Leibniz, Gottfried Wilhelm

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.