Leibniz, Gottfried Wilhelm (1646–1716)
A portrait of the German mathematician and philosopher Gottfried Leibniz. Leibniz discovered calculus at about the same time as Isaac Newton, and made other progress in the field of abstract mathematics. As well as this, he sought the reunion of Catholics and Protestants and wrote metaphysical studies, laying the foundation for 18th century philosophy.
German mathematician, philosopher, and diplomat. Independently of, but concurrently with, English scientist Isaac Newton, he developed the branch of mathematics known as calculus and was one of the founders of symbolic logic. Free from all concepts of space and number, his logic was the prototype of future abstract mathematics.
Calculus and controversy
It was in London in 1673 that Leibniz became acquainted with the work of Newton and Isaac Barrow and began to work on problems that led him to his independent discovery of differential and integral calculus. Leibniz is due the credit for first using the
infinitesimals (very small quantities that were precursors of the modern idea of limits) as differences. He devised a notation for integration and differentiation that was so much more convenient than Newton's
fluxions that it remains in standard use today.
In 1699 the Swiss mathematician and Fellow of the Royal Society, Fatio de Duillier, accused Leibniz of stealing the idea from Newton, a charge which the Royal Society formally upheld in 1711. Leibniz himself never sought to conceal that it was after his 1673 visit to London, by which time Newton had worked out his calculus of fluxions, that he began his investigations into tangents and quadratures, the research that eventually led to his discovery of calculus. Newton's discovery, probably made in 1665, was not published for many years and there is no doubt that Leibniz arrived at his calculus independently. As he put it, he, Newton and Barrow were ‘contemporaries in these discoveries’. Leibniz always communicated his findings to fellow mathematicians; most mathematicians of the time were working on the same problems and they all knew the work that had been done on infinitesimal quantities.
Monads
In his metaphysical works, such as
The Monadology (1714), he argued that everything consisted of innumerable units,
monads, the individual properties of which determined each thing's past, present, and future. Monads, although independent of each other, interacted predictably; this meant that Christian faith and scientific reason need not be in conflict and that ‘this is the best of all possible worlds’. Leibniz's optimism is satirized in French philosopher Voltaire's novel
Candide.
| Leibniz was born in Leipzig and studied there and at Jena. From 1666 he was in the service of the archbishop and elector of Mainz, his special task being to devise plans to preserve the peace of Europe, just then emerging from the Thirty Years' War. This took him to France for three years. From 1676, Leibniz was librarian to the Duke of Brunswick in Hannover, and often charged with diplomatic missions. He was an imperial privy councillor in Vienna 1712–14. In 1714 the Duke of Brunswick acceded to the English throne as George I, but Leibniz was denied permission to accompany him to London. |
| Leibniz designed a calculating machine, completed about 1672, which was able to multiply, divide, and extract roots. He worked intermittently throughout his life at devising what he called a Universal Characteristic, a language that would be accessible to everyone. |
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