HISTORY OF MATHEMATICS – LECTURE 14 – WEDNESDAY 27
TH
OCTOBER
Gottfried Leibniz
While the details regarding Newton’s life and development of calculus described in Lecture 13 are all
correct, they omit one very important detail, namely that Newton was not the only mathematician to
claim credit for the invention of calculus. There is no question that Gottfried Leibniz (1646
‐
1716) was
the first to publish his ideas, in 1684, as although Newton wrote
The Method of Fluxions
in 1671, the
work was not published until 1736. However the question remains to this day: how much of Newton’s
work Leibniz was aware of, and how many of the crucial concepts were borrowed from Newton?
Leibniz was born in Leipzig, Germany, and due to the death of his father was largely self educated,
teaching himself Latin and Greek, which allowed him to read the classical texts in his father’s library. He
entered the University of Leipzig at the age of 14, and completed both a bachelor’s and master’s degree
by his 18th birthday, before transferring to the University of Altdorf in Nuremburg, finishing his
doctorate in law at the age of 20. The dissertation was considered so impressive that Leibniz was offered
a job as a professor upon graduation, but he declined, preferring to become a lawyer and political
advisor in Mainz, and later in Hanover.
Given that the Roman Empire had completely fragmented by that time, the power in Europe was seized
by the French under the rule of Louis XIV, and in 1672 Leibniz was sent to Paris in an attempt to try and
prevent the French army from encroaching into German territory. While his political goal proved to be
largely unsuccessful, the four years Leibniz spent in Paris proved to be very productive, as his knowledge
of mathematics increased exponentially under the tutelage of Christiaan Huygens (1629
‐
1695). As an
early test, Huygens asked Leibniz the following question.
Ex.
In 1673 Leibniz visited England to (unsuccessfully) try and negotiate peace between France and the
Netherlands. Whilst there, he met with Henry Oldenburg (1619
‐
1677), who was the secretary of the
Royal Society, and was introduced to many of England’s leading scientists as a result, even being elected
as a member (and later the Académie des sciences in 1700).
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View Full DocumentOnce back in Paris, Leibniz continued his study of mathematics, in particular infinite series and the work
of Pascal, whom he credited for being instrumental in inspiring his work on calculus. In 1673, Leibniz
became interested in the inverse tangent problem, i.e. deriving the equation of a curve by knowing the
properties of its tangents. He split up curves defined over an interval into subintervals, and calculated
the y value at boundary values of each subinterval, similar to the way we form the (Riemann) integral
today. However Leibniz soon found it difficult to communicate his ideas using the notation of that time.
He hence decided to use the integral symbol to denote a sum, and d to denote a difference.
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 Spring '08
 EVINSON
 Calculus, Candide, Gottfried Leibniz, Leibniz

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