A peaceful means of some consolidation of European territories used to be provided by dynastic unions ; less common were country-level unions, such as the Polish—Lithuanian Commonwealth and Austro-Hungarian Empire. History of the European Coal and Steel Community —57 After two devastating world wars, the political climate favoured an international unity that could preserve peace in Europe effectively.

Like many great thinkers before and after him, Leibniz was a child prodigy and a contributor in many different fields of endeavour. But, between his work on philosophy and logic and his day job as a politician and representative of the royal house of Hanover, Leibniz still found time to work on mathematics.

He was perhaps the first to explicitly employ the mathematical notion of a function to denote geometric concepts derived from a curve, and he developed a system of infinitesimal calculus, independently of his contemporary Sir Isaac Newton.

He also revived the ancient method of solving equations using matrices, invented a practical calculating machine and pioneered the use of the binary system.

Within the short period of about two months he had developed a complete theory of differential calculus and integral calculus see the section on Newton for a brief description and explanation of the development of calculus. When the Royal Society was asked to adjudicate between the rival claims of the two men over the development of the theory of calculus, they gave credit for the first discovery to Newtonand credit for the first publication to Leibniz.

However, the Royal Society, by then under the rather biassed presidency of Newton himself, later also accused Leibniz of plagiarism, a slur from which Leibniz never really recovered. In addition to calculus, Leibniz re-discovered a method of arranging linear equations into an array, now called a matrix, which could then be manipulated to find a solution.

A similar method had been pioneered by Chinese mathematicians almost two millennia earlier, but had long fallen into disuse. Leibniz paved the way for later work on matrices and linear algebra by Carl Friedrich Gauss.

He also introduced notions of self-similarity and the principle of continuity which foreshadowed an area of mathematics which would come to be called topology. He is usually credited with the early development of the binary number system base 2 counting, using only the digits 0 and 1although he himself was aware of similar ideas dating back to the I Ching of Ancient China.

Because of the ability of binary to be represented by the two phases "on" and "off", it would later become the foundation of virtually all modern computer systems, and Leibniz's documentation was essential in the development process.

Even though he actually published nothing on formal logic in his lifetime, he enunciated in his working drafts the principal properties of what we now call conjunction, disjunction, negation, identity, set inclusion and the empty set.the greek-roman invention of civic identity versus the current demotion of european ethnicity.

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Leibniz - 17th Century Mathematics - The Story of Mathematics