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Leibniz : The Polymath

Gottfried Wilhelm von Leibniz (July 1, 1646 – November 14, 1716) was a German mathematician and philosopher. He was the son of a professor of moral philosophy.

Leibniz is described as follows:

     "Leibniz was a man of medium height with a stoop, broad-shouldered but bandy-legged, as capable of thinking for several days sitting in the same chair as of travelling the roads of Europe summer and winter. He was an indefatigable worker, a universal letter writer (he had more than 600 correspondents), a patriot and cosmopolitan, a great scientist, and one of the most powerful spirits of Western civilization."

Leibniz, who occupies a prominent place in the history of mathematics and the history of philosophy, is one of the great renaissance men of Western thought.

Leibniz was one of the great polymaths of the modern world. Moreover, a list of his significant contributions is almost as long as the list of his activities. As an engineer, he worked on calculating machines, clocks, and even mining machinery. As a librarian, he more or less invented the modern idea of cataloging  As a mathematician, he not only produced ground-breaking work in what is now called Topology, but came up with the Calculus independently of (though a few years later than) Newton, and his notation has become the standard. In logic, he worked on Binary Systems, among numerous other areas. As a physicist, he made advances in mechanics, specifically the theory of momentum. He also made contributions to Linguistics, History, Aesthetics, and Political Theory.

He became one of the most prolific inventors in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685 and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the binary number system, which is at the foundation of virtually all digital computers.

As a  Mathematician, Leibniz was a creative genius . During his stay in Paris, Leibniz developed the basic features of his version of the calculus. He was trying  to develop a good notation for his calculus and at first his calculations were clumsy. On 21 November 1675 he wrote a manuscript using the ? f(x)dx notation for the first time. In the same manuscript the product rule for differentiation is given. By autumn 1676 Leibniz discovered the familiar d(xn) = nxn-1dx for both integral and fractional n. This notations are still being used as the standard notations.

In 1684 Leibniz published details of his differential calculus in Nova Methodus pro Maximis et Minimis, itemque Tangentibus... in Acta Eruditorum, a journal established in Leipzig two years earlier. The paper contained the familiar  d  notation, the rules for computing the derivatives of powers, products and quotients.

In 1686 Leibniz published, in Acta Eruditorum, a paper dealing with the integral calculus with the first appearance in print of the ?  notation.

Another of Leibniz's great achievements in mathematics was his development of the Binary System of arithmetic. Another major mathematical work by Leibniz was his work on Determinants which arose from his developing methods to solve systems of Linear Equations. Although he never published this work in his lifetime, he developed many different approaches to the topic with many different notations being tried out to find the one which was most useful.


Image : Leibniz's notes from 1669-1704

Another important piece of mathematical work undertaken by Leibniz was his work on dynamics. He criticized Descartes' ideas of Mechanics and examined what are effectively kinetic energy, potential energy and momentum.

Leibniz's lifelong aims was to collate all human knowledge and he put much energy into promoting scientific societies.

Ross points out-

It is ironical that one so devoted to the cause of mutual understanding should have succeeded only in adding to intellectual chauvinism and dogmatism. There is a similar irony in the fact that he was one of the last great polymaths - not in the frivolous sense of having a wide general knowledge, but in the deeper sense of one who is a citizen of the whole world of intellectual inquiry. He deliberately ignored boundaries between disciplines, and lack of qualifications never deterred him from contributing fresh insights to established specialisms. Indeed, one of the reasons why he was so hostile to universities as institutions was because their faculty structure prevented the cross-fertilization of ideas which he saw as essential to the advance of knowledge and of wisdom. The irony is that he was himself instrumental in bringing about an era of far greater intellectual and scientific specialism, as technical advances pushed more and more disciplines out of the reach of the intelligent layman and amateur.



School of Mathematics and Statistics
University of St Andrews, Scotland
and various other internet sources.



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