Leibniz developed the present day notation for the differential and integral calculus. He never thought of the derivative as a

limit.

Leibniz was the son of a professor of moral philosophy at Leipzig. He taught himself Latin and some Greek by age 12 so that

he might read his father's books. From 1661 to 1666 he studied law at the University of Leipzig. In 1666 his continuation to a

doctorate course was refused and he went to the University of Altdorf, receiving a doctorate in law in 1667.

Leibniz declined a chair at Altdorf because he had very different things in view . He continued a law career in residence at

the courts of Mainz until 1672. In that year he visited Paris to try to dissuade Louis XIV from attacking German areas. Leibniz

remained in Paris until 1676, where he continued to practise law. However in Paris he studied mathematics and physics under

Christiaan Huygens. It was during this period that the basic features of his version of the calculus were developed. The rest of

his life, from 1676 until his death, was spent at Hanover.

By 1673 he was still struggling to develop a good notation for his calculus and his first calculations were clumsy. On 21

November 1675 he wrote a manuscript using the f(x) dx notation for the first time. In the same manuscript the

product rule for differentiation is given. The quotient rule first appeared two years later, in July 1677.

By November 1676 Leibniz discovered the familiar d(x) = nx

dx for both integral and fractional n. Newton was to claim, with justification, that

not a single previously unsolved problem was solved

here but the formalism of Leibniz's approach was to prove vital in the development of the calculus. Leibniz never thought of the

derivative as a limit. This does not appear until the work of d'Alembert.

In 1684 Leibniz published details of his differential calculus in Nova Methodus pro Maximis et Minimis, itemque

Tangentibus... in Acta Eruditorum , a journal established in Leipzig two years earlier. The paper contained the familiar d

notation, the rules for computing the derivatives of powers, products and quotients. However it contained no proofs and Jacob

Bernoulli called it an enigma rather than an explanation.

In 1686 Leibniz published, in Acta Eruditorum , a paper dealing with the integral calculus with the first appearance in print of

the notation.

Newton's Principia appeared the following year. Newton's 'method of fluxions' was written in 1671 but Newton failed to get it

published and it did not appear in print until John Colson produced an English translation in 1736. This time delay in the

publication of Newton's work resulted in a dispute with Leibniz.

Leibniz founded the Berlin Academy in 1700 and was its first president. He became more and more a recluse in his later years.