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Gottfried WiIhelm Leibniz, the great unibersal genius of the seventeenth century
and Newton's rival in the invention of the caculus, was born in Leipzig in
1646. Habing taught himself to read Latin and Greek when he was a mere child,
he had, before he was twenty, mastered the ordinary textbook knowledge of
mathematics, philosophy, theology, and law. At this young age, he began to
develop the first ideas of his characteristica generalis, which involved a universal
mathematics that later blossomed into the symbolic
logic of George Boole
(1815-1864) and, still later,
in 1910, into the great Principia mathematica of
whitehead and Russell.
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When, ostensibly because of his youth, he was refused
the degree of doctor of laws at the University of Leipzig, he moved to Muremberg..
There he wrote a brilliant essay on teaching law by the historical method
and dedicated it to the Elector of Mainz. This led to his appointment by the
Elector to a commission for the recodification of some statutes. The rest of
Leibniz' life from this point on was spent in diplomatic service, first for the
Elector of Mainz and then, from about 1676 until his death, for the estate of the
Duke of Brunswick at Hanover.
In 1672, while in Paris on a diplomatic mission, Leibniz met Huygens,who
was then residing there, and the young diplomat prevailed upon the scientist to
give him lessons in mathematics. The following year,Leibniz was sent on a
political mission to London, where he made the acquaintance of Oldenburg and
others and where he exhibited a caculating machine to the Royal Society.
Before he left Paris to take up his lucrative post as librarian for the Duke of
Brunswick, Leibniz had already discovered the fundamental theorem of the
calculus, developed much of his notation in this subject, and worked out a
number of the elementary formulas of differentiation.
The closing seven years of Leibniz' life were embittered by the controversy
that others had brought upon him and Newton concerning wherther he
had discovered the calculus independently of Newton. In 1714, his employer
became the first German King of England, and Leibniz was left, neglected, at
Hanover. It is said that when he died two years later, in 1716, his funeral was
attended only by his faithful secretary.
Leibniz was an inveterate optimist. Not only did he hope to reunite the
confliction religious sects of his time into a single universal church, but he felt
he might hace a way of Christianizing all of China by what he believed to be the
image of creation in the binary arithmetic. Since God may be represented by
unity, an nothing by zero, he imagined that God created everything from
nothing just as in the binary arithmetic all numbers are expressed by means of
unity and zero. This idea so pleased Leibniz that he communicated it to the
Jesuit Grimaldi, President of the Mathematical Board of China, with the hope
that it might convert the reigning Chinese emperor(who was particularly attached to science),
and thence all of China, to Christianity. As another instance
of Leibniz' theological simulacrums, we have his remark that imaginary numbers
are lide the Holy Ghost of Christian scriptures-a sort of amphibian,
midway between existence and nonexistence.
We conclude our account of Leibniz with a closing paean to his unique
talent. There are two broad and antithetical domains of mathematical thought,
the continuous and the discrete; Leibniz is the one man in the history of
mathematics who possessed both of these qualities of thought to a superlative
degree.
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