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Gottfried Wilhelm Leibniz (or Leibnitz; [a] 1 July 1646 [O.S. 21 June] – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to many other branches of mathematics, such as binary arithmetic and statistics.
Philosophy of Arithmetic: Psychological and Logical Investigations (German: Philosophie der Arithmetik. Psychologische und logische Untersuchungen ) is an 1891 book about the philosophy of mathematics by the philosopher Edmund Husserl .
In mathematics, the Leibniz formula for π, named after Gottfried Wilhelm Leibniz, states that = + + = = +,. an alternating series.. It is sometimes called the Madhava–Leibniz series as it was first discovered by the Indian mathematician Madhava of Sangamagrama or his followers in the 14th–15th century (see Madhava series), [1] and was later independently rediscovered by James Gregory in ...
The test was devised by Gottfried Leibniz and is sometimes known as Leibniz's test, Leibniz's rule, or the Leibniz criterion. The test is only sufficient, not necessary, so some convergent alternating series may fail the first part of the test. [1] [2] [3] For a generalization, see Dirichlet's test. [4] [5] [6]
The following outline is provided as an overview of and topical guide to Gottfried Wilhelm Leibniz: Gottfried Wilhelm (von) Leibniz (1 July 1646 [O.S. 21 June] – 14 November 1716); German polymath, philosopher logician, mathematician. [1] Developed differential and integral calculus at about the same time and independently of Isaac Newton.
Gottfried Wilhelm Leibniz was a major contributor to mathematics, physics, philosophy, theology, logic, and early computer science; independent inventor of calculus in mathematics; inventor of energy and the action principle in physics; jurist, genealogist, diplomat, librarian; worked towards reunification of Catholic and Protestant faiths.
Although calculus was independently co-invented by Isaac Newton, most of the notation in modern calculus is from Leibniz. [3] Leibniz's careful attention to his notation makes some believe that "his contribution to calculus was much more influential than Newton's."
Leibniz used the principle to extend concepts such as arithmetic operations from ordinary numbers to infinitesimals, laying the groundwork for infinitesimal calculus. The transfer principle provides a mathematical implementation of the law of continuity in the context of the hyperreal numbers .
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