Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz was a German philosopher, mathematician and polymath, one of the most wide-ranging minds in European history. He invented the differential and integral calculus independently of Isaac Newton, devised the binary number system and built a calculating machine, while also working as a lawyer, diplomat, historian and librarian. In philosophy he developed an ambitious rationalist system in which the world is made of simple, soul-like units called monads, and he argued that God created the best of all possible worlds.

Leibniz was born in Leipzig, in Saxony, on 1 July 1646, by the calendar now in use, two years before the end of the Thirty Years' War that had devastated much of the Holy Roman Empire. His father, Friedrich, was a professor of moral philosophy at the University of Leipzig and died when Gottfried was six. The boy was given the run of his father's library and taught himself Latin, reading widely in classical authors, theology and scholastic philosophy.

He entered the University of Leipzig at fourteen, studying philosophy and law, and soon read the modern thinkers Francis Bacon, Thomas Hobbes, Galileo and René Descartes. In his Dissertation on the Art of Combinations (1666) he sketched an idea he pursued all his life: a universal symbolic language in which reasoning could be done by calculation, so that disputes could be settled by saying "let us calculate". When Leipzig declined to award him a doctorate in law, apparently because of his youth, he received one from the University of Altdorf near Nuremberg in 1667 and turned down a professorship there.

Leibniz entered the service of the Elector of Mainz, Johann Philipp von Schönborn, through the statesman Johann Christian von Boineburg, working on legal reform and diplomacy. In 1672 he went to Paris on a mission to persuade Louis XIV to turn his armies away from Germany and towards a conquest of Egypt. The plan came to nothing, but Leibniz stayed in Paris for four years, the most creative period of his life.

There he was taught advanced mathematics by the Dutch scientist Christiaan Huygens. In 1673 he visited London, showed the Royal Society a model of his calculating machine, which could multiply and divide as well as add, and was elected a Fellow. By late 1675 he had worked out the essentials of his calculus, with the notation of dx and the integral sign that mathematicians still use. On his way to a new post in Germany in 1676 he stopped in The Hague and had several long conversations with Baruch Spinoza.

From 1676 until his death Leibniz served the dukes of Brunswick-Lüneburg in Hanover as librarian, legal adviser and counsellor. He worked on schemes to drain silver mines in the Harz mountains with windmills, on reuniting the Catholic and Protestant churches, and on a vast history of the ruling House of Guelph, which he never completed. He travelled widely in search of archives, including a long journey to Austria and Italy in 1687 to 1690. He promoted learned academies and became the first president of the Berlin Society of Sciences, founded in 1700. He met Peter the Great several times and advised him on education and science in Russia.

He was fascinated by China, corresponded with Jesuit missionaries there, admired Confucius as a moral teacher and saw in the hexagrams of the Yijing a parallel to his binary arithmetic, in which all numbers are written with 0 and 1.

Leibniz published his calculus in 1684, before Isaac Newton, who had developed his own method of fluxions in the 1660s but had kept it largely to himself. A bitter dispute over priority broke out in the early 1700s. In 1712 the Royal Society, of which Newton was president, appointed a committee that accused Leibniz of plagiarism; its report was drafted largely by Newton himself. Historians now agree that the two men discovered the calculus independently. Leibniz's notation proved more practical and was adopted throughout continental Europe.

Leibniz's philosophy rests on two great principles: the principle of contradiction, and the principle of sufficient reason, which says that nothing happens without a reason why it is so and not otherwise. He held that physical things, which can always be divided, cannot be the ultimate reality. The basic constituents of the world are monads, simple and indivisible substances without parts, each of which has perceptions and mirrors the whole universe from its own point of view. Monads do not really act on one another. Instead, God has set them up in a pre-established harmony, like clocks wound to keep the same time, which is how Leibniz explained the apparent link between mind and body.

God, being perfectly good and wise, chose to create the best of all the possible worlds he could conceive. Evil exists because the best world as a whole contains some evils that make greater goods possible. Leibniz set out this answer to the problem of evil in his Theodicy (1710), the only full-length philosophical book he published in his lifetime. His other key texts, the Discourse on Metaphysics (1686) and the Monadology (1714), circulated in manuscript or appeared after his death. His New Essays on Human Understanding, a dialogue criticising John Locke and defending innate ideas, was completed around 1704 but published only in 1765. In his correspondence with Samuel Clarke in 1715 and 1716 he attacked Newton's view of absolute space, arguing that space is only a system of relations between things.

When the Elector of Hanover became King George I of Great Britain in 1714, Leibniz was left behind in Hanover, out of favour and still working on the unfinished history. He died there on 14 November 1716. Only his secretary is reported to have attended his funeral.

His optimism was famously mocked by Voltaire in Candide (1759), whose Dr Pangloss insists that all is for the best. Yet through the systematising of Christian Wolff his ideas dominated German university philosophy for decades and formed the background against which Immanuel Kant worked. Much of his thought lay hidden in tens of thousands of letters and papers, whose complete edition is still in progress. In the twentieth century logicians recognised him as a forerunner of symbolic logic, and computer scientists as a pioneer of binary computation. He is one of the great rationalists of early modern philosophy and a major figure in the history of Germany.