Gottfried Wilhelm Leibniz

Overview

Leibniz was a diplomat, lawyer, and philosopher who worked on mathematics alongside everything else. He published the differential calculus in 1684 and the integral calculus in 1686, several years before Newton published anything on the subject and several years after Newton had developed his own version privately. His notation, dy/dx for the derivative and the elongated S for the integral, made the operations easy to manipulate and is the reason his form of the calculus is the one taught. He also described binary arithmetic and spent much of his life on the idea of a symbolic language in which reasoning could be carried out by calculation, an ambition that reappears in nineteenth-century logic. His 1684 paper is short and worth reading in translation.

Where to start reading

• Nova Methodus pro Maximis et Minimis 1684

  The first published account of the differential calculus, introducing the notation and the rules for differentiating products and quotients.

• Explication de l'Arithmétique Binaire 1703

  Sets out arithmetic in base two, the system all digital computation later used.

• De Arte Combinatoria 1666

  An early work proposing that reasoning could be reduced to the combination of basic symbols, the seed of his lifelong project for a calculus of thought.

Part of

• Analysis and the calculus

Sources

1. Gottfried Leibniz MacTutor History of Mathematics
2. Gottfried Wilhelm Leibniz Wikipedia