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Contents >> Index >> Gottfried Leibniz (1646--1716) --- Historical Sketch

Gottfried Wilhelm von Leibniz (rhymes with fried grits) was born in 1646 in Leipzig into a learned family. His father was a philosophy professor at the university. His father died when Gottfried was but five and he was reared by his mother. His school was deficient, but he learned on his own how to read Latin and some Greek by the time he was 12, and helped himself to the offerings of his father's library, including Aristotelean logic.

In 1660, at age 14, Leibniz enrolled at the University of Leipzig, graduating with a bachelor's degree three years later. He earned a master's degree in philosophy and law at the University of Jena just before his mother died. He then went to the University of Altdorf where he got a doctorate in law in 1667.

Over the next few years, Leibniz engaged in various projects, some political, and eventually got to Paris where he came to know the Dutch mathematician and astronomer Christiaan Huygens. In 1673, he visited the Royal Society in London in connection with a calculating machine he had (almost) built.

In April 1673, Leibniz was elected a fellow of the Royal Society. Huygens encouraged him to study mathematics and he soon began his formulation of calculus paying special attention to notation. He considered proper notation to be extremely important in the development of the subject. His notation $\dint $ for integrals---the elongated S from the word sum---and his $\dfrac{dy}{dx}$ notation for derivatives is still used today. In 1675, Leibniz used the notationMATHfor the first time, and formulated the product rule for differentiation (Leibniz's rule). A year later, he discovered the formula MATHfor the derivative of $x^{n}$, where $n$ is an integer or a fraction, but he never thought of the derivative as being the result of a limit process.

At this point, Isaac Newton---who was developing calculus as well---and Leibniz engaged in correspondence. Newton was convinced that Leibniz had somehow stolen his methods. This led to a bitter argument between the two which eventually took on nationalistic overtones. The argument continues to this day.

Leibniz was never married and died of poor health in 1716.


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Derivative notation

Historical sketches


Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.

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