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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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Once 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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This note was uploaded on 09/22/2011 for the course MAC 2311 taught by Professor Evinson during the Spring '08 term at University of Central Florida.

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lecture14 -...

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