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http://upload.wikimedia.org/wikipedia/commons/6/6a/Gottfried_Wilhelm_von_Leibniz.jpg
Gottfried Wilhelm von Leibniz (German: [ˈɡɔtfʁiːt ˈvɪlhɛlm fɔn ˈlaɪbnɪts] or [ˈlaɪpnɪts]) (July 1, 1646 – November 14, 1716) was a German mathematician and philosopher. He occupies a prominent place in the history of mathematics and the history of philosophy.
Leibniz developed the infinitesimal calculus independently of Isaac Newton, and Leibniz's mathematical notation has been widely used ever since it was published. It was only in the 20th century that his Law of Continuity and Transcendental Law of Homogeneity found mathematical implementation (by means of non-standard analysis). 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.
In philosophy, Leibniz is most noted for his optimism, e.g., his conclusion that our Universe is, in a restricted sense, the best possible one that God could have created. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th century advocates of rationalism. The work of Leibniz anticipated modern logic and analytic philosophy, but his philosophy also looks back to the scholastic tradition, in which conclusions are produced by applying reason to first principles or prior definitions rather than to empirical evidence.
Leibniz made major contributions to physics and technology, and anticipated notions that surfaced much later in philosophy, probability theory, biology, medicine, geology, psychology, linguistics, and computer science. He wrote works on philosophy, politics, law, ethics, theology, history, and philology. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters, and in unpublished manuscripts. He wrote in several languages, but primarily in Latin, French, and German. As of 2013, there is no complete gathering of the writings of Leibniz.
Leibniz mainly wrote in three languages: scholastic Latin, French and German. During his lifetime, he published many pamphlets and scholarly articles, but only two "philosophical" books, the Combinatorial Art and the Théodicée. (He published numerous pamphlets, often anonymous, on behalf of the House of Brunswick-Lüneburg, most notably the "De jure suprematum" a major consideration of the nature of sovereignty.) One substantial book appeared posthumously, his Nouveaux essais sur l'entendement humain, which Leibniz had withheld from publication after the death of John Locke. Only in 1895, when Bodemann completed his catalogues of Leibniz's manuscripts and correspondence, did the enormous extent of Leibniz's Nachlass become clear: about 15,000 letters to more than 1000 recipients plus more than 40,000 other items. Moreover, quite a few of these letters are of essay length. Much of his vast correspondence, especially the letters dated after 1685, remains unpublished, and much of what is published has been so only in recent decades. The amount, variety, and disorder of Leibniz's writings are a predictable result of a situation he described in a letter as follows:
I cannot tell you how extraordinarily distracted and spread out I am. I am trying to find various things in the archives; I look at old papers and hunt up unpublished documents. From these I hope to shed some light on the history of the [House of] Brunswick. I receive and answer a huge number of letters. At the same time, I have so many mathematical results, philosophical thoughts, and other literary innovations that should not be allowed to vanish that I often do not know where to begin.
The extant parts of the critical edition of Leibniz's writings are organized as follows:
Series 1. Political, Historical, and General Correspondence. 21 vols., 1666–1701.
Series 2. Philosophical Correspondence. 1 vol., 1663–85.
Series 3. Mathematical, Scientific, and Technical Correspondence. 6 vols., 1672–96.
Series 4. Political Writings. 6 vols., 1667–98.
Series 5. Historical and Linguistic Writings. Inactive.
Series 6. Philosophical Writings. 7 vols., 1663–90, and Nouveaux essais sur l'entendement humain.
Series 7. Mathematical Writings. 3 vols., 1672–76.
Series 8. Scientific, Medical, and Technical Writings. In preparation.
The systematic cataloguing of all of Leibniz's Nachlass began in 1901. It was hampered by two world wars, the Nazi dictatorship (with the Holocaust, which affected a Jewish employee of the project, and other personal consequences), and decades of German division (two states with the cold war's "iron curtain" in between, separating scholars and also scattering portions of his literary estates). The ambitious project has had to deal with seven languages contained in some 200,000 pages of written and printed paper. In 1985 it was reorganized and included in a joint program of German federal and state (Länder) academies. Since then the branches in Potsdam, Münster, Hanover and Berlin have jointly published 25 volumes of the critical edition, with an average of 870 pages, and prepared index and concordance works.
October 29, 1675 – Leibniz makes the first use of the long s (∫) as a symbol of the integral in calculus.
http://upload.wikimedia.org/math/d/6/e/d6e9aefed6960b5c62acd09f05da9293.png
is used to denote integrals and antiderivatives in mathematics. The notation was introduced by the German mathematician Gottfried Wilhelm Leibniz towards the end of the 17th century. The symbol was based on the ſ (long s) character, and was chosen because Leibniz thought of the integral as an infinite sum of infinitesimal summands. See long s for more details on the history of ſ.
In other languages, the shape of the integral symbol differs slightly from the shape commonly seen in English-language textbooks. While the English integral symbol leans to the right, the German symbol (used throughout Central Europe) is upright, and the Russian variant leans to the left.
Another difference is in the placement of limits for definite integrals. Generally, in English-language books, limits go to the right of the integral symbol: http://upload.wikimedia.org/math/9/6/7/967b8fca2cd45d00257d41200a99f535.png.
By contrast, in German and Russian texts, limits for definite integrals are placed above and below the integral symbol, and, as a result, the notation requires larger line spacing: http://upload.wikimedia.org/math/5/c/6/5c636c62f6ecf04ac131306dfb5fb2d8.png.
Gottfried Wilhelm von Leibniz (German: [ˈɡɔtfʁiːt ˈvɪlhɛlm fɔn ˈlaɪbnɪts] or [ˈlaɪpnɪts]) (July 1, 1646 – November 14, 1716) was a German mathematician and philosopher. He occupies a prominent place in the history of mathematics and the history of philosophy.
Leibniz developed the infinitesimal calculus independently of Isaac Newton, and Leibniz's mathematical notation has been widely used ever since it was published. It was only in the 20th century that his Law of Continuity and Transcendental Law of Homogeneity found mathematical implementation (by means of non-standard analysis). 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.
In philosophy, Leibniz is most noted for his optimism, e.g., his conclusion that our Universe is, in a restricted sense, the best possible one that God could have created. Leibniz, along with René Descartes and Baruch Spinoza, was one of the three great 17th century advocates of rationalism. The work of Leibniz anticipated modern logic and analytic philosophy, but his philosophy also looks back to the scholastic tradition, in which conclusions are produced by applying reason to first principles or prior definitions rather than to empirical evidence.
Leibniz made major contributions to physics and technology, and anticipated notions that surfaced much later in philosophy, probability theory, biology, medicine, geology, psychology, linguistics, and computer science. He wrote works on philosophy, politics, law, ethics, theology, history, and philology. Leibniz's contributions to this vast array of subjects were scattered in various learned journals, in tens of thousands of letters, and in unpublished manuscripts. He wrote in several languages, but primarily in Latin, French, and German. As of 2013, there is no complete gathering of the writings of Leibniz.
Leibniz mainly wrote in three languages: scholastic Latin, French and German. During his lifetime, he published many pamphlets and scholarly articles, but only two "philosophical" books, the Combinatorial Art and the Théodicée. (He published numerous pamphlets, often anonymous, on behalf of the House of Brunswick-Lüneburg, most notably the "De jure suprematum" a major consideration of the nature of sovereignty.) One substantial book appeared posthumously, his Nouveaux essais sur l'entendement humain, which Leibniz had withheld from publication after the death of John Locke. Only in 1895, when Bodemann completed his catalogues of Leibniz's manuscripts and correspondence, did the enormous extent of Leibniz's Nachlass become clear: about 15,000 letters to more than 1000 recipients plus more than 40,000 other items. Moreover, quite a few of these letters are of essay length. Much of his vast correspondence, especially the letters dated after 1685, remains unpublished, and much of what is published has been so only in recent decades. The amount, variety, and disorder of Leibniz's writings are a predictable result of a situation he described in a letter as follows:
I cannot tell you how extraordinarily distracted and spread out I am. I am trying to find various things in the archives; I look at old papers and hunt up unpublished documents. From these I hope to shed some light on the history of the [House of] Brunswick. I receive and answer a huge number of letters. At the same time, I have so many mathematical results, philosophical thoughts, and other literary innovations that should not be allowed to vanish that I often do not know where to begin.
The extant parts of the critical edition of Leibniz's writings are organized as follows:
Series 1. Political, Historical, and General Correspondence. 21 vols., 1666–1701.
Series 2. Philosophical Correspondence. 1 vol., 1663–85.
Series 3. Mathematical, Scientific, and Technical Correspondence. 6 vols., 1672–96.
Series 4. Political Writings. 6 vols., 1667–98.
Series 5. Historical and Linguistic Writings. Inactive.
Series 6. Philosophical Writings. 7 vols., 1663–90, and Nouveaux essais sur l'entendement humain.
Series 7. Mathematical Writings. 3 vols., 1672–76.
Series 8. Scientific, Medical, and Technical Writings. In preparation.
The systematic cataloguing of all of Leibniz's Nachlass began in 1901. It was hampered by two world wars, the Nazi dictatorship (with the Holocaust, which affected a Jewish employee of the project, and other personal consequences), and decades of German division (two states with the cold war's "iron curtain" in between, separating scholars and also scattering portions of his literary estates). The ambitious project has had to deal with seven languages contained in some 200,000 pages of written and printed paper. In 1985 it was reorganized and included in a joint program of German federal and state (Länder) academies. Since then the branches in Potsdam, Münster, Hanover and Berlin have jointly published 25 volumes of the critical edition, with an average of 870 pages, and prepared index and concordance works.
October 29, 1675 – Leibniz makes the first use of the long s (∫) as a symbol of the integral in calculus.
http://upload.wikimedia.org/math/d/6/e/d6e9aefed6960b5c62acd09f05da9293.png
is used to denote integrals and antiderivatives in mathematics. The notation was introduced by the German mathematician Gottfried Wilhelm Leibniz towards the end of the 17th century. The symbol was based on the ſ (long s) character, and was chosen because Leibniz thought of the integral as an infinite sum of infinitesimal summands. See long s for more details on the history of ſ.
In other languages, the shape of the integral symbol differs slightly from the shape commonly seen in English-language textbooks. While the English integral symbol leans to the right, the German symbol (used throughout Central Europe) is upright, and the Russian variant leans to the left.
Another difference is in the placement of limits for definite integrals. Generally, in English-language books, limits go to the right of the integral symbol: http://upload.wikimedia.org/math/9/6/7/967b8fca2cd45d00257d41200a99f535.png.
By contrast, in German and Russian texts, limits for definite integrals are placed above and below the integral symbol, and, as a result, the notation requires larger line spacing: http://upload.wikimedia.org/math/5/c/6/5c636c62f6ecf04ac131306dfb5fb2d8.png.