Gottfried Wilhelm Leibniz

Lore & Background

Leibniz was born in Leipzig to Friedrich Leibniz, a professor of moral philosophy, and Catharina Schmuck. His father died when he was six, and he was raised by his mother and uncle. He gained free access to his father's library from age seven, which allowed him to study advanced philosophical and theological works and achieve proficiency in Latin by age 12. At 13, he composed 300 hexameters of Latin verse in a single morning. He enrolled at his father's former university at age 14, earning a bachelor's degree in philosophy in 1662 and a master's in 1664. After legal studies, he received a bachelor's degree in law in 1665. In early 1666, he wrote his first book, De Arte Combinatoria, which contained a proof of the existence of God based on the argument from motion. The University of Leipzig turned down his doctoral application, likely due to his youth, so he enrolled at the University of Altdorf, earning his doctorate in law in November 1666. He declined an academic appointment there, saying his thoughts were turned in an entirely different direction.

Leibniz's first position was as a salaried secretary to an alchemical society in Nuremberg. He soon met Johann Christian von Boyneburg, who hired him as an assistant and introduced him to the Elector of Mainz. Leibniz dedicated an essay on law to the Elector, leading to a role assisting with the redrafting of the legal code. In 1669, he was appointed assessor in the Court of Appeal. After von Boyneburg's death in 1672, Leibniz remained employed by his widow until 1674. He also took on a diplomatic role, publishing an essay under a pseudonym arguing for the German candidate for the Polish crown. He proposed distracting Louis XIV by inviting France to take Egypt as a stepping stone towards conquering the Dutch.

Reader's Guide

Leibniz's significance lies in his independent development of differential and integral calculus, with his notation becoming the conventional and more exact expression of calculus. He devised the modern binary number system, which is the basis of modern communications and digital computing, though Thomas Harriot had devised the same system decades before. He envisioned combinatorial topology in 1679 and helped initiate fractional calculus. In the 20th century, his notions of the law of continuity and transcendental law of homogeneity found mathematical formulation through non-standard analysis. He was a pioneer in mechanical calculators, describing a pinwheel calculator in 1685 and inventing the Leibniz wheel, later used in the arithmometer, the first mass-produced mechanical calculator. As a philosopher, he was a leading representative of 17th-century rationalism and idealism, noted for his optimism that our world is the best possible world God could have created. His work anticipated modern logic and still influences contemporary analytic philosophy, particularly the use of the term 'possible world' to define modal notions. He also contributed to library science, developing a cataloguing system at the Herzog August Library that served as a model for many of Europe's largest libraries.

Did You Know?

• Leibniz was baptized two days after his birth at St. Nicholas Church, Leipzig, with Lutheran theologian Martin Geier as his godfather.
• He composed 300 hexameters of Latin verse in a single morning at age 13 for a school event.
• Leibniz's first book, De Arte Combinatoria, written at age 19, contained a proof of the existence of God cast in geometrical form.
• He invented the Leibniz wheel, later used in the arithmometer, the first mass-produced mechanical calculator.

Notable Quotes (Wikiquote)

"Gottfried Wilhelm von Leibniz (1 July 1646 {21 June O.S.} – 14 November 1716) was a German philosopher and mathematician." — Gottfried Wilhelm Leibniz "De arte characteristica ad perficiendas scientias ratione nitentes in C. I. Gerhardt (ed.), Die philosophischen Schriften von Gottfried Wilhelm Leibniz (7 vols. 1875–1890) VII 200." — Gottfried Wilhelm Leibniz "Languages are the best mirror of the human mind [and] the most ancient monu­ments of peoples." — Gottfried Wilhelm Leibniz "Theologus: Amare autem?Philosophus: Felicitate alterius delectari." — Gottfried Wilhelm Leibniz