Gottfried Wilhelm von Leibniz
                                      
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Leibniz developed the present day notation for the differential and integral
          calculus. He never thought of the derivative as a limit.
                                      
             Born: 1 July 1646 in Leipzig, Saxony (now Germany)
            Died: 14 Nov 1716 in Hannover, Hanover (now Germany)
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Introduction

   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 practice 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 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 formulae 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.
   
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References

    1. Dictionary of Scientific Biography
    2. Biography in Encyclopaedia Britannica
    3. J T Mertz, Leibniz (1948).
    4. N Rescher, Leibniz: An Introduction to His Philosophy (1979).
    5. C D Broad and C Lewy, Leibniz: An Introduction (1975).
    6. G E Guhrauer (trans. by J M Mackie), Life of Godfrey William von
       Leibniz (1966).
    7. E J Aiton, Leibniz : A biography (Bristol- Boston, 1984).
    8. H Wussing, Leibniz, in H Wussing and W Arnold, Biographien
       bedeutender Mathematiker (Berlin, 1983).
       
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