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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