics and dynamics made little sense. For instance, Leibniz anticipated Albert Einstein when he devised a new theory of motion (dynamics) based on kinetic energy and potential energy, which posited space, time, and motion as relative, not absolute as Newton thought.

Sources

Cleveland, Cutler (Lead Author); Peter Saundry (Topic Editor). 2008. "Leibniz, Gottfried Wilhelm." In: Encyclopedia of Earth. Eds. Cutler J. Cleveland (Washington, D.C.: Environmental Information Coalition, National Council for Science and the Environment). [First published in the Encyclopedia of Earth September 15, 2006; Last revised August 21, 2008; Retrieved March 29, 2009]. 

Wikipedia Contributors, Gottfried Leibniz, Wikipedia The Free Encyclopedia, Accessed 29 March 2009.