The Britannica Guide to Analysis and Calculus by Britannica Educational Publishing

Author:Britannica Educational Publishing
Language: eng
Format: epub
Publisher: Britannica Educational Publishing
Published: 2011-10-15T00:00:00+00:00

GOTTFRIED WILHELM LEIBNIZ

(b. July 1 [June 21, Old Style], 1646, Leipzig, Ger.—d. Nov. 14, 1716, Hannover, Hanover)

The German philosopher, mathematician, and political adviser Gottfried Wilhelm Leibniz was important both as a metaphysician and as a logician and distinguished also for his independent invention of the differential and integral calculus.

Leibniz was born into a pious Lutheran family near the end of the Thirty Years’ War, which had laid Germany in ruins. As a child, he was educated in the Nicolai School but was largely self-taught in the library of his father, who had died in 1652. At Easter time in 1661, he entered the University of Leipzig as a law student. There he came into contact with the thought of men who had revolutionized science and philosophy—men such as Galileo, Francis Bacon, Thomas Hobbes, and René Descartes. Leibniz dreamed of reconciling—a verb that he did not hesitate to use time and again throughout his career—these modern thinkers with the Aristotle of the Scholastics. In 1666 he wrote De Arte Combinatoria (“On the Art of Combination”), in which he formulated a model that is the theoretical ancestor of some modern computers: all reasoning, all discovery, verbal or not, is reducible to an ordered combination of elements, such as numbers, words, sounds, or colours.

After completing his legal studies in 1666, Leibniz applied for the degree of doctor of law. He was refused because of his age and consequently left his native city forever. At Altdorf—the university town of the free city of Nürnberg—his dissertation De Casibus Perplexis (“On Perplexing Cases”) procured him the doctor’s degree at once, as well as the immediate offer of a professor’s chair, which, however, he declined. During his stay in Nürnberg, he met Johann Christian, Freiherr von Boyneburg, one of the most distinguished German statesmen of the day. Boyneburg took him into his service and introduced him to the court of the prince elector, the archbishop of Mainz, Johann Philipp von Schönborn, where he was concerned with questions of law and politics.

King Louis XIV of France was a growing threat to the German Holy Roman Empire. To ward off this danger and divert the king’s interests elsewhere, the archbishop hoped to propose to Louis a project for an expedition into Egypt. Because he was using religion as a pretext, he expressed the hope that the project would promote the reunion of the church. Leibniz, with a view toward this reunion, worked on the Demonstrationes Catholicae. His research led him to situate the soul in a point—this was new progress toward the monad—and to develop the principle of sufficient reason (nothing occurs without a reason). His meditations on the difficult theory of the point were related to problems encountered in optics, space, and movement. They were published in 1671 under the general title Hypothesis Physica Nova (“New Physical Hypothesis”). He asserted that movement depends, as in the theory of the German astronomer Johannes Kepler, on the action of a spirit (God).

In 1672 the Elector sent the young jurist on a mission to Paris, where he arrived at the end of March.

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